/*
    * Copyright (C) 2020 Alberto Irurueta Carro (alberto@irurueta.com)
    *
    * Licensed under the Apache License, Version 2.0 (the "License");
    * you may not use this file except in compliance with the License.
    * You may obtain a copy of the License at
    *
    *         http://www.apache.org/licenses/LICENSE-2.0
    *
   * Unless required by applicable law or agreed to in writing, software
   * distributed under the License is distributed on an "AS IS" BASIS,
   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
   * See the License for the specific language governing permissions and
   * limitations under the License.
   */
  package com.irurueta.navigation.inertial.calibration.magnetometer;
  
  import com.irurueta.algebra.AlgebraException;
  import com.irurueta.algebra.Matrix;
  import com.irurueta.algebra.Utils;
  import com.irurueta.algebra.WrongSizeException;
  import com.irurueta.navigation.LockedException;
  import com.irurueta.navigation.NotReadyException;
  import com.irurueta.navigation.frames.CoordinateTransformation;
  import com.irurueta.navigation.frames.ECEFFrame;
  import com.irurueta.navigation.frames.FrameType;
  import com.irurueta.navigation.frames.NEDFrame;
  import com.irurueta.navigation.frames.converters.ECEFtoNEDFrameConverter;
  import com.irurueta.navigation.inertial.BodyMagneticFluxDensity;
  import com.irurueta.navigation.inertial.calibration.CalibrationException;
  import com.irurueta.navigation.inertial.calibration.FrameBodyMagneticFluxDensity;
  import com.irurueta.navigation.inertial.calibration.MagneticFluxDensityTriad;
  import com.irurueta.navigation.inertial.estimators.BodyMagneticFluxDensityEstimator;
  import com.irurueta.navigation.inertial.wmm.NEDMagneticFluxDensity;
  import com.irurueta.navigation.inertial.wmm.WMMEarthMagneticFluxDensityEstimator;
  import com.irurueta.navigation.inertial.wmm.WorldMagneticModel;
  import com.irurueta.units.MagneticFluxDensity;
  import com.irurueta.units.MagneticFluxDensityConverter;
  import com.irurueta.units.MagneticFluxDensityUnit;
  
  import java.io.IOException;
  import java.util.Collection;
  
  /**
   * Estimates magnetometer soft-iron cross couplings and scaling factors.
   * <p>
   * This calibrator uses a linear approach to find a minimum least squared error
   * solution.
   * <p>
   * To use this calibrator at least 3 measurements at different known frames
   * must be provided. In other words, magnetometer samples must be obtained at
   * 3 different positions or orientations.
   * Notice that frame velocities are ignored by this calibrator.
   * <p>
   * Measured magnetic flux density is assumed to follow the model shown below:
   * <pre>
   *     mBmeas = bm + (I + Mm) * mBtrue + w
   * </pre>
   * Where:
   * - mBmeas is the measured magnetic flux density. This is a 3x1 vector.
   * - bm is magnetometer hard-iron bias. Ideally, on a perfect magnetometer,
   * this should be a 3x1 zero vector.
   * - I is the 3x3 identity matrix.
   * - Mm is the 3x3 soft-iron matrix containing cross-couplings and scaling
   * factors. Ideally, on a perfect magnetometer, this should be a 3x3 zero
   * matrix.
   * - mBtrue is ground-truth magnetic flux density. This is a 3x1 vector.
   * - w is measurement noise. This is a 3x1 vector.
   */
  @SuppressWarnings("DuplicatedCode")
  public class KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator implements
          KnownHardIronAndFrameMagnetometerCalibrator<FrameBodyMagneticFluxDensity,
                  KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibratorListener>,
          UnorderedFrameBodyMagneticFluxDensityMagnetometerCalibrator {
  
      /**
       * Indicates whether by default a common z-axis is assumed for the accelerometer,
       * gyroscope and magnetometer.
       */
      public static final boolean DEFAULT_USE_COMMON_Z_AXIS = false;
  
      /**
       * Required minimum number of measurements.
       */
      public static final int MINIMUM_MEASUREMENTS = 3;
  
      /**
       * Number of equations generated for each measurement.
       */
      private static final int EQUATIONS_PER_MEASUREMENT = 3;
  
      /**
       * Number of unknowns when common z-axis is assumed for the accelerometer,
       * gyroscope and magnetometer.
       */
      private static final int COMMON_Z_AXIS_UNKNOWNS = 6;
  
      /**
       * Number of unknowns for the general case.
      */
     private static final int GENERAL_UNKNOWNS = 9;
 
     /**
      * X-coordinate of known hard-iron bias.
      * This is expressed in Teslas (T).
      */
     private double hardIronX;
 
     /**
      * Y-coordinate of known hard-iron bias.
      * This is expressed in Teslas (T).
      */
     private double hardIronY;
 
     /**
      * Z-coordinate of known hard-iron bias.
      * This is expressed in Teslas (T).
      */
     private double hardIronZ;
 
     /**
      * Contains a collection of body magnetic flux density measurements taken
      * at different frames (positions and orientations).
      * If a single device magnetometer needs to be calibrated, typically all
      * measurements are taken at the same position, with zero velocity and
      * multiple orientations.
      * However, if we just want to calibrate a given magnetometer model (e.g.
      * obtain an average and less precise calibration for the magnetometer of
      * a given phone model), we could take measurements collected throughout
      * the planet at multiple positions while the phone remains static (e.g.
      * while charging), hence each measurement position will change, velocity
      * will remain zero and orientation will be typically constant at
      * horizontal orientation while the phone remains on a
      * flat surface.
      */
     private Collection<FrameBodyMagneticFluxDensity> measurements;
 
     /**
      * This flag indicates whether z-axis is assumed to be common for accelerometer,
      * gyroscope and magnetometer.
      * When enabled, this eliminates 3 variables from Mm matrix.
      */
     private boolean commonAxisUsed = DEFAULT_USE_COMMON_Z_AXIS;
 
     /**
      * Listener to handle events raised by this calibrator.
      */
     private KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibratorListener listener;
 
     /**
      * Estimated magnetometer soft-iron matrix containing scale factors
      * and cross coupling errors.
      * This is the product of matrix Tm containing cross coupling errors and Km
      * containing scaling factors.
      * So tat:
      * <pre>
      *     Mm = [sx    mxy  mxz] = Tm*Km
      *          [myx   sy   myz]
      *          [mzx   mzy  sz ]
      * </pre>
      * Where:
      * <pre>
      *     Km = [sx 0   0 ]
      *          [0  sy  0 ]
      *          [0  0   sz]
      * </pre>
      * and
      * <pre>
      *     Tm = [1          -alphaXy    alphaXz ]
      *          [alphaYx    1           -alphaYz]
      *          [-alphaZx   alphaZy     1       ]
      * </pre>
      * Hence:
      * <pre>
      *     Mm = [sx    mxy  mxz] = Tm*Km =  [sx             -sy * alphaXy   sz * alphaXz ]
      *          [myx   sy   myz]            [sx * alphaYx   sy              -sz * alphaYz]
      *          [mzx   mzy  sz ]            [-sx * alphaZx  sy * alphaZy    sz           ]
      * </pre>
      * This instance allows any 3x3 matrix however, typically alphaYx, alphaZx and alphaZy
      * are considered to be zero if the accelerometer z-axis is assumed to be the same
      * as the body z-axis. When this is assumed, myx = mzx = mzy = 0 and the Mm matrix
      * becomes upper diagonal:
      * <pre>
      *     Mm = [sx    mxy  mxz]
      *          [0     sy   myz]
      *          [0     0    sz ]
      * </pre>
      * Values of this matrix are unit-less.
      */
     private Matrix estimatedMm;
 
     /**
      * Indicates whether calibrator is running.
      */
     private boolean running;
 
     /**
      * Contains Earth's magnetic model.
      */
     private WorldMagneticModel magneticModel;
 
     /**
      * Constructor.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator() {
     }
 
     /**
      * Constructor.
      *
      * @param listener listener to handle events raised by this calibrator.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibratorListener listener) {
         this.listener = listener;
     }
 
     /**
      * Constructor.
      *
      * @param measurements collection of body magnetic flux density measurements
      *                     taken at different frames (positions and orientations).
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final Collection<? extends FrameBodyMagneticFluxDensity> measurements) {
         //noinspection unchecked
         this.measurements = (Collection<FrameBodyMagneticFluxDensity>) measurements;
     }
 
     /**
      * Constructor.
      *
      * @param measurements collection of body magnetic flux density measurements
      *                     taken at different frames (positions and orientations).
      * @param listener     listener to handle events raised by this calibrator.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final Collection<? extends FrameBodyMagneticFluxDensity> measurements,
             final KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibratorListener listener) {
         this(measurements);
         this.listener = listener;
     }
 
     /**
      * Constructor.
      *
      * @param commonAxisUsed indicates whether z-axis is assumed to be common
      *                       for the accelerometer, gyroscope and magnetometer.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(final boolean commonAxisUsed) {
         this.commonAxisUsed = commonAxisUsed;
     }
 
     /**
      * Constructor.
      *
      * @param commonAxisUsed indicates whether z-axis is assumed to be common
      *                       for the accelerometer, gyroscope and magnetometer.
      * @param listener       listener to handle events raised by this calibrator.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final boolean commonAxisUsed,
             final KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibratorListener listener) {
         this(commonAxisUsed);
         this.listener = listener;
     }
 
     /**
      * Constructor.
      *
      * @param measurements   collection of body magnetic flux density measurements
      *                       taken at different frames (positions and orientations).
      * @param commonAxisUsed indicates whether z-axis is assumed to be common
      *                       for the accelerometer, gyroscope and magnetometer.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final Collection<? extends FrameBodyMagneticFluxDensity> measurements, final boolean commonAxisUsed) {
         this(measurements);
         this.commonAxisUsed = commonAxisUsed;
     }
 
     /**
      * Constructor.
      *
      * @param measurements   collection of body magnetic flux density measurements
      *                       taken at different frames (positions and orientations).
      * @param commonAxisUsed indicates whether z-axis is assumed to be common
      *                       for the accelerometer, gyroscope and magnetometer.
      * @param listener       listener to handle events raised by this calibrator.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final Collection<? extends FrameBodyMagneticFluxDensity> measurements, final boolean commonAxisUsed,
             final KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibratorListener listener) {
         this(measurements, commonAxisUsed);
         this.listener = listener;
     }
 
     /**
      * Constructor.
      *
      * @param magneticModel Earth's magnetic model. If null, a default model
      *                      will be used instead.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(final WorldMagneticModel magneticModel) {
         this.magneticModel = magneticModel;
     }
 
     /**
      * Constructor.
      *
      * @param magneticModel Earth's magnetic model. If null, a default model
      *                      will be used instead.
      * @param listener      listener to handle events raised by this calibrator.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final WorldMagneticModel magneticModel,
             final KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibratorListener listener) {
         this(listener);
         this.magneticModel = magneticModel;
     }
 
