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    * CS licenses this file to You under the Apache License, Version 2.0
    * (the "License"); you may not use this file except in compliance with
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    *   http://www.apache.org/licenses/LICENSE-2.0
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   * Unless required by applicable law or agreed to in writing, software
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  package org.orekit.estimation.sequential;
  
  import org.hipparchus.exception.MathRuntimeException;
  import org.hipparchus.filtering.kalman.ProcessEstimate;
  import org.hipparchus.filtering.kalman.extended.ExtendedKalmanFilter;
  import org.hipparchus.filtering.kalman.extended.NonLinearEvolution;
  import org.hipparchus.filtering.kalman.extended.NonLinearProcess;
  import org.hipparchus.linear.Array2DRowRealMatrix;
  import org.hipparchus.linear.ArrayRealVector;
  import org.hipparchus.linear.MatrixUtils;
  import org.hipparchus.linear.QRDecomposition;
  import org.hipparchus.linear.RealMatrix;
  import org.hipparchus.linear.RealVector;
  import org.hipparchus.util.FastMath;
  import org.orekit.errors.OrekitException;
  import org.orekit.estimation.measurements.EstimatedMeasurement;
  import org.orekit.estimation.measurements.ObservedMeasurement;
  import org.orekit.orbits.Orbit;
  import org.orekit.orbits.OrbitType;
  import org.orekit.propagation.PropagationType;
  import org.orekit.propagation.SpacecraftState;
  import org.orekit.propagation.conversion.DSSTPropagatorBuilder;
  import org.orekit.propagation.semianalytical.dsst.DSSTHarvester;
  import org.orekit.propagation.semianalytical.dsst.DSSTPropagator;
  import org.orekit.propagation.semianalytical.dsst.forces.DSSTForceModel;
  import org.orekit.propagation.semianalytical.dsst.forces.ShortPeriodTerms;
  import org.orekit.propagation.semianalytical.dsst.utilities.AuxiliaryElements;
  import org.orekit.time.AbsoluteDate;
  import org.orekit.time.ChronologicalComparator;
  import org.orekit.utils.ParameterDriver;
  import org.orekit.utils.ParameterDriversList;
  import org.orekit.utils.ParameterDriversList.DelegatingDriver;
  import org.orekit.utils.TimeSpanMap.Span;
  
  import java.util.ArrayList;
  import java.util.Comparator;
  import java.util.HashMap;
  import java.util.List;
  import java.util.Map;
  
  /** Process model to use with a {@link SemiAnalyticalKalmanEstimator}.
   *
   * @see "Folcik Z., Orbit Determination Using Modern Filters/Smoothers and Continuous Thrust Modeling,
   *       Master of Science Thesis, Department of Aeronautics and Astronautics, MIT, June, 2008."
   *
   * @see "Cazabonne B., Bayard J., Journot M., and Cefola P. J., A Semi-analytical Approach for Orbit
   *       Determination based on Extended Kalman Filter, AAS Paper 21-614, AAS/AIAA Astrodynamics
   *       Specialist Conference, Big Sky, August 2021."
   *
   * @author Julie Bayard
   * @author Bryan Cazabonne
   * @author Maxime Journot
   * @since 11.1
   */
  public  class SemiAnalyticalKalmanModel implements KalmanEstimation, NonLinearProcess<MeasurementDecorator>, SemiAnalyticalProcess {
  
      /** Builders for DSST propagator. */
      private final DSSTPropagatorBuilder builder;
  
      /** Estimated orbital parameters. */
      private final ParameterDriversList estimatedOrbitalParameters;
  
      /** Per-builder estimated propagation drivers. */
      private final ParameterDriversList estimatedPropagationParameters;
  
      /** Estimated measurements parameters. */
      private final ParameterDriversList estimatedMeasurementsParameters;
  
      /** Map for propagation parameters columns. */
      private final Map<String, Integer> propagationParameterColumns;
  
      /** Map for measurements parameters columns. */
      private final Map<String, Integer> measurementParameterColumns;
  
      /** Scaling factors. */
      private final double[] scale;
  
      /** Provider for covariance matrix. */
      private final CovarianceMatrixProvider covarianceMatrixProvider;
  
      /** Process noise matrix provider for measurement parameters. */
      private final CovarianceMatrixProvider measurementProcessNoiseMatrix;
  
     /** Harvester between two-dimensional Jacobian matrices and one-dimensional additional state arrays. */
     private DSSTHarvester harvester;
 
     /** Propagators for the reference trajectories, up to current date. */
     private DSSTPropagator dsstPropagator;
 
     /** Observer to retrieve current estimation info. */
     private KalmanObserver observer;
 
     /** Current number of measurement. */
     private int currentMeasurementNumber;
 
     /** Current date. */
     private AbsoluteDate currentDate;
 
     /** Predicted mean element filter correction. */
     private RealVector predictedFilterCorrection;
 
     /** Corrected mean element filter correction. */
     private RealVector correctedFilterCorrection;
 
     /** Predicted measurement. */
     private EstimatedMeasurement<?> predictedMeasurement;
 
     /** Corrected measurement. */
     private EstimatedMeasurement<?> correctedMeasurement;
 
     /** Nominal mean spacecraft state. */
     private SpacecraftState nominalMeanSpacecraftState;
 
     /** Previous nominal mean spacecraft state. */
     private SpacecraftState previousNominalMeanSpacecraftState;
 
     /** Current corrected estimate. */
     private ProcessEstimate correctedEstimate;
 
     /** Inverse of the orbital part of the state transition matrix. */
     private RealMatrix phiS;
 
     /** Propagation parameters part of the state transition matrix. */
     private RealMatrix psiS;
 
     /** Kalman process model constructor (package private).
      * @param propagatorBuilder propagators builders used to evaluate the orbits.
      * @param covarianceMatrixProvider provider for covariance matrix
      * @param estimatedMeasurementParameters measurement parameters to estimate
      * @param measurementProcessNoiseMatrix provider for measurement process noise matrix
      */
     protected SemiAnalyticalKalmanModel(final DSSTPropagatorBuilder propagatorBuilder,
                                         final CovarianceMatrixProvider covarianceMatrixProvider,
                                         final ParameterDriversList estimatedMeasurementParameters,
                                         final CovarianceMatrixProvider measurementProcessNoiseMatrix) {
 
         this.builder                         = propagatorBuilder;
         this.estimatedMeasurementsParameters = estimatedMeasurementParameters;
         this.measurementParameterColumns     = new HashMap<>(estimatedMeasurementsParameters.getDrivers().size());
         this.observer                        = null;
         this.currentMeasurementNumber        = 0;
         this.currentDate                     = propagatorBuilder.getInitialOrbitDate();
         this.covarianceMatrixProvider        = covarianceMatrixProvider;
         this.measurementProcessNoiseMatrix   = measurementProcessNoiseMatrix;
 
         // Number of estimated parameters
         int columns = 0;
 
         // Set estimated orbital parameters
         estimatedOrbitalParameters = new ParameterDriversList();
         for (final ParameterDriver driver : builder.getOrbitalParametersDrivers().getDrivers()) {
 
             // Verify if the driver reference date has been set
             if (driver.getReferenceDate() == null) {
                 driver.setReferenceDate(currentDate);
             }
 
             // Verify if the driver is selected
             if (driver.isSelected()) {
                 estimatedOrbitalParameters.add(driver);
                 columns++;
             }
 
         }
 
         // Set estimated propagation parameters
         estimatedPropagationParameters = new ParameterDriversList();
         final List<String> estimatedPropagationParametersNames = new ArrayList<>();
         for (final ParameterDriver driver : builder.getPropagationParametersDrivers().getDrivers()) {
 
             // Verify if the driver reference date has been set
             if (driver.getReferenceDate() == null) {
                 driver.setReferenceDate(currentDate);
             }
 
             // Verify if the driver is selected
             if (driver.isSelected()) {
                 estimatedPropagationParameters.add(driver);
                 // Add the driver name if it has not been added yet
                 for (Span<String> span = driver.getNamesSpanMap().getFirstSpan(); span != null; span = span.next()) {
 
                     if (!estimatedPropagationParametersNames.contains(span.getData())) {
                         estimatedPropagationParametersNames.add(span.getData());
                     }
                 }
             }
 
         }
         estimatedPropagationParametersNames.sort(Comparator.naturalOrder());
 
         // Populate the map of propagation drivers' columns and update the total number of columns
         propagationParameterColumns = new HashMap<>(estimatedPropagationParametersNames.size());
         for (final String driverName : estimatedPropagationParametersNames) {
             propagationParameterColumns.put(driverName, columns);
             ++columns;
         }
 
         // Set the estimated measurement parameters
         for (final ParameterDriver parameter : estimatedMeasurementsParameters.getDrivers()) {
             if (parameter.getReferenceDate() == null) {
                 parameter.setReferenceDate(currentDate);
             }
             for (Span<String> span = parameter.getNamesSpanMap().getFirstSpan(); span != null; span = span.next()) {
                 measurementParameterColumns.put(span.getData(), columns);
                 ++columns;
             }
         }
 
         // Compute the scale factors
         this.scale = new double[columns];
         int index = 0;
         for (final ParameterDriver driver : estimatedOrbitalParameters.getDrivers()) {
             scale[index++] = driver.getScale();
         }
         for (final ParameterDriver driver : estimatedPropagationParameters.getDrivers()) {
             for (Span<String> span = driver.getNamesSpanMap().getFirstSpan(); span != null; span = span.next()) {
                 scale[index++] = driver.getScale();
             }
         }
         for (final ParameterDriver driver : estimatedMeasurementsParameters.getDrivers()) {
             for (Span<String> span = driver.getNamesSpanMap().getFirstSpan(); span != null; span = span.next()) {
                 scale[index++] = driver.getScale();
             }
         }
 
         // Build the reference propagator and add its partial derivatives equations implementation
         updateReferenceTrajectory(getEstimatedPropagator());
         this.nominalMeanSpacecraftState = dsstPropagator.getInitialState();
         this.previousNominalMeanSpacecraftState = nominalMeanSpacecraftState;
 
         // Initialize "field" short periodic terms
         harvester.initializeFieldShortPeriodTerms(nominalMeanSpacecraftState);
 
         // Initialize the estimated normalized mean element filter correction (See Ref [1], Eq. 3.2a)
         this.predictedFilterCorrection = MatrixUtils.createRealVector(columns);
         this.correctedFilterCorrection = predictedFilterCorrection;
 