     /**
      * Constructor.
      *
      * @param measurements  collection of body magnetic flux density measurements
      *                      taken at different frames (positions and orientations).
      * @param magneticModel Earth's magnetic model. If null, a default model
      *                      will be used instead.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final Collection<? extends FrameBodyMagneticFluxDensity> measurements,
             final WorldMagneticModel magneticModel) {
         this(measurements);
         this.magneticModel = magneticModel;
     }
 
     /**
      * Constructor.
      *
      * @param measurements  collection of body magnetic flux density measurements
      *                      taken at different frames (positions and orientations).
      * @param magneticModel Earth's magnetic model. If null, a default model
      *                      will be used instead.
      * @param listener      listener to handle events raised by this calibrator.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final Collection<? extends FrameBodyMagneticFluxDensity> measurements,
             final WorldMagneticModel magneticModel,
             final KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibratorListener listener) {
         this(measurements, listener);
         this.magneticModel = magneticModel;
     }
 
     /**
      * Constructor.
      *
      * @param commonAxisUsed indicates whether z-axis is assumed to be common
      *                       for the accelerometer, gyroscope and magnetometer.
      * @param magneticModel  Earth's magnetic model. If null, a default model
      *                       will be used instead.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final boolean commonAxisUsed, final WorldMagneticModel magneticModel) {
         this(commonAxisUsed);
         this.magneticModel = magneticModel;
     }
 
     /**
      * Constructor.
      *
      * @param commonAxisUsed indicates whether z-axis is assumed to be common
      *                       for the accelerometer, gyroscope and magnetometer.
      * @param magneticModel  Earth's magnetic model. If null, a default model
      *                       will be used instead.
      * @param listener       listener to handle events raised by this calibrator.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final boolean commonAxisUsed, final WorldMagneticModel magneticModel,
             final KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibratorListener listener) {
         this(commonAxisUsed, listener);
         this.magneticModel = magneticModel;
     }
 
     /**
      * Constructor.
      *
      * @param measurements   collection of body magnetic flux density measurements
      *                       taken at different frames (positions and orientations).
      * @param commonAxisUsed indicates whether z-axis is assumed to be common
      *                       for the accelerometer, gyroscope and magnetometer.
      * @param magneticModel  Earth's magnetic model. If null, a default model
      *                       will be used instead.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final Collection<? extends FrameBodyMagneticFluxDensity> measurements, final boolean commonAxisUsed,
             final WorldMagneticModel magneticModel) {
         this(measurements, commonAxisUsed);
         this.magneticModel = magneticModel;
     }
 
     /**
      * Constructor.
      *
      * @param measurements   collection of body magnetic flux density measurements
      *                       taken at different frames (positions and orientations).
      * @param commonAxisUsed indicates whether z-axis is assumed to be common
      *                       for the accelerometer, gyroscope and magnetometer.
      * @param magneticModel  Earth's magnetic model. If null, a default model
      *                       will be used instead.
      * @param listener       listener to handle events raised by this calibrator.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final Collection<? extends FrameBodyMagneticFluxDensity> measurements, final boolean commonAxisUsed,
             final WorldMagneticModel magneticModel,
             final KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibratorListener listener) {
         this(measurements, commonAxisUsed, listener);
         this.magneticModel = magneticModel;
     }
 
     /**
      * Constructor.
      *
      * @param hardIronX x-coordinate of magnetometer hard-iron bias
      *                  expressed in Teslas (T).
      * @param hardIronY y-coordinate of magnetometer hard-iron bias
      *                  expressed in Teslas (T).
      * @param hardIronZ z-coordinate of magnetometer hard-iron bias
      *                  expressed in Teslas (T).
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final double hardIronX, final double hardIronY, final double hardIronZ) {
         try {
             setHardIronCoordinates(hardIronX, hardIronY, hardIronZ);
         } catch (final LockedException ignore) {
             // never happens
         }
     }
 
     /**
      * Constructor.
      *
      * @param hardIronX x-coordinate of magnetometer hard-iron bias
      *                  expressed in Teslas (T).
      * @param hardIronY y-coordinate of magnetometer hard-iron bias
      *                  expressed in Teslas (T).
      * @param hardIronZ z-coordinate of magnetometer hard-iron bias
      *                  expressed in Teslas (T).
      * @param listener  listener to handle events raised by this calibrator.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final double hardIronX, final double hardIronY, final double hardIronZ,
             final KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibratorListener listener) {
         this(hardIronX, hardIronY, hardIronZ);
         this.listener = listener;
     }
 
     /**
      * Constructor.
      *
      * @param measurements collection of body magnetic flux density measurements
      *                     taken at different frames (positions and orientations).
      * @param hardIronX    x-coordinate of magnetometer hard-iron bias
      *                     expressed in Teslas (T).
      * @param hardIronY    y-coordinate of magnetometer hard-iron bias
      *                     expressed in Teslas (T).
      * @param hardIronZ    z-coordinate of magnetometer hard-iron bias
      *                     expressed in Teslas (T).
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final Collection<? extends FrameBodyMagneticFluxDensity> measurements,
             final double hardIronX, final double hardIronY, final double hardIronZ) {
         this(hardIronX, hardIronY, hardIronZ);
         //noinspection unchecked
         this.measurements = (Collection<FrameBodyMagneticFluxDensity>) measurements;
     }
 
     /**
      * Constructor.
      *
      * @param measurements collection of body magnetic flux density measurements
      *                     taken at different frames (positions and orientations).
      * @param hardIronX    x-coordinate of magnetometer hard-iron bias
      *                     expressed in Teslas (T).
      * @param hardIronY    y-coordinate of magnetometer hard-iron bias
      *                     expressed in Teslas (T).
      * @param hardIronZ    z-coordinate of magnetometer hard-iron bias
      *                     expressed in Teslas (T).
      * @param listener     listener to handle events raised by this calibrator.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final Collection<? extends FrameBodyMagneticFluxDensity> measurements,
             final double hardIronX, final double hardIronY, final double hardIronZ,
             final KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibratorListener listener) {
         this(measurements, hardIronX, hardIronY, hardIronZ);
         this.listener = listener;
     }
 
     /**
      * Constructor.
      *
      * @param commonAxisUsed indicates whether z-axis is assumed to be common
      *                       for the accelerometer, gyroscope and magnetometer.
      * @param hardIronX      x-coordinate of magnetometer hard-iron bias
      *                       expressed in Teslas (T).
      * @param hardIronY      y-coordinate of magnetometer hard-iron bias
      *                       expressed in Teslas (T).
      * @param hardIronZ      z-coordinate of magnetometer hard-iron bias
      *                       expressed in Teslas (T).
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final boolean commonAxisUsed, final double hardIronX, final double hardIronY, final double hardIronZ) {
         this(hardIronX, hardIronY, hardIronZ);
         this.commonAxisUsed = commonAxisUsed;
     }
 
     /**
      * Constructor.
      *
      * @param commonAxisUsed indicates whether z-axis is assumed to be common
      *                       for the accelerometer, gyroscope and magnetometer.
      * @param hardIronX      x-coordinate of magnetometer hard-iron bias
      *                       expressed in Teslas (T).
      * @param hardIronY      y-coordinate of magnetometer hard-iron bias
      *                       expressed in Teslas (T).
      * @param hardIronZ      z-coordinate of magnetometer hard-iron bias
      *                       expressed in Teslas (T).
      * @param listener       listener to handle events raised by this calibrator.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final boolean commonAxisUsed, final double hardIronX, final double hardIronY, final double hardIronZ,
             final KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibratorListener listener) {
         this(commonAxisUsed, hardIronX, hardIronY, hardIronZ);
         this.listener = listener;
     }
 
     /**
      * Constructor.
      *
      * @param measurements   collection of body magnetic flux density measurements
      *                       taken at different frames (positions and orientations).
      * @param commonAxisUsed indicates whether z-axis is assumed to be common
      *                       for the accelerometer, gyroscope and magnetometer.
      * @param hardIronX      x-coordinate of magnetometer hard-iron bias
      *                       expressed in Teslas (T).
      * @param hardIronY      y-coordinate of magnetometer hard-iron bias
      *                       expressed in Teslas (T).
      * @param hardIronZ      z-coordinate of magnetometer hard-iron bias
      *                       expressed in Teslas (T).
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final Collection<? extends FrameBodyMagneticFluxDensity> measurements, final boolean commonAxisUsed,
             final double hardIronX, final double hardIronY, final double hardIronZ) {
         this(commonAxisUsed, hardIronX, hardIronY, hardIronZ);
         //noinspection unchecked
         this.measurements = (Collection<FrameBodyMagneticFluxDensity>) measurements;
     }
 
     /**
      * Constructor.
      *
      * @param measurements   collection of body magnetic flux density measurements
      *                       taken at different frames (positions and orientations).
      * @param commonAxisUsed indicates whether z-axis is assumed to be common
      *                       for the accelerometer, gyroscope and magnetometer.
      * @param hardIronX      x-coordinate of magnetometer hard-iron bias
      *                       expressed in Teslas (T).
      * @param hardIronY      y-coordinate of magnetometer hard-iron bias
      *                       expressed in Teslas (T).
      * @param hardIronZ      z-coordinate of magnetometer hard-iron bias
      *                       expressed in Teslas (T).
      * @param listener       listener to handle events raised by this calibrator.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final Collection<? extends FrameBodyMagneticFluxDensity> measurements,
             final boolean commonAxisUsed, final double hardIronX, final double hardIronY, final double hardIronZ,
             final KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibratorListener listener) {
         this(measurements, commonAxisUsed, hardIronX, hardIronY, hardIronZ);
         this.listener = listener;
     }
 
     /**
      * Constructor.
      *
      * @param magneticModel Earth's magnetic model. If null, a default model
      *                      will be used instead.
      * @param hardIronX     x-coordinate of magnetometer hard-iron bias
      *                      expressed in Teslas (T).
      * @param hardIronY     y-coordinate of magnetometer hard-iron bias
      *                      expressed in Teslas (T).
      * @param hardIronZ     z-coordinate of magnetometer hard-iron bias
      *                      expressed in Teslas (T).
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final WorldMagneticModel magneticModel,
             final double hardIronX, final double hardIronY, final double hardIronZ) {
         this(hardIronX, hardIronY, hardIronZ);
         this.magneticModel = magneticModel;
     }
 
     /**
      * Constructor.
      *
      * @param magneticModel Earth's magnetic model. If null, a default model
      *                      will be used instead.
      * @param hardIronX     x-coordinate of magnetometer hard-iron bias
      *                      expressed in Teslas (T).
      * @param hardIronY     y-coordinate of magnetometer hard-iron bias
      *                      expressed in Teslas (T).
      * @param hardIronZ     z-coordinate of magnetometer hard-iron bias
      *                      expressed in Teslas (T).
      * @param listener      listener to handle events raised by this calibrator.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final WorldMagneticModel magneticModel,
             final double hardIronX, final double hardIronY, final double hardIronZ,
             final KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibratorListener listener) {
         this(magneticModel, hardIronX, hardIronY, hardIronZ);
         this.listener = listener;
     }
 
     /**
      * Constructor.
      *
      * @param measurements  collection of body magnetic flux density measurements
      *                      taken at different frames (positions and orientations).
      * @param magneticModel Earth's magnetic model. If null, a default model
      *                      will be used instead.
      * @param hardIronX     x-coordinate of magnetometer hard-iron bias
      *                      expressed in Teslas (T).
      * @param hardIronY     y-coordinate of magnetometer hard-iron bias
      *                      expressed in Teslas (T).
      * @param hardIronZ     z-coordinate of magnetometer hard-iron bias
      *                      expressed in Teslas (T).
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final Collection<? extends FrameBodyMagneticFluxDensity> measurements,
             final WorldMagneticModel magneticModel,
             final double hardIronX, final double hardIronY, final double hardIronZ) {
         this(hardIronX, hardIronY, hardIronZ);
         //noinspection unchecked
         this.measurements = (Collection<FrameBodyMagneticFluxDensity>) measurements;
         this.magneticModel = magneticModel;
     }
 
     /**
      * Constructor.
      *
      * @param measurements  collection of body magnetic flux density measurements
      *                      taken at different frames (positions and orientations).
      * @param magneticModel Earth's magnetic model. If null, a default model
      *                      will be used instead.
      * @param hardIronX     x-coordinate of magnetometer hard-iron bias
      *                      expressed in Teslas (T).
      * @param hardIronY     y-coordinate of magnetometer hard-iron bias
      *                      expressed in Teslas (T).
      * @param hardIronZ     z-coordinate of magnetometer hard-iron bias
      *                      expressed in Teslas (T).
      * @param listener      listener to handle events raised by this calibrator.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final Collection<? extends FrameBodyMagneticFluxDensity> measurements,
             final WorldMagneticModel magneticModel,
             final double hardIronX, final double hardIronY, final double hardIronZ,
             final KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibratorListener listener) {
         this(measurements, magneticModel, hardIronX, hardIronY, hardIronZ);
         this.listener = listener;
     }
 
     /**
      * Constructor
      *
      * @param commonAxisUsed indicates whether z-axis is assumed to be common
      *                       for the accelerometer, gyroscope and magnetometer.
      * @param magneticModel  Earth's magnetic model. If null, a default model
      *                       will be used instead.
      * @param hardIronX      x-coordinate of magnetometer hard-iron bias
      *                       expressed in Teslas (T).
      * @param hardIronY      y-coordinate of magnetometer hard-iron bias
      *                       expressed in Teslas (T).
      * @param hardIronZ      z-coordinate of magnetometer hard-iron bias
      *                       expressed in Teslas (T).
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final boolean commonAxisUsed, final WorldMagneticModel magneticModel,
             final double hardIronX, final double hardIronY, final double hardIronZ) {
         this(magneticModel, hardIronX, hardIronY, hardIronZ);
         this.commonAxisUsed = commonAxisUsed;
     }
 
     /**
      * Constructor.
      *
      * @param commonAxisUsed indicates whether z-axis is assumed to be common
      *                       for the accelerometer, gyroscope and magnetometer.
      * @param magneticModel  Earth's magnetic model. If null, a default model
      *                       will be used instead.
      * @param hardIronX      x-coordinate of magnetometer hard-iron bias
      *                       expressed in Teslas (T).
      * @param hardIronY      y-coordinate of magnetometer hard-iron bias
      *                       expressed in Teslas (T).
      * @param hardIronZ      z-coordinate of magnetometer hard-iron bias
      *                       expressed in Teslas (T).
      * @param listener       listener to handle events raised by this calibrator.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final boolean commonAxisUsed, final WorldMagneticModel magneticModel,
             final double hardIronX, final double hardIronY, final double hardIronZ,
             final KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibratorListener listener) {
         this(commonAxisUsed, magneticModel, hardIronX, hardIronY, hardIronZ);
         this.listener = listener;
     }
 
     /**
      * Constructor.
      *
      * @param measurements   collection of body magnetic flux density measurements
      *                       taken at different frames (positions and orientations).
      * @param commonAxisUsed indicates whether z-axis is assumed to be common
      *                       for the accelerometer, gyroscope and magnetometer.
      * @param magneticModel  Earth's magnetic model. If null, a default model
      *                       will be used instead.
      * @param hardIronX      x-coordinate of magnetometer hard-iron bias
      *                       expressed in Teslas (T).
      * @param hardIronY      y-coordinate of magnetometer hard-iron bias
      *                       expressed in Teslas (T).
      * @param hardIronZ      z-coordinate of magnetometer hard-iron bias
      *                       expressed in Teslas (T).
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final Collection<? extends FrameBodyMagneticFluxDensity> measurements, final boolean commonAxisUsed,
             final WorldMagneticModel magneticModel,
             final double hardIronX, final double hardIronY, final double hardIronZ) {
         this(commonAxisUsed, magneticModel, hardIronX, hardIronY, hardIronZ);
         //noinspection unchecked
         this.measurements = (Collection<FrameBodyMagneticFluxDensity>) measurements;
     }
 
     /**
      * Constructor.
      *
      * @param measurements   collection of body magnetic flux density measurements
      *                       taken at different frames (positions and orientations).
      * @param commonAxisUsed indicates whether z-axis is assumed to be common
      *                       for the accelerometer, gyroscope and magnetometer.
      * @param magneticModel  Earth's magnetic model. If null, a default model
      *                       will be used instead.
      * @param hardIronX      x-coordinate of magnetometer hard-iron bias
      *                       expressed in Teslas (T).
      * @param hardIronY      y-coordinate of magnetometer hard-iron bias
      *                       expressed in Teslas (T).
      * @param hardIronZ      z-coordinate of magnetometer hard-iron bias
      *                       expressed in Teslas (T).
      * @param listener       listener to handle events raised by this calibrator.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final Collection<? extends FrameBodyMagneticFluxDensity> measurements, final boolean commonAxisUsed,
             final WorldMagneticModel magneticModel,
             final double hardIronX, final double hardIronY, final double hardIronZ,
             final KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibratorListener listener) {
         this(measurements, commonAxisUsed, magneticModel, hardIronX, hardIronY, hardIronZ);
         this.listener = listener;
     }
 
     /**
      * Constructor.
      *
      * @param hardIron known hard-iron bias.
      * @throws IllegalArgumentException if provided hard-iron array does not
      *                                  have length 3.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(final double[] hardIron) {
         try {
             setHardIron(hardIron);
         } catch (final LockedException ignore) {
             // never happens
         }
     }
 
     /**
      * Constructor.
      *
      * @param hardIron known hard-iron bias.
      * @param listener listener to handle events raised by this calibrator.
      * @throws IllegalArgumentException if provided hard-iron array does not
      *                                  have length 3.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final double[] hardIron,
             final KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibratorListener listener) {
         this(hardIron);
         this.listener = listener;
     }
 
     /**
      * Constructor.
      *
      * @param measurements collection of body magnetic flux density measurements
      *                     taken at different frames (positions and orientations).
      * @param hardIron     known hard-iron bias.
      * @throws IllegalArgumentException if provided hard-iron array does not
      *                                  have length 3.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final Collection<? extends FrameBodyMagneticFluxDensity> measurements, final double[] hardIron) {
         this(hardIron);
         //noinspection unchecked
         this.measurements = (Collection<FrameBodyMagneticFluxDensity>) measurements;
     }
 
     /**
      * Constructor.
      *
      * @param measurements collection of body magnetic flux density measurements
      *                     taken at different frames (positions and orientations).
      * @param hardIron     known hard-iron bias.
      * @param listener     listener to handle events raised by this calibrator.
      * @throws IllegalArgumentException if provided hard-iron array does not
      *                                  have length 3.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final Collection<? extends FrameBodyMagneticFluxDensity> measurements, final double[] hardIron,
             final KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibratorListener listener) {
         this(measurements, hardIron);
         this.listener = listener;
     }
 
     /**
      * Constructor.
      *
      * @param commonAxisUsed indicates whether z-axis is assumed to be common
      *                       for the accelerometer, gyroscope and magnetometer.
      * @param hardIron       known hard-iron bias.
      * @throws IllegalArgumentException if provided hard-iron array does not
      *                                  have length 3.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final boolean commonAxisUsed, final double[] hardIron) {
         this(hardIron);
         this.commonAxisUsed = commonAxisUsed;
     }
 
     /**
      * Constructor.
      *
      * @param commonAxisUsed indicates whether z-axis is assumed to be common
      *                       for the accelerometer, gyroscope and magnetometer.
      * @param hardIron       known hard-iron bias.
      * @param listener       listener to handle events raised by this calibrator.
      * @throws IllegalArgumentException if provided hard-iron array does not
      *                                  have length 3.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final boolean commonAxisUsed, final double[] hardIron,
             final KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibratorListener listener) {
         this(commonAxisUsed, hardIron);
         this.listener = listener;
     }
 
     /**
      * Constructor.
      *
      * @param measurements   collection of body magnetic flux density measurements
      *                       taken at different frames (positions and orientations).
      * @param commonAxisUsed indicates whether z-axis is assumed to be common
      *                       for the accelerometer, gyroscope and magnetometer.
      * @param hardIron       known hard-iron bias.
      * @throws IllegalArgumentException if provided hard-iron array does not
      *                                  have length 3.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final Collection<? extends FrameBodyMagneticFluxDensity> measurements, final boolean commonAxisUsed,
             final double[] hardIron) {
         this(commonAxisUsed, hardIron);
         //noinspection unchecked
         this.measurements = (Collection<FrameBodyMagneticFluxDensity>) measurements;
     }
 
     /**
      * Constructor.
      *
      * @param measurements   collection of body magnetic flux density measurements
      *                       taken at different frames (positions and orientations).
      * @param commonAxisUsed indicates whether z-axis is assumed to be common
      *                       for the accelerometer, gyroscope and magnetometer.
      * @param hardIron       known hard-iron bias.
      * @param listener       listener to handle events raised by this calibrator.
      * @throws IllegalArgumentException if provided hard-iron array does not
      *                                  have length 3.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final Collection<? extends FrameBodyMagneticFluxDensity> measurements,
             final boolean commonAxisUsed, final double[] hardIron,
             final KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibratorListener listener) {
         this(measurements, commonAxisUsed, hardIron);
         this.listener = listener;
     }
 