         // Initialize propagation parameters part of the state transition matrix (See Ref [1], Eq. 3.2c)
         this.psiS = null;
         if (estimatedPropagationParameters.getNbParams() != 0) {
             this.psiS = MatrixUtils.createRealMatrix(getNumberSelectedOrbitalDriversValuesToEstimate(),
                                                      getNumberSelectedPropagationDriversValuesToEstimate());
         }
 
         // Initialize inverse of the orbital part of the state transition matrix (See Ref [1], Eq. 3.2d)
         this.phiS = MatrixUtils.createRealIdentityMatrix(getNumberSelectedOrbitalDriversValuesToEstimate());
 
         // Number of estimated measurement parameters
         final int nbMeas = getNumberSelectedMeasurementDriversValuesToEstimate();
 
         // Number of estimated dynamic parameters (orbital + propagation)
         final int nbDyn  = getNumberSelectedOrbitalDriversValuesToEstimate() + getNumberSelectedPropagationDriversValuesToEstimate();
 
         // Covariance matrix
         final RealMatrix noiseK = MatrixUtils.createRealMatrix(nbDyn + nbMeas, nbDyn + nbMeas);
         final RealMatrix noiseP = covarianceMatrixProvider.getInitialCovarianceMatrix(nominalMeanSpacecraftState);
         noiseK.setSubMatrix(noiseP.getData(), 0, 0);
         if (measurementProcessNoiseMatrix != null) {
             final RealMatrix noiseM = measurementProcessNoiseMatrix.getInitialCovarianceMatrix(nominalMeanSpacecraftState);
             noiseK.setSubMatrix(noiseM.getData(), nbDyn, nbDyn);
         }
 
         // Verify dimension
         KalmanEstimatorUtil.checkDimension(noiseK.getRowDimension(),
                                            builder.getOrbitalParametersDrivers(),
                                            builder.getPropagationParametersDrivers(),
                                            estimatedMeasurementsParameters);
 
         final RealMatrix correctedCovariance = KalmanEstimatorUtil.normalizeCovarianceMatrix(noiseK, scale);
 
         // Initialize corrected estimate
         this.correctedEstimate = new ProcessEstimate(0.0, correctedFilterCorrection, correctedCovariance);
 
     }
 
     /** {@inheritDoc} */
     @Override
     public KalmanObserver getObserver() {
         return observer;
     }
 
     /** Set the observer.
      * @param observer the observer
      */
     public void setObserver(final KalmanObserver observer) {
         this.observer = observer;
     }
 
     /** Get the current corrected estimate.
      * @return current corrected estimate
      */
     public ProcessEstimate getEstimate() {
         return correctedEstimate;
     }
 
     /** Process a single measurement.
      * <p>
      * Update the filter with the new measurements.
      * </p>
      * @param observedMeasurements the list of measurements to process
      * @param filter Extended Kalman Filter
      * @return estimated propagator
      */
     public DSSTPropagator processMeasurements(final List<ObservedMeasurement<?>> observedMeasurements,
                                               final ExtendedKalmanFilter<MeasurementDecorator> filter) {
         try {
 
             // Sort the measurement
             observedMeasurements.sort(new ChronologicalComparator());
             final AbsoluteDate tStart             = observedMeasurements.get(0).getDate();
             final AbsoluteDate tEnd               = observedMeasurements.get(observedMeasurements.size() - 1).getDate();
             final double       overshootTimeRange = FastMath.nextAfter(tEnd.durationFrom(tStart),
                                                     Double.POSITIVE_INFINITY);
 
             // Initialize step handler and set it to the propagator
             final SemiAnalyticalMeasurementHandler stepHandler = new SemiAnalyticalMeasurementHandler(this, filter, observedMeasurements, builder.getInitialOrbitDate());
             dsstPropagator.getMultiplexer().add(stepHandler);
             dsstPropagator.propagate(tStart, tStart.shiftedBy(overshootTimeRange));
 
             // Return the last estimated propagator
             return getEstimatedPropagator();
 
         } catch (MathRuntimeException mrte) {
             throw new OrekitException(mrte);
         }
     }
 
     /** Get the propagator estimated with the values set in the propagator builder.
      * @return propagator based on the current values in the builder
      */
     public DSSTPropagator getEstimatedPropagator() {
         // Return propagator built with current instantiation of the propagator builder
         return (DSSTPropagator) builder.buildPropagator();
     }
 
     /** {@inheritDoc} */
     @Override
     public NonLinearEvolution getEvolution(final double previousTime, final RealVector previousState,
                                            final MeasurementDecorator measurement) {
 
         // Set a reference date for all measurements parameters that lack one (including the not estimated ones)
         final ObservedMeasurement<?> observedMeasurement = measurement.getObservedMeasurement();
         for (final ParameterDriver driver : observedMeasurement.getParametersDrivers()) {
             if (driver.getReferenceDate() == null) {
                 driver.setReferenceDate(builder.getInitialOrbitDate());
             }
         }
 
         // Increment measurement number
         ++currentMeasurementNumber;
 
         // Update the current date
         currentDate = measurement.getObservedMeasurement().getDate();
 
         // Normalized state transition matrix
         final RealMatrix stm = getErrorStateTransitionMatrix();
 
         // Predict filter correction
         predictedFilterCorrection = predictFilterCorrection(stm);
 
         // Short period term derivatives
         analyticalDerivativeComputations(nominalMeanSpacecraftState);
 