     /**
      * Constructor.
      *
      * @param magneticModel Earth's magnetic model. If null, a default model
      *                      will be used instead.
      * @param hardIron      known hard-iron bias.
      * @throws IllegalArgumentException if provided hard-iron array does not
      *                                  have length 3.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final WorldMagneticModel magneticModel, final double[] hardIron) {
         this(hardIron);
         this.magneticModel = magneticModel;
     }
 
     /**
      * Constructor.
      *
      * @param magneticModel Earth's magnetic model. If null, a default model
      *                      will be used instead.
      * @param hardIron      known hard-iron bias.
      * @param listener      listener to handle events raised by this calibrator.
      * @throws IllegalArgumentException if provided hard-iron array does not
      *                                  have length 3.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final WorldMagneticModel magneticModel, final double[] hardIron,
             final KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibratorListener listener) {
         this(magneticModel, hardIron);
         this.listener = listener;
     }
 
     /**
      * Constructor.
      *
      * @param measurements  collection of body magnetic flux density measurements
      *                      taken at different frames (positions and orientations).
      * @param magneticModel Earth's magnetic model. If null, a default model
      *                      will be used instead.
      * @param hardIron      known hard-iron bias.
      * @throws IllegalArgumentException if provided hard-iron array does not
      *                                  have length 3.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final Collection<? extends FrameBodyMagneticFluxDensity> measurements,
             final WorldMagneticModel magneticModel, final double[] hardIron) {
         this(magneticModel, hardIron);
         //noinspection unchecked
         this.measurements = (Collection<FrameBodyMagneticFluxDensity>) measurements;
     }
 
     /**
      * Constructor.
      *
      * @param measurements  collection of body magnetic flux density measurements
      *                      taken at different frames (positions and orientations).
      * @param magneticModel Earth's magnetic model. If null, a default model
      *                      will be used instead.
      * @param hardIron      known hard-iron bias.
      * @param listener      listener to handle events raised by this calibrator.
      * @throws IllegalArgumentException if provided hard-iron array does not
      *                                  have length 3.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final Collection<? extends FrameBodyMagneticFluxDensity> measurements,
             final WorldMagneticModel magneticModel, final double[] hardIron,
             final KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibratorListener listener) {
         this(measurements, magneticModel, hardIron);
         this.listener = listener;
     }
 
     /**
      * Constructor.
      *
      * @param commonAxisUsed indicates whether z-axis is assumed to be common
      *                       for the accelerometer, gyroscope and magnetometer.
      * @param magneticModel  Earth's magnetic model. If null, a default model
      *                       will be used instead.
      * @param hardIron       known hard-iron bias.
      * @throws IllegalArgumentException if provided hard-iron array does not
      *                                  have length 3.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final boolean commonAxisUsed, final WorldMagneticModel magneticModel, final double[] hardIron) {
         this(magneticModel, hardIron);
         this.commonAxisUsed = commonAxisUsed;
     }
 
     /**
      * Constructor.
      *
      * @param commonAxisUsed indicates whether z-axis is assumed to be common
      *                       for the accelerometer, gyroscope and magnetometer.
      * @param magneticModel  Earth's magnetic model. If null, a default model
      *                       will be used instead.
      * @param hardIron       known hard-iron bias.
      * @param listener       listener to handle events raised by this calibrator.
      * @throws IllegalArgumentException if provided hard-iron array does not
      *                                  have length 3.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final boolean commonAxisUsed, final WorldMagneticModel magneticModel, final double[] hardIron,
             final KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibratorListener listener) {
         this(commonAxisUsed, magneticModel, hardIron);
         this.listener = listener;
     }
 
     /**
      * Constructor.
      *
      * @param measurements   collection of body magnetic flux density measurements
      *                       taken at different frames (positions and orientations).
      * @param commonAxisUsed indicates whether z-axis is assumed to be common
      *                       for the accelerometer, gyroscope and magnetometer.
      * @param magneticModel  Earth's magnetic model. If null, a default model
      *                       will be used instead.
      * @param hardIron       known hard-iron bias.
      * @throws IllegalArgumentException if provided hard-iron array does not
      *                                  have length 3.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final Collection<? extends FrameBodyMagneticFluxDensity> measurements, final boolean commonAxisUsed,
             final WorldMagneticModel magneticModel, final double[] hardIron) {
         this(commonAxisUsed, magneticModel, hardIron);
         //noinspection unchecked
         this.measurements = (Collection<FrameBodyMagneticFluxDensity>) measurements;
     }
 
     /**
      * Constructor.
      *
      * @param measurements   collection of body magnetic flux density measurements
      *                       taken at different frames (positions and orientations).
      * @param commonAxisUsed indicates whether z-axis is assumed to be common
      *                       for the accelerometer, gyroscope and magnetometer.
      * @param magneticModel  Earth's magnetic model. If null, a default model
      *                       will be used instead.
      * @param hardIron       known hard-iron bias.
      * @param listener       listener to handle events raised by this calibrator.
      * @throws IllegalArgumentException if provided hard-iron array does not
      *                                  have length 3.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final Collection<? extends FrameBodyMagneticFluxDensity> measurements, final boolean commonAxisUsed,
             final WorldMagneticModel magneticModel, final double[] hardIron,
             final KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibratorListener listener) {
         this(measurements, commonAxisUsed, magneticModel, hardIron);
         this.listener = listener;
     }
 
     /**
      * Constructor.
      *
      * @param hardIron known hard-iron bias.
      * @throws IllegalArgumentException if provided hard-iron matrix is not
      *                                  3x1.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(final Matrix hardIron) {
         try {
             setHardIron(hardIron);
         } catch (final LockedException ignore) {
             // never happens
         }
     }
 
     /**
      * Constructor.
      *
      * @param hardIron known hard-iron bias.
      * @param listener listener to handle events raised by this calibrator.
      * @throws IllegalArgumentException if provided hard-iron matrix is not
      *                                  3x1.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final Matrix hardIron,
             final KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibratorListener listener) {
         this(hardIron);
         this.listener = listener;
     }
 
     /**
      * Constructor.
      *
      * @param measurements collection of body magnetic flux density measurements
      *                     taken at different frames (positions and orientations).
      * @param hardIron     known hard-iron bias.
      * @throws IllegalArgumentException if provided hard-iron matrix is not
      *                                  3x1.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final Collection<? extends FrameBodyMagneticFluxDensity> measurements, final Matrix hardIron) {
         this(hardIron);
         //noinspection unchecked
         this.measurements = (Collection<FrameBodyMagneticFluxDensity>) measurements;
     }
 
     /**
      * Constructor.
      *
      * @param measurements collection of body magnetic flux density measurements
      *                     taken at different frames (positions and orientations).
      * @param hardIron     known hard-iron bias.
      * @param listener     listener to handle events raised by this calibrator.
      * @throws IllegalArgumentException if provided hard-iron matrix is not
      *                                  3x1.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final Collection<? extends FrameBodyMagneticFluxDensity> measurements, final Matrix hardIron,
             final KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibratorListener listener) {
         this(measurements, hardIron);
         this.listener = listener;
     }
 
     /**
      * Constructor.
      *
      * @param commonAxisUsed indicates whether z-axis is assumed to be common
      *                       for the accelerometer, gyroscope and magnetometer.
      * @param hardIron       known hard-iron bias.
      * @throws IllegalArgumentException if provided hard-iron matrix is not
      *                                  3x1.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final boolean commonAxisUsed, final Matrix hardIron) {
         this(hardIron);
         this.commonAxisUsed = commonAxisUsed;
     }
 
     /**
      * Constructor.
      *
      * @param commonAxisUsed indicates whether z-axis is assumed to be common
      *                       for the accelerometer, gyroscope and magnetometer.
      * @param hardIron       known hard-iron bias.
      * @param listener       listener to handle events raised by this calibrator.
      * @throws IllegalArgumentException if provided hard-iron matrix is not
      *                                  3x1.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final boolean commonAxisUsed, final Matrix hardIron,
             final KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibratorListener listener) {
         this(commonAxisUsed, hardIron);
         this.listener = listener;
     }
 
     /**
      * Constructor.
      *
      * @param measurements   collection of body magnetic flux density measurements
      *                       taken at different frames (positions and orientations).
      * @param commonAxisUsed indicates whether z-axis is assumed to be common
      *                       for the accelerometer, gyroscope and magnetometer.
      * @param hardIron       known hard-iron bias.
      * @throws IllegalArgumentException if provided hard-iron matrix is not
      *                                  3x1.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final Collection<? extends FrameBodyMagneticFluxDensity> measurements, final boolean commonAxisUsed,
             final Matrix hardIron) {
         this(commonAxisUsed, hardIron);
         //noinspection unchecked
         this.measurements = (Collection<FrameBodyMagneticFluxDensity>) measurements;
     }
 
     /**
      * Constructor.
      *
      * @param measurements   collection of body magnetic flux density measurements
      *                       taken at different frames (positions and orientations).
      * @param commonAxisUsed indicates whether z-axis is assumed to be common
      *                       for the accelerometer, gyroscope and magnetometer.
      * @param hardIron       known hard-iron bias.
      * @param listener       listener to handle events raised by this calibrator.
      * @throws IllegalArgumentException if provided hard-iron matrix is not
      *                                  3x1.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final Collection<? extends FrameBodyMagneticFluxDensity> measurements, final boolean commonAxisUsed,
             final Matrix hardIron,
             final KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibratorListener listener) {
         this(measurements, commonAxisUsed, hardIron);
         this.listener = listener;
     }
 
     /**
      * Constructor.
      *
      * @param magneticModel Earth's magnetic model. If null, a default model
      *                      will be used instead.
      * @param hardIron      known hard-iron bias.
      * @throws IllegalArgumentException if provided hard-iron matrix is not
      *                                  3x1.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final WorldMagneticModel magneticModel, final Matrix hardIron) {
         this(hardIron);
         this.magneticModel = magneticModel;
     }
 
     /**
      * Constructor.
      *
      * @param magneticModel Earth's magnetic model. If null, a default model
      *                      will be used instead.
      * @param hardIron      known hard-iron bias.
      * @param listener      listener to handle events raised by this calibrator.
      * @throws IllegalArgumentException if provided hard-iron matrix is not
      *                                  3x1.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final WorldMagneticModel magneticModel, final Matrix hardIron,
             final KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibratorListener listener) {
         this(magneticModel, hardIron);
         this.listener = listener;
     }
 
     /**
      * Constructor.
      *
      * @param measurements  collection of body magnetic flux density measurements
      *                      taken at different frames (positions and orientations).
      * @param magneticModel Earth's magnetic model. If null, a default model
      *                      will be used instead.
      * @param hardIron      known hard-iron bias.
      * @throws IllegalArgumentException if provided hard-iron matrix is not
      *                                  3x1.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final Collection<? extends FrameBodyMagneticFluxDensity> measurements,
             final WorldMagneticModel magneticModel, final Matrix hardIron) {
         this(magneticModel, hardIron);
         //noinspection unchecked
         this.measurements = (Collection<FrameBodyMagneticFluxDensity>) measurements;
     }
 