         // Calculate the predicted osculating elements
         final double[] osculating = computeOsculatingElements(predictedFilterCorrection);
         final Orbit osculatingOrbit = OrbitType.EQUINOCTIAL.mapArrayToOrbit(osculating, null, builder.getPositionAngleType(),
                                                                             currentDate, nominalMeanSpacecraftState.getMu(),
                                                                             nominalMeanSpacecraftState.getFrame());
 
         // Compute the predicted measurements  (See Ref [1], Eq. 3.8)
         predictedMeasurement = observedMeasurement.estimate(currentMeasurementNumber,
                                                             currentMeasurementNumber,
                                                             new SpacecraftState[] {
                                                                 new SpacecraftState(osculatingOrbit,
                                                                                     nominalMeanSpacecraftState.getAttitude(),
                                                                                     nominalMeanSpacecraftState.getMass(),
                                                                                     nominalMeanSpacecraftState.getAdditionalStatesValues(),
                                                                                     nominalMeanSpacecraftState.getAdditionalStatesDerivatives())
                                                             });
 
         // Normalized measurement matrix
         final RealMatrix measurementMatrix = getMeasurementMatrix();
 
         // Number of estimated measurement parameters
         final int nbMeas = getNumberSelectedMeasurementDriversValuesToEstimate();
 
         // Number of estimated dynamic parameters (orbital + propagation)
         final int nbDyn  = getNumberSelectedOrbitalDriversValuesToEstimate() + getNumberSelectedPropagationDriversValuesToEstimate();
 
         // Covariance matrix
         final RealMatrix noiseK = MatrixUtils.createRealMatrix(nbDyn + nbMeas, nbDyn + nbMeas);
         final RealMatrix noiseP = covarianceMatrixProvider.getProcessNoiseMatrix(previousNominalMeanSpacecraftState, nominalMeanSpacecraftState);
         noiseK.setSubMatrix(noiseP.getData(), 0, 0);
         if (measurementProcessNoiseMatrix != null) {
             final RealMatrix noiseM = measurementProcessNoiseMatrix.getProcessNoiseMatrix(previousNominalMeanSpacecraftState, nominalMeanSpacecraftState);
             noiseK.setSubMatrix(noiseM.getData(), nbDyn, nbDyn);
         }
 
         // Verify dimension
         KalmanEstimatorUtil.checkDimension(noiseK.getRowDimension(),
                                            builder.getOrbitalParametersDrivers(),
                                            builder.getPropagationParametersDrivers(),
                                            estimatedMeasurementsParameters);
 
         final RealMatrix normalizedProcessNoise = KalmanEstimatorUtil.normalizeCovarianceMatrix(noiseK, scale);
 
         // Return
         return new NonLinearEvolution(measurement.getTime(), predictedFilterCorrection, stm,
                                       normalizedProcessNoise, measurementMatrix);
     }
 
     /** {@inheritDoc} */
     @Override
     public RealVector getInnovation(final MeasurementDecorator measurement, final NonLinearEvolution evolution,
                                     final RealMatrix innovationCovarianceMatrix) {
 
         // Apply the dynamic outlier filter, if it exists
         KalmanEstimatorUtil.applyDynamicOutlierFilter(predictedMeasurement, innovationCovarianceMatrix);
         // Compute the innovation vector
         return KalmanEstimatorUtil.computeInnovationVector(predictedMeasurement, predictedMeasurement.getObservedMeasurement().getTheoreticalStandardDeviation());
     }
 
     /** {@inheritDoc} */
     @Override
     public void finalizeEstimation(final ObservedMeasurement<?> observedMeasurement,
                                    final ProcessEstimate estimate) {
         // Update the process estimate
         correctedEstimate = estimate;
         // Corrected filter correction
         correctedFilterCorrection = estimate.getState();
         // Update the previous nominal mean spacecraft state
         previousNominalMeanSpacecraftState = nominalMeanSpacecraftState;
         // Calculate the corrected osculating elements
         final double[] osculating = computeOsculatingElements(correctedFilterCorrection);
         final Orbit osculatingOrbit = OrbitType.EQUINOCTIAL.mapArrayToOrbit(osculating, null, builder.getPositionAngleType(),
                                                                             currentDate, nominalMeanSpacecraftState.getMu(),
                                                                             nominalMeanSpacecraftState.getFrame());
 
         // Compute the corrected measurements
         correctedMeasurement = observedMeasurement.estimate(currentMeasurementNumber,
                                                             currentMeasurementNumber,
                                                             new SpacecraftState[] {
                                                                 new SpacecraftState(osculatingOrbit,
                                                                                     nominalMeanSpacecraftState.getAttitude(),
                                                                                     nominalMeanSpacecraftState.getMass(),
                                                                                     nominalMeanSpacecraftState.getAdditionalStatesValues(),
                                                                                     nominalMeanSpacecraftState.getAdditionalStatesDerivatives())
                                                             });
         // Call the observer if the user add one
         if (observer != null) {
             observer.evaluationPerformed(this);
         }
     }
 
     /** {@inheritDoc} */
     @Override
     public void finalizeOperationsObservationGrid() {
         // Update parameters
         updateParameters();
     }
 
     /** {@inheritDoc} */
     @Override
     public ParameterDriversList getEstimatedOrbitalParameters() {
         return estimatedOrbitalParameters;
     }
 