     /**
      * Constructor.
      *
      * @param measurements  collection of body magnetic flux density measurements
      *                      taken at different frames (positions and orientations).
      * @param magneticModel Earth's magnetic model. If null, a default model
      *                      will be used instead.
      * @param hardIron      known hard-iron bias.
      * @param listener      listener to handle events raised by this calibrator.
      * @throws IllegalArgumentException if provided hard-iron matrix is not
      *                                  3x1.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final Collection<? extends FrameBodyMagneticFluxDensity> measurements,
             final WorldMagneticModel magneticModel, final Matrix hardIron,
             final KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibratorListener listener) {
         this(measurements, magneticModel, hardIron);
         this.listener = listener;
     }
 
     /**
      * Constructor.
      *
      * @param commonAxisUsed indicates whether z-axis is assumed to be common
      *                       for the accelerometer, gyroscope and magnetometer.
      * @param magneticModel  Earth's magnetic model. If null, a default model
      *                       will be used instead.
      * @param hardIron       known hard-iron bias.
      * @throws IllegalArgumentException if provided hard-iron matrix is not
      *                                  3x1.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final boolean commonAxisUsed, final WorldMagneticModel magneticModel, final Matrix hardIron) {
         this(magneticModel, hardIron);
         this.commonAxisUsed = commonAxisUsed;
     }
 
     /**
      * Constructor.
      *
      * @param commonAxisUsed indicates whether z-axis is assumed to be common
      *                       for the accelerometer, gyroscope and magnetometer.
      * @param magneticModel  Earth's magnetic model. If null, a default model
      *                       will be used instead.
      * @param hardIron       known hard-iron bias.
      * @param listener       listener to handle events raised by this calibrator.
      * @throws IllegalArgumentException if provided hard-iron matrix is not
      *                                  3x1.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final boolean commonAxisUsed, final WorldMagneticModel magneticModel, final Matrix hardIron,
             final KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibratorListener listener) {
         this(commonAxisUsed, magneticModel, hardIron);
         this.listener = listener;
     }
 
     /**
      * Constructor.
      *
      * @param measurements   collection of body magnetic flux density measurements
      *                       taken at different frames (positions and orientations).
      * @param commonAxisUsed indicates whether z-axis is assumed to be common
      *                       for the accelerometer, gyroscope and magnetometer.
      * @param magneticModel  Earth's magnetic model. If null, a default model
      *                       will be used instead.
      * @param hardIron       known hard-iron bias.
      * @throws IllegalArgumentException if provided hard-iron matrix is not
      *                                  3x1.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final Collection<? extends FrameBodyMagneticFluxDensity> measurements, final boolean commonAxisUsed,
             final WorldMagneticModel magneticModel, final Matrix hardIron) {
         this(commonAxisUsed, magneticModel, hardIron);
         //noinspection unchecked
         this.measurements = (Collection<FrameBodyMagneticFluxDensity>) measurements;
     }
 
     /**
      * Constructor.
      *
      * @param measurements   collection of body magnetic flux density measurements
      *                       taken at different frames (positions and orientations).
      * @param commonAxisUsed indicates whether z-axis is assumed to be common
      *                       for the accelerometer, gyroscope and magnetometer.
      * @param magneticModel  Earth's magnetic model. If null, a default model
      *                       will be used instead.
      * @param hardIron       known hard-iron bias.
      * @param listener       listener to handle events raised by this calibrator.
      * @throws IllegalArgumentException if provided hard-iron matrix is not
      *                                  3x1.
      */
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibrator(
             final Collection<? extends FrameBodyMagneticFluxDensity> measurements, final boolean commonAxisUsed,
             final WorldMagneticModel magneticModel, final Matrix hardIron,
             final KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibratorListener listener) {
         this(measurements, commonAxisUsed, magneticModel, hardIron);
         this.listener = listener;
     }
 
     /**
      * Gets x-coordinate of known magnetometer hard-iron bias.
      * This is expressed in Teslas (T).
      *
      * @return x-coordinate of known magnetometer hard-iron bias.
      */
     @Override
     public double getHardIronX() {
         return hardIronX;
     }
 
     /**
      * Sets x-coordinate of known magnetometer hard-iron bias.
      * This is expressed in Teslas (T).
      *
      * @param hardIronX x coordinate of magnetometer hard-iron.
      * @throws LockedException if calibrator is currently running.
      */
     @Override
     public void setHardIronX(final double hardIronX) throws LockedException {
         if (running) {
             throw new LockedException();
         }
         this.hardIronX = hardIronX;
     }
 
     /**
      * Gets y-coordinate of known magnetometer hard-iron bias.
      * This is expressed in Teslas (T).
      *
      * @return y-coordinate of known magnetometer hard-iron bias.
      */
     @Override
     public double getHardIronY() {
         return hardIronY;
     }
 
     /**
      * Sets y-coordinate of known magnetometer hard-iron bias.
      * This is expressed in Teslas (T).
      *
      * @param hardIronY y coordinate of magnetometer hard-iron.
      * @throws LockedException if calibrator is currently running.
      */
     @Override
     public void setHardIronY(final double hardIronY) throws LockedException {
         if (running) {
             throw new LockedException();
         }
         this.hardIronY = hardIronY;
     }
 
     /**
      * Gets z-coordinate of known magnetometer hard-iron bias.
      * This is expressed in Teslas (T).
      *
      * @return z-coordinate of known magnetometer hard-iron bias.
      */
     @Override
     public double getHardIronZ() {
         return hardIronZ;
     }
 
     /**
      * Sets z-coordinate of known magnetometer hard-iron bias.
      * This is expressed in Teslas (T).
      *
      * @param hardIronZ z coordinate of magnetometer hard-iron.
      * @throws LockedException if calibrator is currently running.
      */
     @Override
     public void setHardIronZ(final double hardIronZ) throws LockedException {
         if (running) {
             throw new LockedException();
         }
         this.hardIronZ = hardIronZ;
     }
 
     /**
      * Gets known x coordinate of magnetometer hard-iron.
      *
      * @return x coordinate of magnetometer hard-iron.
      */
     @Override
     public MagneticFluxDensity getHardIronXAsMagneticFluxDensity() {
         return new MagneticFluxDensity(hardIronX, MagneticFluxDensityUnit.TESLA);
     }
 
     /**
      * Gets known x coordinate of magnetometer hard-iron.
      *
      * @param result instance where result will be stored.
      */
     @Override
     public void getHardIronXAsMagneticFluxDensity(final MagneticFluxDensity result) {
         result.setValue(hardIronX);
         result.setUnit(MagneticFluxDensityUnit.TESLA);
     }
 
     /**
      * Sets known x-coordinate of magnetometer hard-iron.
      *
      * @param hardIronX known x-coordinate of magnetometer hard-iron.
      * @throws LockedException if calibrator is currently running.
      */
     @Override
     public void setHardIronX(final MagneticFluxDensity hardIronX) throws LockedException {
         if (running) {
             throw new LockedException();
         }
         this.hardIronX = convertMagneticFluxDensity(hardIronX);
     }
 
     /**
      * Gets known y coordinate of magnetometer hard-iron.
      *
      * @return y coordinate of magnetometer hard-iron.
      */
     @Override
     public MagneticFluxDensity getHardIronYAsMagneticFluxDensity() {
         return new MagneticFluxDensity(hardIronY, MagneticFluxDensityUnit.TESLA);
     }
 
     /**
      * Gets known y coordinate of magnetometer hard-iron.
      *
      * @param result instance where result will be stored.
      */
     @Override
     public void getHardIronYAsMagneticFluxDensity(final MagneticFluxDensity result) {
         result.setValue(hardIronY);
         result.setUnit(MagneticFluxDensityUnit.TESLA);
     }
 
     /**
      * Sets known y-coordinate of magnetometer hard-iron.
      *
      * @param hardIronY known y-coordinate of magnetometer hard-iron.
      * @throws LockedException if calibrator is currently running.
      */
     @Override
     public void setHardIronY(final MagneticFluxDensity hardIronY) throws LockedException {
         if (running) {
             throw new LockedException();
         }
         this.hardIronY = convertMagneticFluxDensity(hardIronY);
     }
 
     /**
      * Gets known z coordinate of magnetometer hard-iron.
      *
      * @return z coordinate of magnetometer hard-iron.
      */
     @Override
     public MagneticFluxDensity getHardIronZAsMagneticFluxDensity() {
         return new MagneticFluxDensity(hardIronZ, MagneticFluxDensityUnit.TESLA);
     }
 
     /**
      * Gets known z coordinate of magnetometer hard-iron.
      *
      * @param result instance where result will be stored.
      */
     @Override
     public void getHardIronZAsMagneticFluxDensity(final MagneticFluxDensity result) {
         result.setValue(hardIronZ);
         result.setUnit(MagneticFluxDensityUnit.TESLA);
     }
 
     /**
      * Sets known z-coordinate of magnetometer hard-iron.
      *
      * @param hardIronZ known z-coordinate of magnetometer hard-iron.
      * @throws LockedException if calibrator is currently running.
      */
     @Override
     public void setHardIronZ(final MagneticFluxDensity hardIronZ) throws LockedException {
         if (running) {
             throw new LockedException();
         }
         this.hardIronZ = convertMagneticFluxDensity(hardIronZ);
     }
 
     /**
      * Sets known hard-iron bias coordinates of magnetometer expressed
      * in Teslas (T).
      *
      * @param hardIronX x-coordinate of magnetometer hard-iron.
      * @param hardIronY y-coordinate of magnetometer hard-iron.
      * @param hardIronZ z-coordinate of magnetometer hard-iron.
      * @throws LockedException if calibrator is currently running.
      */
     @Override
     public void setHardIronCoordinates(
             final double hardIronX, final double hardIronY, final double hardIronZ) throws LockedException {
         if (running) {
             throw new LockedException();
         }
         this.hardIronX = hardIronX;
         this.hardIronY = hardIronY;
         this.hardIronZ = hardIronZ;
     }
 
     /**
      * Sets known hard-iron coordinates.
      *
      * @param hardIronX x-coordinate of magnetometer hard-iron.
      * @param hardIronY y-coordinate of magnetometer hard-iron.
      * @param hardIronZ z-coordinate of magnetometer hard-iron.
      * @throws LockedException if calibrator is currently running.
      */
     @Override
     public void setHardIronCoordinates(
             final MagneticFluxDensity hardIronX, final MagneticFluxDensity hardIronY,
             final MagneticFluxDensity hardIronZ) throws LockedException {
         if (running) {
             throw new LockedException();
         }
         this.hardIronX = convertMagneticFluxDensity(hardIronX);
         this.hardIronY = convertMagneticFluxDensity(hardIronY);
         this.hardIronZ = convertMagneticFluxDensity(hardIronZ);
     }
 