     /** {@inheritDoc} */
     @Override
     public ParameterDriversList getEstimatedPropagationParameters() {
         return estimatedPropagationParameters;
     }
 
     /** {@inheritDoc} */
     @Override
     public ParameterDriversList getEstimatedMeasurementsParameters() {
         return estimatedMeasurementsParameters;
     }
 
     /** {@inheritDoc} */
     @Override
     public SpacecraftState[] getPredictedSpacecraftStates() {
         return new SpacecraftState[] {nominalMeanSpacecraftState};
     }
 
     /** {@inheritDoc} */
     @Override
     public SpacecraftState[] getCorrectedSpacecraftStates() {
         return new SpacecraftState[] {getEstimatedPropagator().getInitialState()};
     }
 
     /** {@inheritDoc} */
     @Override
     public RealVector getPhysicalEstimatedState() {
         // Method {@link ParameterDriver#getValue()} is used to get
         // the physical values of the state.
         // The scales'array is used to get the size of the state vector
         final RealVector physicalEstimatedState = new ArrayRealVector(scale.length);
         int i = 0;
         for (final DelegatingDriver driver : getEstimatedOrbitalParameters().getDrivers()) {
             for (Span<Double> span = driver.getValueSpanMap().getFirstSpan(); span != null; span = span.next()) {
                 physicalEstimatedState.setEntry(i++, span.getData());
             }
         }
         for (final DelegatingDriver driver : getEstimatedPropagationParameters().getDrivers()) {
             for (Span<Double> span = driver.getValueSpanMap().getFirstSpan(); span != null; span = span.next()) {
                 physicalEstimatedState.setEntry(i++, span.getData());
             }
         }
         for (final DelegatingDriver driver : getEstimatedMeasurementsParameters().getDrivers()) {
             for (Span<Double> span = driver.getValueSpanMap().getFirstSpan(); span != null; span = span.next()) {
                 physicalEstimatedState.setEntry(i++, span.getData());
             }
         }
 
         return physicalEstimatedState;
     }
 
     /** {@inheritDoc} */
     @Override
     public RealMatrix getPhysicalEstimatedCovarianceMatrix() {
         // Un-normalize the estimated covariance matrix (P) from Hipparchus and return it.
         // The covariance P is an mxm matrix where m = nbOrb + nbPropag + nbMeas
         // For each element [i,j] of P the corresponding normalized value is:
         // Pn[i,j] = P[i,j] / (scale[i]*scale[j])
         // Consequently: P[i,j] = Pn[i,j] * scale[i] * scale[j]
         return KalmanEstimatorUtil.unnormalizeCovarianceMatrix(correctedEstimate.getCovariance(), scale);
     }
 
     /** {@inheritDoc} */
     @Override
     public RealMatrix getPhysicalStateTransitionMatrix() {
         //  Un-normalize the state transition matrix (φ) from Hipparchus and return it.
         // φ is an mxm matrix where m = nbOrb + nbPropag + nbMeas
         // For each element [i,j] of normalized φ (φn), the corresponding physical value is:
         // φ[i,j] = φn[i,j] * scale[i] / scale[j]
         return correctedEstimate.getStateTransitionMatrix() == null ?
                 null : KalmanEstimatorUtil.unnormalizeStateTransitionMatrix(correctedEstimate.getStateTransitionMatrix(), scale);
     }
 
     /** {@inheritDoc} */
     @Override
     public RealMatrix getPhysicalMeasurementJacobian() {
         // Un-normalize the measurement matrix (H) from Hipparchus and return it.
         // H is an nxm matrix where:
         //  - m = nbOrb + nbPropag + nbMeas is the number of estimated parameters
         //  - n is the size of the measurement being processed by the filter
         // For each element [i,j] of normalized H (Hn) the corresponding physical value is:
         // H[i,j] = Hn[i,j] * σ[i] / scale[j]
         return correctedEstimate.getMeasurementJacobian() == null ?
                 null : KalmanEstimatorUtil.unnormalizeMeasurementJacobian(correctedEstimate.getMeasurementJacobian(),
                                                                           scale,
                                                                           correctedMeasurement.getObservedMeasurement().getTheoreticalStandardDeviation());
     }
 
     /** {@inheritDoc} */
     @Override
     public RealMatrix getPhysicalInnovationCovarianceMatrix() {
         // Un-normalize the innovation covariance matrix (S) from Hipparchus and return it.
         // S is an nxn matrix where n is the size of the measurement being processed by the filter
         // For each element [i,j] of normalized S (Sn) the corresponding physical value is:
         // S[i,j] = Sn[i,j] * σ[i] * σ[j]
         return correctedEstimate.getInnovationCovariance() == null ?
                 null : KalmanEstimatorUtil.unnormalizeInnovationCovarianceMatrix(correctedEstimate.getInnovationCovariance(),
                                                                                  predictedMeasurement.getObservedMeasurement().getTheoreticalStandardDeviation());
     }
 