     /**
      * Gets known hard-iron.
      *
      * @return known hard-iron.
      */
     @Override
     public MagneticFluxDensityTriad getHardIronAsTriad() {
         return new MagneticFluxDensityTriad(MagneticFluxDensityUnit.TESLA, hardIronX, hardIronY, hardIronZ);
     }
 
     /**
      * Gets known hard-iron.
      *
      * @param result instance where result will be stored.
      */
     @Override
     public void getHardIronAsTriad(final MagneticFluxDensityTriad result) {
         result.setValueCoordinatesAndUnit(hardIronX, hardIronY, hardIronZ, MagneticFluxDensityUnit.TESLA);
     }
 
     /**
      * Sets known hard-iron.
      *
      * @param hardIron hard-iron to be set.
      * @throws LockedException if calibrator is currently running.
      */
     @Override
     public void setHardIron(final MagneticFluxDensityTriad hardIron) throws LockedException {
         if (running) {
             throw new LockedException();
         }
 
         hardIronX = convertMagneticFluxDensity(hardIron.getValueX(), hardIron.getUnit());
         hardIronY = convertMagneticFluxDensity(hardIron.getValueY(), hardIron.getUnit());
         hardIronZ = convertMagneticFluxDensity(hardIron.getValueZ(), hardIron.getUnit());
     }
 
     /**
      * Gets a collection of body magnetic flux density measurements taken at different
      * frames (positions, orientations and velocities).
      * If a single device IMU needs to be calibrated, typically all measurements are
      * taken at the same position, with zero velocity and multiple orientations.
      * However, if we just want to calibrate a given IMU model (e.g. obtain
      * an average and less precise calibration for the IMU of a given phone model),
      * we could take measurements collected throughout the planet at multiple positions
      * while the phone remains static (e.g. while charging), hence each measurement
      * position will change, velocity will remain zero and orientation will be
      * typically constant at horizontal orientation while the phone remains on a
      * flat surface.
      *
      * @return a collection of body magnetic flux density measurements taken at different
      * frames (positions, orientations and velocities).
      */
     @Override
     public Collection<FrameBodyMagneticFluxDensity> getMeasurements() {
         return measurements;
     }
 
     /**
      * Sets a collection of body magnetic flux density measurements taken at different
      * frames (positions, orientations and velocities).
      * If a single device IMU needs to be calibrated, typically all measurements are
      * taken at the same position, with zero velocity and multiple orientations.
      * However, if we just want to calibrate the a given IMU model (e.g. obtain
      * an average and less precise calibration for the IMU of a given phone model),
      * we could take measurements collected throughout the planet at multiple positions
      * while the phone remains static (e.g. while charging), hence each measurement
      * position will change, velocity will remain zero and orientation will be
      * typically constant at horizontal orientation while the phone remains on a
      * flat surface.
      *
      * @param measurements collection of body magnetic flux density measurements
      *                     taken at different frames (positions, orientations
      *                     and velocities).
      * @throws LockedException if estimator is currently running.
      */
     @Override
     public void setMeasurements(
             final Collection<? extends FrameBodyMagneticFluxDensity> measurements) throws LockedException {
         if (running) {
             throw new LockedException();
         }
         //noinspection unchecked
         this.measurements = (Collection<FrameBodyMagneticFluxDensity>) measurements;
     }
 
     /**
      * Indicates the type of measurement used by this calibrator.
      *
      * @return type of measurement used by this calibrator.
      */
     @Override
     public MagnetometerCalibratorMeasurementType getMeasurementType() {
         return MagnetometerCalibratorMeasurementType.FRAME_BODY_MAGNETIC_FLUX_DENSITY;
     }
 
     /**
      * Indicates whether this calibrator requires ordered measurements in a
      * list or not.
      *
      * @return true if measurements must be ordered, false otherwise.
      */
     @Override
     public boolean isOrderedMeasurementsRequired() {
         return false;
     }
 
     /**
      * Indicates whether this calibrator requires quality scores for each
      * measurement or not.
      *
      * @return true if quality scores are required, false otherwise.
      */
     @Override
     public boolean isQualityScoresRequired() {
         return false;
     }
 
     /**
      * Indicates whether z-axis is assumed to be common for accelerometer,
      * gyroscope and magnetometer.
      * When enabled, this eliminates 3 variables from Mm (soft-iron) matrix.
      *
      * @return true if z-axis is assumed to be common for accelerometer,
      * gyroscope and magnetometer, false otherwise.
      */
     @Override
     public boolean isCommonAxisUsed() {
         return commonAxisUsed;
     }
 
     /**
      * Specifies whether z-axis is assumed to be common for accelerometer and
      * gyroscope.
      * When enabled, this eliminates 3 variables from Mm matrix.
      *
      * @param commonAxisUsed true if z-axis is assumed to be common for
      *                       accelerometer, gyroscope and magnetometer, false
      *                       otherwise.
      * @throws LockedException if estimator is currently running.
      */
     @Override
     public void setCommonAxisUsed(final boolean commonAxisUsed) throws LockedException {
         if (running) {
             throw new LockedException();
         }
 
         this.commonAxisUsed = commonAxisUsed;
     }
 
     /**
      * Gets listener to handle events raised by this calibrator.
      *
      * @return listener to handle events raised by this calibrator.
      */
     @Override
     public KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibratorListener getListener() {
         return listener;
     }
 
     /**
      * Sets listener to handle events raised by this calibrator.
      *
      * @param listener listener to handle events raised by this calibrator.
      * @throws LockedException if estimator is currently running.
      */
     @Override
     public void setListener(final KnownHardIronAndFrameMagnetometerLinearLeastSquaresCalibratorListener listener)
             throws LockedException {
         if (running) {
             throw new LockedException();
         }
 
         this.listener = listener;
     }
 
     /**
      * Gets minimum number of required measurements.
      *
      * @return minimum number of required measurements.
      */
     @Override
     public int getMinimumRequiredMeasurements() {
         return MINIMUM_MEASUREMENTS;
     }
 
     /**
      * Indicates whether calibrator is ready to start the estimator.
      *
      * @return true if calibrator is ready, false otherwise.
      */
     @Override
     public boolean isReady() {
         return measurements != null && measurements.size() >= MINIMUM_MEASUREMENTS;
     }
 
     /**
      * Indicates whether calibrator is currently running or no.
      *
      * @return true if calibrator is running, false otherwise.
      */
     @Override
     public boolean isRunning() {
         return running;
     }
 
     /**
      * Gets Earth's magnetic model.
      *
      * @return Earth's magnetic model or null if not provided.
      */
     public WorldMagneticModel getMagneticModel() {
         return magneticModel;
     }
 
     /**
      * Sets Earth's magnetic model.
      * If not provided a default model will be loaded internally.
      *
      * @param magneticModel Earth's magnetic model to be set.
      * @throws LockedException if calibrator is currently running.
      */
     public void setMagneticModel(final WorldMagneticModel magneticModel) throws LockedException {
         if (running) {
             throw new LockedException();
         }
         this.magneticModel = magneticModel;
     }
 
     /**
      * Gets known hard-iron bias as an array.
      * Array values are expressed in Teslas (T).
      *
      * @return array containing coordinates of initial bias.
      */
     @Override
     public double[] getHardIron() {
         final var result = new double[BodyMagneticFluxDensity.COMPONENTS];
         getHardIron(result);
         return result;
     }
 
     /**
      * Gets known hard-iron bias as an array.
      * Array values are expressed in Teslas (T).
      *
      * @param result instance where result data will be copied to.
      * @throws IllegalArgumentException if provided array does not have
      *                                  length 3.
      */
     @Override
     public void getHardIron(final double[] result) {
         if (result.length != BodyMagneticFluxDensity.COMPONENTS) {
             throw new IllegalArgumentException();
         }
         result[0] = hardIronX;
         result[1] = hardIronY;
         result[2] = hardIronZ;
     }
 
     /**
      * Sets known hard-iron bias as an array.
      * Array values are expressed in Teslas (T).
      *
      * @param hardIron known hard-iron bias.
      * @throws LockedException          if calibrator is currently running.
      * @throws IllegalArgumentException if provided array does not have
      *                                  length 3.
      */
     @Override
     public void setHardIron(final double[] hardIron) throws LockedException {
         if (running) {
             throw new LockedException();
         }
 
         if (hardIron.length != BodyMagneticFluxDensity.COMPONENTS) {
             throw new IllegalArgumentException();
         }
         hardIronX = hardIron[0];
         hardIronY = hardIron[1];
         hardIronZ = hardIron[2];
     }
 
     /**
      * Gets known hard-iron bias as a column matrix.
      *
      * @return hard-iron bias as a column matrix.
      */
     @Override
     public Matrix getHardIronMatrix() {
         Matrix result;
         try {
             result = new Matrix(BodyMagneticFluxDensity.COMPONENTS, 1);
             getHardIronMatrix(result);
         } catch (final WrongSizeException ignore) {
             // never happens
             result = null;
         }
         return result;
     }
 
     /**
      * Gets known hard-iron bias as a column matrix.
      *
      * @param result instance where result data will be copied to.
      * @throws IllegalArgumentException if provided matrix is not 3x1.
      */
     @Override
     public void getHardIronMatrix(final Matrix result) {
         if (result.getRows() != BodyMagneticFluxDensity.COMPONENTS || result.getColumns() != 1) {
             throw new IllegalArgumentException();
         }
         result.setElementAtIndex(0, hardIronX);
         result.setElementAtIndex(1, hardIronY);
         result.setElementAtIndex(2, hardIronZ);
     }
 
     /**
      * Sets known hard-iron bias.
      *
      * @param hardIron magnetometer hard-iron bias to be set.
      * @throws LockedException          if calibrator is currently running.
      * @throws IllegalArgumentException if provided matrix is not 3x1.
      */
     @Override
     public void setHardIron(final Matrix hardIron) throws LockedException {
         if (running) {
             throw new LockedException();
         }
         if (hardIron.getRows() != BodyMagneticFluxDensity.COMPONENTS || hardIron.getColumns() != 1) {
             throw new IllegalArgumentException();
         }
 
         hardIronX = hardIron.getElementAtIndex(0);
         hardIronY = hardIron.getElementAtIndex(1);
         hardIronZ = hardIron.getElementAtIndex(2);
     }
 
     /**
      * Estimates magnetometer calibration parameters containing scale factors
      * and cross-coupling errors.
      *
      * @throws LockedException      if calibrator is currently running.
      * @throws NotReadyException    if calibrator is not ready.
      * @throws CalibrationException if calibration fails for numerical reasons.
      */
     @Override
     public void calibrate() throws LockedException, NotReadyException, CalibrationException {
         if (running) {
             throw new LockedException();
         }
 
         if (!isReady()) {
             throw new NotReadyException();
         }
 
         try {
             running = true;
 
             if (listener != null) {
                 listener.onCalibrateStart(this);
             }
 
             if (commonAxisUsed) {
                 calibrateCommonAxis();
             } else {
                 calibrateGeneral();
             }
 
             if (listener != null) {
                 listener.onCalibrateEnd(this);
             }
 