     /** {@inheritDoc} */
     @Override
     public RealMatrix getPhysicalKalmanGain() {
         // Un-normalize the Kalman gain (K) from Hipparchus and return it.
         // K is an mxn matrix where:
         //  - m = nbOrb + nbPropag + nbMeas is the number of estimated parameters
         //  - n is the size of the measurement being processed by the filter
         // For each element [i,j] of normalized K (Kn) the corresponding physical value is:
         // K[i,j] = Kn[i,j] * scale[i] / σ[j]
         return correctedEstimate.getKalmanGain() == null ?
                 null : KalmanEstimatorUtil.unnormalizeKalmanGainMatrix(correctedEstimate.getKalmanGain(),
                                                                        scale,
                                                                        correctedMeasurement.getObservedMeasurement().getTheoreticalStandardDeviation());
     }
 
     /** {@inheritDoc} */
     @Override
     public int getCurrentMeasurementNumber() {
         return currentMeasurementNumber;
     }
 
     /** {@inheritDoc} */
     @Override
     public AbsoluteDate getCurrentDate() {
         return currentDate;
     }
 
     /** {@inheritDoc} */
     @Override
     public EstimatedMeasurement<?> getPredictedMeasurement() {
         return predictedMeasurement;
     }
 
     /** {@inheritDoc} */
     @Override
     public EstimatedMeasurement<?> getCorrectedMeasurement() {
         return correctedMeasurement;
     }
 
     /** {@inheritDoc} */
     @Override
     public void updateNominalSpacecraftState(final SpacecraftState nominal) {
         this.nominalMeanSpacecraftState = nominal;
         // Update the builder with the nominal mean elements orbit
         builder.resetOrbit(nominal.getOrbit(), PropagationType.MEAN);
     }
 
     /** Update the reference trajectories using the propagator as input.
      * @param propagator The new propagator to use
      */
     public void updateReferenceTrajectory(final DSSTPropagator propagator) {
 
         dsstPropagator = propagator;
 
         // Equation name
         final String equationName = SemiAnalyticalKalmanEstimator.class.getName() + "-derivatives-";
 
         // Mean state
         final SpacecraftState meanState = dsstPropagator.initialIsOsculating() ?
                        DSSTPropagator.computeMeanState(dsstPropagator.getInitialState(), dsstPropagator.getAttitudeProvider(), dsstPropagator.getAllForceModels()) :
                        dsstPropagator.getInitialState();
 
         // Update the jacobian harvester
         dsstPropagator.setInitialState(meanState, PropagationType.MEAN);
         harvester = dsstPropagator.setupMatricesComputation(equationName, null, null);
 
     }
 
     /** {@inheritDoc} */
     @Override
     public void updateShortPeriods(final SpacecraftState state) {
         // Loop on DSST force models
         for (final DSSTForceModel model : builder.getAllForceModels()) {
             model.updateShortPeriodTerms(model.getParametersAllValues(), state);
         }
         harvester.updateFieldShortPeriodTerms(state);
     }
 
     /** {@inheritDoc} */
     @Override
     public void initializeShortPeriodicTerms(final SpacecraftState meanState) {
         final List<ShortPeriodTerms> shortPeriodTerms = new ArrayList<>();
         // initialize ForceModels in OSCULATING mode even if propagation is MEAN
         final PropagationType type = PropagationType.OSCULATING;
         for (final DSSTForceModel force :  builder.getAllForceModels()) {
             shortPeriodTerms.addAll(force.initializeShortPeriodTerms(new AuxiliaryElements(meanState.getOrbit(), 1), type, force.getParameters(meanState.getDate())));
         }
         dsstPropagator.setShortPeriodTerms(shortPeriodTerms);
         // also need to initialize the Field terms in the same mode
         harvester.initializeFieldShortPeriodTerms(meanState, type);
     }
 
     /** Get the normalized state transition matrix (STM) from previous point to current point.
      * The STM contains the partial derivatives of current state with respect to previous state.
      * The  STM is an mxm matrix where m is the size of the state vector.
      * m = nbOrb + nbPropag + nbMeas
      * @return the normalized error state transition matrix
      */
     private RealMatrix getErrorStateTransitionMatrix() {
 
         /* The state transition matrix is obtained as follows, with:
          *  - Phi(k, k-1) : Transitional orbital matrix
          *  - Psi(k, k-1) : Transitional propagation parameters matrix
          *
          *       |             |             |   .    |
          *       | Phi(k, k-1) | Psi(k, k-1) | ..0..  |
          *       |             |             |   .    |
          *       |-------------|-------------|--------|
          *       |      .      |    1 0 0    |   .    |
          * STM = |    ..0..    |    0 1 0    | ..0..  |
          *       |      .      |    0 0 1    |   .    |
          *       |-------------|-------------|--------|
          *       |      .      |      .      | 1 0 0..|
          *       |    ..0..    |    ..0..    | 0 1 0..|
          *       |      .      |      .      | 0 0 1..|
          */
 
         // Initialize to the proper size identity matrix
         final RealMatrix stm = MatrixUtils.createRealIdentityMatrix(correctedEstimate.getState().getDimension());
 
         // Derivatives of the state vector with respect to initial state vector
         final int nbOrb = getNumberSelectedOrbitalDriversValuesToEstimate();
         final RealMatrix dYdY0 = harvester.getB2(nominalMeanSpacecraftState);
 
         // Calculate transitional orbital matrix (See Ref [1], Eq. 3.4a)
         final RealMatrix phi = dYdY0.multiply(phiS);
 