         } catch (final AlgebraException | IOException e) {
             throw new CalibrationException(e);
         } finally {
             running = false;
         }
     }
 
     /**
      * Gets estimated magnetometer soft-iron matrix containing scale factors
      * and cross coupling errors.
      * This is the product of matrix Tm containing cross coupling errors and Km
      * containing scaling factors.
      * So tat:
      * <pre>
      *     Mm = [sx    mxy  mxz] = Tm*Km
      *          [myx   sy   myz]
      *          [mzx   mzy  sz ]
      * </pre>
      * Where:
      * <pre>
      *     Km = [sx 0   0 ]
      *          [0  sy  0 ]
      *          [0  0   sz]
      * </pre>
      * and
      * <pre>
      *     Tm = [1          -alphaXy    alphaXz ]
      *          [alphaYx    1           -alphaYz]
      *          [-alphaZx   alphaZy     1       ]
      * </pre>
      * Hence:
      * <pre>
      *     Mm = [sx    mxy  mxz] = Tm*Km =  [sx             -sy * alphaXy   sz * alphaXz ]
      *          [myx   sy   myz]            [sx * alphaYx   sy              -sz * alphaYz]
      *          [mzx   mzy  sz ]            [-sx * alphaZx  sy * alphaZy    sz           ]
      * </pre>
      * This instance allows any 3x3 matrix however, typically alphaYx, alphaZx and alphaZy
      * are considered to be zero if the accelerometer z-axis is assumed to be the same
      * as the body z-axis. When this is assumed, myx = mzx = mzy = 0 and the Mm matrix
      * becomes upper diagonal:
      * <pre>
      *     Mm = [sx    mxy  mxz]
      *          [0     sy   myz]
      *          [0     0    sz ]
      * </pre>
      * Values of this matrix are unit-less.
      *
      * @return estimated magnetometer soft-iron scale factors and cross coupling errors,
      * or null if not available.
      */
     @Override
     public Matrix getEstimatedMm() {
         return estimatedMm;
     }
 
     /**
      * Gets estimated x-axis scale factor.
      *
      * @return estimated x-axis scale factor or null if not available.
      */
     @Override
     public Double getEstimatedSx() {
         return estimatedMm != null ? estimatedMm.getElementAt(0, 0) : null;
     }
 
     /**
      * Gets estimated y-axis scale factor.
      *
      * @return estimated y-axis scale factor or null if not available.
      */
     @Override
     public Double getEstimatedSy() {
         return estimatedMm != null ? estimatedMm.getElementAt(1, 1) : null;
     }
 
     /**
      * Gets estimated z-axis scale factor.
      *
      * @return estimated z-axis scale factor or null if not available.
      */
     @Override
     public Double getEstimatedSz() {
         return estimatedMm != null ? estimatedMm.getElementAt(2, 2) : null;
     }
 
     /**
      * Gets estimated x-y cross-coupling error.
      *
      * @return estimated x-y cross-coupling error or null if not available.
      */
     @Override
     public Double getEstimatedMxy() {
         return estimatedMm != null ? estimatedMm.getElementAt(0, 1) : null;
     }
 
     /**
      * Gets estimated x-z cross-coupling error.
      *
      * @return estimated x-z cross-coupling error or null if not available.
      */
     @Override
     public Double getEstimatedMxz() {
         return estimatedMm != null ? estimatedMm.getElementAt(0, 2) : null;
     }
 
     /**
      * Gets estimated y-x cross-coupling error.
      *
      * @return estimated y-x cross-coupling error or null if not available.
      */
     @Override
     public Double getEstimatedMyx() {
         return estimatedMm != null ? estimatedMm.getElementAt(1, 0) : null;
     }
 
     /**
      * Gets estimated y-z cross-coupling error.
      *
      * @return estimated y-z cross-coupling error or null if not available.
      */
     @Override
     public Double getEstimatedMyz() {
         return estimatedMm != null ? estimatedMm.getElementAt(1, 2) : null;
     }
 
     /**
      * Gets estimated z-x cross-coupling error.
      *
      * @return estimated z-x cross-coupling error or null if not available.
      */
     @Override
     public Double getEstimatedMzx() {
         return estimatedMm != null ? estimatedMm.getElementAt(2, 0) : null;
     }
 
     /**
      * Gets estimated z-y cross-coupling error.
      *
      * @return estimated z-y cross-coupling error or null if not available.
      */
     @Override
     public Double getEstimatedMzy() {
         return estimatedMm != null ? estimatedMm.getElementAt(2, 1) : null;
     }
 
     /**
      * Internal method to perform calibration when common z-axis is assumed
      * for the accelerometer, gyroscope and magnetometer.
      *
      * @throws AlgebraException if there are numerical errors.
      * @throws IOException      if world magnetic model cannot be loaded.
      */
     private void calibrateCommonAxis() throws AlgebraException, IOException {
         // The magnetometer model is:
         // mBmeas = bm + (I + Mm) * mBtrue + w
 
         // Ideally a least squares solution tries to minimize noise component, so:
         // mBmeas = bm + (I + Mm) * mBtrue
 
         // Hence:
         // [mBmeasx] = [bx] + ( [1  0   0] + [sx    mxy mxz])   [mBtruex]
         // [mBmeasy] = [by]     [0  1   0]   [myx   sy  myz]    [mBtruey]
         // [mBmeasz] = [bz]     [0  0   1]   [mzx   mzy sz ]    [mBtruez]
 
         // where myx = mzx = mzy = 0
 
         // Hence:
         // [mBmeasx] = [bx] + ( [1  0   0] + [sx    mxy mxz])   [mBtruex]
         // [mBmeasy] = [by]     [0  1   0]   [0     sy  myz]    [mBtruey]
         // [mBmeasz] = [bz]     [0  0   1]   [0     0   sz ]    [mBtruez]
 
         // [mBmeasx] = [bx] +   [1+sx   mxy     mxz ][mBtruex]
         // [mBmeasy]   [by]     [0      1+sy    myz ][mBtruey]
         // [mBmeasz]   [bz]     [0      0       1+sz][mBtruez]
 
         // mBmeasx = bx + (1+sx) * mBtruex + mxy * mBtruey + mxz * mBtruez
         // mBmeasy = by + (1+sy) * mBtruey + myz * mBtruez
         // mBmeasz = bz + (1+sz) * mBtruez
 
         // Where the unknowns are: sx, sy, sz, mxy mxz, myz
         // Reordering:
         // mBmeasx = bx + mBtruex + sx * mBtruex + mxy * mBtruey + mxz * mBtruez
         // mBmeasy = by + mBtruey + sy * mBtruey + myz * mBtruez
         // mBmeasz = bz + mBtruez + sz * mBtruez
 
         // mBmeasx - mBtruex - bx = sx * mBtruex + mxy * mBtruey + mxz * mBtruez
         // mBmeasy - mBtruey - by = sy * mBtruey + myz * mBtruez
         // mBmeasz - mBtruez - bz = sz * mBtruez
 
         // [mBtruex  0        0        mBtruey  mBtruez  0      ][sx ] = [mBmeasx - mBtruex - bx]
         // [0        mBtruey  0        0        0        mBtruez][sy ]   [mBmeasy - mBtruey - by]
         // [0        0        mBtruez  0        0        0      ][sz ]   [mBmeasz - mBtruez - bz]
         //                                                       [mxy]
         //                                                       [mxz]
         //                                                       [myz]
 
         final WMMEarthMagneticFluxDensityEstimator wmmEstimator;
         if (magneticModel != null) {
             wmmEstimator = new WMMEarthMagneticFluxDensityEstimator(magneticModel);
         } else {
             wmmEstimator = new WMMEarthMagneticFluxDensityEstimator();
         }
 
         final var expectedMagneticFluxDensity = new BodyMagneticFluxDensity();
         final var nedFrame = new NEDFrame();
         final var earthB = new NEDMagneticFluxDensity();
         final var cbn = new CoordinateTransformation(FrameType.BODY_FRAME, FrameType.LOCAL_NAVIGATION_FRAME);
         final var cnb = new CoordinateTransformation(FrameType.LOCAL_NAVIGATION_FRAME, FrameType.BODY_FRAME);
 
         final var rows = EQUATIONS_PER_MEASUREMENT * measurements.size();
         final var a = new Matrix(rows, COMMON_Z_AXIS_UNKNOWNS);
         final var b = new Matrix(rows, 1);
         var i = 0;
         for (final var measurement : measurements) {
             final var measuredMagneticFluxDensity = measurement.getMagneticFluxDensity();
 
             // estimate Earth magnetic flux density at frame position and
             // timestamp using WMM
             final var ecefFrame = measurement.getFrame();
             ECEFtoNEDFrameConverter.convertECEFtoNED(ecefFrame, nedFrame);
 
             final var year = measurement.getYear();
 
             final var latitude = nedFrame.getLatitude();
             final var longitude = nedFrame.getLongitude();
             final var height = nedFrame.getHeight();
 
             nedFrame.getCoordinateTransformation(cbn);
             cbn.inverse(cnb);
 
             wmmEstimator.estimate(latitude, longitude, height, year, earthB);
 
             // estimate expected body magnetic flux density taking into
             // account body attitude (inverse of frame orientation) and
             // estimated Earth magnetic flux density
             BodyMagneticFluxDensityEstimator.estimate(earthB, cnb, expectedMagneticFluxDensity);
 
             final var bMeasX = measuredMagneticFluxDensity.getBx();
             final var bMeasY = measuredMagneticFluxDensity.getBy();
             final var bMeasZ = measuredMagneticFluxDensity.getBz();
 
             final var bTrueX = expectedMagneticFluxDensity.getBx();
             final var bTrueY = expectedMagneticFluxDensity.getBy();
             final var bTrueZ = expectedMagneticFluxDensity.getBz();
 
             a.setElementAt(i, 0, bTrueX);
             a.setElementAt(i, 1, 0.0);
             a.setElementAt(i, 2, 0.0);
             a.setElementAt(i, 3, bTrueY);
             a.setElementAt(i, 4, bTrueZ);
             a.setElementAt(i, 5, 0.0);
 
             b.setElementAtIndex(i, bMeasX - bTrueX - hardIronX);
             i++;
 
             a.setElementAt(i, 0, 0.0);
             a.setElementAt(i, 1, bTrueY);
             a.setElementAt(i, 2, 0.0);
             a.setElementAt(i, 3, 0.0);
             a.setElementAt(i, 4, 0.0);
             a.setElementAt(i, 5, bTrueZ);
 
             b.setElementAtIndex(i, bMeasY - bTrueY - hardIronY);
             i++;
 
             a.setElementAt(i, 0, 0.0);
             a.setElementAt(i, 1, 0.0);
             a.setElementAt(i, 2, bTrueZ);
             a.setElementAt(i, 3, 0.0);
             a.setElementAt(i, 4, 0.0);
             a.setElementAt(i, 5, 0.0);
 
             b.setElementAtIndex(i, bMeasZ - bTrueZ - hardIronZ);
             i++;
         }
 
         final var unknowns = Utils.solve(a, b);
 
         final var sx = unknowns.getElementAtIndex(0);
         final var sy = unknowns.getElementAtIndex(1);
         final var sz = unknowns.getElementAtIndex(2);
         final var mxy = unknowns.getElementAtIndex(3);
         final var mxz = unknowns.getElementAtIndex(4);
         final var myz = unknowns.getElementAtIndex(5);
 
         fillMm(sx, sy, sz, mxy, mxz, 0.0, myz, 0.0, 0.0);
     }
 
     /**
      * Internal method to perform general calibration.
      *
      * @throws AlgebraException if there are numerical errors.
      * @throws IOException      if world magnetic model cannot be loaded.
      */
     private void calibrateGeneral() throws AlgebraException, IOException {
         // The magnetometer model is:
         // mBmeas = bm + (I + Mm) * mBtrue + w
 