         // Fill the state transition matrix with the orbital drivers
         final List<DelegatingDriver> drivers = builder.getOrbitalParametersDrivers().getDrivers();
         for (int i = 0; i < nbOrb; ++i) {
             if (drivers.get(i).isSelected()) {
                 int jOrb = 0;
                 for (int j = 0; j < nbOrb; ++j) {
                     if (drivers.get(j).isSelected()) {
                         stm.setEntry(i, jOrb++, phi.getEntry(i, j));
                     }
                 }
             }
         }
 
         // Update PhiS
         phiS = new QRDecomposition(dYdY0).getSolver().getInverse();
 
         // Derivatives of the state vector with respect to propagation parameters
         if (psiS != null) {
 
             final int nbProp = getNumberSelectedPropagationDriversValuesToEstimate();
             final RealMatrix dYdPp = harvester.getB3(nominalMeanSpacecraftState);
 
             // Calculate transitional parameters matrix (See Ref [1], Eq. 3.4b)
             final RealMatrix psi = dYdPp.subtract(phi.multiply(psiS));
 
             // Fill 1st row, 2nd column (dY/dPp)
             for (int i = 0; i < nbOrb; ++i) {
                 for (int j = 0; j < nbProp; ++j) {
                     stm.setEntry(i, j + nbOrb, psi.getEntry(i, j));
                 }
             }
 
             // Update PsiS
             psiS = dYdPp;
 
         }
 
         // Normalization of the STM
         // normalized(STM)ij = STMij*Sj/Si
         for (int i = 0; i < scale.length; i++) {
             for (int j = 0; j < scale.length; j++ ) {
                 stm.setEntry(i, j, stm.getEntry(i, j) * scale[j] / scale[i]);
             }
         }
 
         // Return the error state transition matrix
         return stm;
 
     }
 
     /** Get the normalized measurement matrix H.
      * H contains the partial derivatives of the measurement with respect to the state.
      * H is an nxm matrix where n is the size of the measurement vector and m the size of the state vector.
      * @return the normalized measurement matrix H
      */
     private RealMatrix getMeasurementMatrix() {
 
         // Observed measurement characteristics
         final SpacecraftState        evaluationState     = predictedMeasurement.getStates()[0];
         final ObservedMeasurement<?> observedMeasurement = predictedMeasurement.getObservedMeasurement();
         final double[] sigma  = predictedMeasurement.getObservedMeasurement().getTheoreticalStandardDeviation();
 
         // Initialize measurement matrix H: nxm
         // n: Number of measurements in current measurement
         // m: State vector size
         final RealMatrix measurementMatrix = MatrixUtils.
                 createRealMatrix(observedMeasurement.getDimension(),
                                  correctedEstimate.getState().getDimension());
 
         // Predicted orbit
         final Orbit predictedOrbit = evaluationState.getOrbit();
 
         // Measurement matrix's columns related to orbital and propagation parameters
         // ----------------------------------------------------------
 
         // Partial derivatives of the current Cartesian coordinates with respect to current orbital state
         final int nbOrb  = getNumberSelectedOrbitalDrivers();
         final int nbProp = getNumberSelectedPropagationDrivers();
         final double[][] aCY = new double[nbOrb][nbOrb];
         predictedOrbit.getJacobianWrtParameters(builder.getPositionAngleType(), aCY);
         final RealMatrix dCdY = new Array2DRowRealMatrix(aCY, false);
 
         // Jacobian of the measurement with respect to current Cartesian coordinates
         final RealMatrix dMdC = new Array2DRowRealMatrix(predictedMeasurement.getStateDerivatives(0), false);
 
         // Jacobian of the measurement with respect to current orbital state
         RealMatrix dMdY = dMdC.multiply(dCdY);
 
         // Compute factor dShortPeriod_dMeanState = I+B1 | B4
         final RealMatrix IpB1B4 = MatrixUtils.createRealMatrix(nbOrb, nbOrb + nbProp);
 
         // B1
         final RealMatrix B1 = harvester.getB1();
 
         // I + B1
         final RealMatrix I = MatrixUtils.createRealIdentityMatrix(nbOrb);
         final RealMatrix IpB1 = I.add(B1);
         IpB1B4.setSubMatrix(IpB1.getData(), 0, 0);
 
         // If there are not propagation parameters, B4 is null
         if (psiS != null) {
             final RealMatrix B4 = harvester.getB4();
             IpB1B4.setSubMatrix(B4.getData(), 0, nbOrb);
         }
 
         // Ref [1], Eq. 3.10
         dMdY = dMdY.multiply(IpB1B4);
 
         for (int i = 0; i < dMdY.getRowDimension(); i++) {
             for (int j = 0; j < nbOrb; j++) {
                 final double driverScale = builder.getOrbitalParametersDrivers().getDrivers().get(j).getScale();
                 measurementMatrix.setEntry(i, j, dMdY.getEntry(i, j) / sigma[i] * driverScale);
             }
 
             int col = 0;
             for (int j = 0; j < nbProp; j++) {
                 final double driverScale = estimatedPropagationParameters.getDrivers().get(j).getScale();
                 for (Span<Double> span = estimatedPropagationParameters.getDrivers().get(j).getValueSpanMap().getFirstSpan();
                                   span != null; span = span.next()) {
 
                     measurementMatrix.setEntry(i, col + nbOrb,
                                                dMdY.getEntry(i, col + nbOrb) / sigma[i] * driverScale);
                     col++;
                 }
             }
         }
 