         // Ideally a least squares solution tries to minimize noise component, so:
         // mBmeas = bm + (I + Mm) * mBtrue
 
         // Hence:
         // [mBmeasx] = [bx] + ( [1  0   0] + [sx    mxy mxz])   [mBtruex]
         // [mBmeasy] = [by]     [0  1   0]   [myx   sy  myz]    [mBtruey]
         // [mBmeasz] = [bz]     [0  0   1]   [mzx   mzy sz ]    [mBtruez]
 
         // [mBmeasx] = [bx] +   [1+sx   mxy     mxz ][mBtruex]
         // [mBmeasy]   [by]     [myx    1+sy    myz ][mBtruey]
         // [mBmeasz]   [bz]     [mzx    mzy     1+sz][mBtruez]
 
         // mBmeasx = bx + (1+sx) * mBtruex + mxy * mBtruey + mxz * mBtruez
         // mBmeasy = by + myx * mBtruex + (1+sy) * mBtruey + myz * mBtruez
         // mBmeasz = bz + mzx * mBtruex + mzy * mBtruey + (1+sz) * mBtruez
 
         // Where the unknowns are: bx, by, bz, sx, sy, sz, mxy mxz, myx, myz, mzx, mzy
         // Reordering:
         // mBmeasx = bx + mBtruex + sx * mBtruex + mxy * mBtruey + mxz * mBtruez
         // mBmeasy = by + myx * mBtruex + mBtruey + sy * mBtruey + myz * mBtruez
         // mBmeasz = bz + mzx * mBtruex + mzy * mBtruey + mBtruez + sz * mBtruez
 
         // mBmeasx - mBtruex - bx = sx * mBtruex + mxy * mBtruey + mxz * mBtruez
         // mBmeasy - mBtruey - by = myx * mBtruex + sy * mBtruey + myz * mBtruez
         // mBmeasz - mBtruez - bz = mzx * mBtruex + mzy * mBtruey + sz * mBtruez
 
         // [mBtruex  0        0        mBtruey  mBtruez  0        0        0        0      ][sx ] = [mBmeasx - mBtruex - bx]
         // [0        mBtruey  0        0        0        mBtruex  mBtruez  0        0      ][sy ]   [mBmeasy - mBtruey - by]
         // [0        0        mBtruez  0        0        0        0        mBtruex  mBtruey][sz ]   [mBmeasz - mBtruez - bz]
         //                                                                                  [mxy]
         //                                                                                  [mxz]
         //                                                                                  [myx]
         //                                                                                  [myz]
         //                                                                                  [mzx]
         //                                                                                  [mzy]
 
         final WMMEarthMagneticFluxDensityEstimator wmmEstimator;
         if (magneticModel != null) {
             wmmEstimator = new WMMEarthMagneticFluxDensityEstimator(magneticModel);
         } else {
             wmmEstimator = new WMMEarthMagneticFluxDensityEstimator();
         }
 
         final var expectedMagneticFluxDensity = new BodyMagneticFluxDensity();
         final var nedFrame = new NEDFrame();
         final var earthB = new NEDMagneticFluxDensity();
         final var cbn = new CoordinateTransformation(FrameType.BODY_FRAME, FrameType.LOCAL_NAVIGATION_FRAME);
         final var cnb = new CoordinateTransformation(FrameType.LOCAL_NAVIGATION_FRAME, FrameType.BODY_FRAME);
 
         final var rows = EQUATIONS_PER_MEASUREMENT * measurements.size();
         final var a = new Matrix(rows, GENERAL_UNKNOWNS);
         final var b = new Matrix(rows, 1);
         var i = 0;
         for (final var measurement : measurements) {
             final var measuredMagneticFluxDensity = measurement.getMagneticFluxDensity();
 
             // estimate Earth magnetic flux density at frame position and
             // timestamp using WMM
             final var ecefFrame = measurement.getFrame();
             ECEFtoNEDFrameConverter.convertECEFtoNED(ecefFrame, nedFrame);
 
             final var year = measurement.getYear();
 
             final var latitude = nedFrame.getLatitude();
             final var longitude = nedFrame.getLongitude();
             final var height = nedFrame.getHeight();
 
             nedFrame.getCoordinateTransformation(cbn);
             cbn.inverse(cnb);
 
             wmmEstimator.estimate(latitude, longitude, height, year, earthB);
 
             // estimate expected body magnetic flux density taking into
             // account body attitude (inverse of frame orientation) and
             // estimated Earth magnetic flux density
             BodyMagneticFluxDensityEstimator.estimate(earthB, cnb, expectedMagneticFluxDensity);
 
             final var bMeasX = measuredMagneticFluxDensity.getBx();
             final var bMeasY = measuredMagneticFluxDensity.getBy();
             final var bMeasZ = measuredMagneticFluxDensity.getBz();
 
             final var bTrueX = expectedMagneticFluxDensity.getBx();
             final var bTrueY = expectedMagneticFluxDensity.getBy();
             final var bTrueZ = expectedMagneticFluxDensity.getBz();
 
             a.setElementAt(i, 0, bTrueX);
             a.setElementAt(i, 1, 0.0);
             a.setElementAt(i, 2, 0.0);
             a.setElementAt(i, 3, bTrueY);
             a.setElementAt(i, 4, bTrueZ);
             a.setElementAt(i, 5, 0.0);
             a.setElementAt(i, 6, 0.0);
             a.setElementAt(i, 7, 0.0);
             a.setElementAt(i, 8, 0.0);
 
             b.setElementAtIndex(i, bMeasX - bTrueX - hardIronX);
             i++;
 
             a.setElementAt(i, 0, 0.0);
             a.setElementAt(i, 1, bTrueY);
             a.setElementAt(i, 2, 0.0);
             a.setElementAt(i, 3, 0.0);
             a.setElementAt(i, 4, 0.0);
             a.setElementAt(i, 5, bTrueX);
             a.setElementAt(i, 6, bTrueZ);
             a.setElementAt(i, 7, 0.0);
             a.setElementAt(i, 8, 0.0);
 
             b.setElementAtIndex(i, bMeasY - bTrueY - hardIronY);
             i++;
 
             a.setElementAt(i, 0, 0.0);
             a.setElementAt(i, 1, 0.0);
             a.setElementAt(i, 2, bTrueZ);
             a.setElementAt(i, 3, 0.0);
             a.setElementAt(i, 4, 0.0);
             a.setElementAt(i, 5, 0.0);
             a.setElementAt(i, 6, 0.0);
             a.setElementAt(i, 7, bTrueX);
             a.setElementAt(i, 8, bTrueY);
 
             b.setElementAtIndex(i, bMeasZ - bTrueZ - hardIronZ);
             i++;
         }
 
         final var unknowns = Utils.solve(a, b);
 
         final var sx = unknowns.getElementAtIndex(0);
         final var sy = unknowns.getElementAtIndex(1);
         final var sz = unknowns.getElementAtIndex(2);
         final var mxy = unknowns.getElementAtIndex(3);
         final var mxz = unknowns.getElementAtIndex(4);
         final var myx = unknowns.getElementAtIndex(5);
         final var myz = unknowns.getElementAtIndex(6);
         final var mzx = unknowns.getElementAtIndex(7);
         final var mzy = unknowns.getElementAtIndex(8);
 
         fillMm(sx, sy, sz, mxy, mxz, myx, myz, mzx, mzy);
     }
 
     /**
      * Fills scale factor and cross coupling error matrix with estimated values.
      *
      * @param sx  x scale factor
      * @param sy  y scale factor
      * @param sz  z scale factor
      * @param mxy x-y cross coupling
      * @param mxz x-z cross coupling
      * @param myx y-x cross coupling
      * @param myz y-z cross coupling
      * @param mzx z-x cross coupling
      * @param mzy z-y cross coupling
      * @throws WrongSizeException never happens.
      */
     private void fillMm(final double sx, final double sy, final double sz,
                         final double mxy, final double mxz, final double myx,
                         final double myz, final double mzx, final double mzy) throws WrongSizeException {
         if (estimatedMm == null) {
             estimatedMm = new Matrix(BodyMagneticFluxDensity.COMPONENTS, BodyMagneticFluxDensity.COMPONENTS);
         }
 
         estimatedMm.setElementAt(0, 0, sx);
         estimatedMm.setElementAt(1, 0, myx);
         estimatedMm.setElementAt(2, 0, mzx);
 
         estimatedMm.setElementAt(0, 1, mxy);
         estimatedMm.setElementAt(1, 1, sy);
         estimatedMm.setElementAt(2, 1, mzy);
 
         estimatedMm.setElementAt(0, 2, mxz);
         estimatedMm.setElementAt(1, 2, myz);
         estimatedMm.setElementAt(2, 2, sz);
     }
 
     /**
      * Converts magnetic flux density value and unit to Teslas.
      *
      * @param value magnetic flux density value.
      * @param unit  unit of magnetic flux density value.
      * @return converted value.
      */
     private static double convertMagneticFluxDensity(final double value, final MagneticFluxDensityUnit unit) {
         return MagneticFluxDensityConverter.convert(value, unit, MagneticFluxDensityUnit.TESLA);
     }
 
     /**
      * Converts magnetic flux density instance to Teslas.
      *
      * @param magneticFluxDensity magnetic flux density instance to be converted.
      * @return converted value.
      */
     private static double convertMagneticFluxDensity(final MagneticFluxDensity magneticFluxDensity) {
         return convertMagneticFluxDensity(magneticFluxDensity.getValue().doubleValue(), magneticFluxDensity.getUnit());
     }
 }