         // Normalized measurement matrix's columns related to measurement parameters
         // --------------------------------------------------------------
 
         // Jacobian of the measurement with respect to measurement parameters
         // Gather the measurement parameters linked to current measurement
         for (final ParameterDriver driver : observedMeasurement.getParametersDrivers()) {
             if (driver.isSelected()) {
                 for (Span<String> span = driver.getNamesSpanMap().getFirstSpan(); span != null; span = span.next()) {
                     // Derivatives of current measurement w/r to selected measurement parameter
                     final double[] aMPm = predictedMeasurement.getParameterDerivatives(driver, span.getStart());
 
                     // Check that the measurement parameter is managed by the filter
                     if (measurementParameterColumns.get(span.getData()) != null) {
                         // Column of the driver in the measurement matrix
                         final int driverColumn = measurementParameterColumns.get(span.getData());
 
                         // Fill the corresponding indexes of the measurement matrix
                         for (int i = 0; i < aMPm.length; ++i) {
                             measurementMatrix.setEntry(i, driverColumn, aMPm[i] / sigma[i] * driver.getScale());
                         }
                     }
                 }
             }
         }
 
         return measurementMatrix;
     }
 
     /** Predict the filter correction for the new observation.
      * @param stm normalized state transition matrix
      * @return the predicted filter correction for the new observation
      */
     private RealVector predictFilterCorrection(final RealMatrix stm) {
         // Ref [1], Eq. 3.5a and 3.5b
         return stm.operate(correctedFilterCorrection);
     }
 
     /** Compute the predicted osculating elements.
      * @param filterCorrection kalman filter correction
      * @return the predicted osculating element
      */
     private double[] computeOsculatingElements(final RealVector filterCorrection) {
 
         // Number of estimated orbital parameters
         final int nbOrb = getNumberSelectedOrbitalDrivers();
 
         // B1
         final RealMatrix B1 = harvester.getB1();
 
         // Short periodic terms
         final double[] shortPeriodTerms = dsstPropagator.getShortPeriodTermsValue(nominalMeanSpacecraftState);
 
         // Physical filter correction
         final RealVector physicalFilterCorrection = MatrixUtils.createRealVector(nbOrb);
         for (int index = 0; index < nbOrb; index++) {
             physicalFilterCorrection.addToEntry(index, filterCorrection.getEntry(index) * scale[index]);
         }
 
         // B1 * physicalCorrection
         final RealVector B1Correction = B1.operate(physicalFilterCorrection);
 
         // Nominal mean elements
         final double[] nominalMeanElements = new double[nbOrb];
         OrbitType.EQUINOCTIAL.mapOrbitToArray(nominalMeanSpacecraftState.getOrbit(), builder.getPositionAngleType(), nominalMeanElements, null);
 
         // Ref [1] Eq. 3.6
         final double[] osculatingElements = new double[nbOrb];
         for (int i = 0; i < nbOrb; i++) {
             osculatingElements[i] = nominalMeanElements[i] +
                                     physicalFilterCorrection.getEntry(i) +
                                     shortPeriodTerms[i] +
                                     B1Correction.getEntry(i);
         }
 
         // Return
         return osculatingElements;
 
     }
 
     /** Analytical computation of derivatives.
      * This method allow to compute analytical derivatives.
      * @param state mean state used to calculate short period perturbations
      */
     private void analyticalDerivativeComputations(final SpacecraftState state) {
         harvester.setReferenceState(state);
     }
 
     /** Get the number of estimated orbital parameters.
      * @return the number of estimated orbital parameters
      */
     private int getNumberSelectedOrbitalDrivers() {
         return estimatedOrbitalParameters.getNbParams();
     }
 
     /** Get the number of estimated propagation parameters.
      * @return the number of estimated propagation parameters
      */
     private int getNumberSelectedPropagationDrivers() {
         return estimatedPropagationParameters.getNbParams();
     }
 
     /** Get the number of estimated orbital parameters values (some parameter
      * driver may have several values to estimate for different time range
      * {@link ParameterDriver}.
      * @return the number of estimated values for , orbital parameters
      */
     private int getNumberSelectedOrbitalDriversValuesToEstimate() {
         int nbOrbitalValuesToEstimate = 0;
         for (final ParameterDriver driver : estimatedOrbitalParameters.getDrivers()) {
             nbOrbitalValuesToEstimate += driver.getNbOfValues();
         }
         return nbOrbitalValuesToEstimate;
     }
 
     /** Get the number of estimated propagation parameters values (some parameter
      * driver may have several values to estimate for different time range
      * {@link ParameterDriver}.
      * @return the number of estimated values for propagation parameters
      */
     private int getNumberSelectedPropagationDriversValuesToEstimate() {
         int nbPropagationValuesToEstimate = 0;
         for (final ParameterDriver driver : estimatedPropagationParameters.getDrivers()) {
             nbPropagationValuesToEstimate += driver.getNbOfValues();
         }
         return nbPropagationValuesToEstimate;
     }
 
     /** Get the number of estimated measurement parameters values (some parameter
      * driver may have several values to estimate for different time range
      * {@link ParameterDriver}.
      * @return the number of estimated values for measurement parameters
      */
     private int getNumberSelectedMeasurementDriversValuesToEstimate() {
         int nbMeasurementValuesToEstimate = 0;
         for (final ParameterDriver driver : estimatedMeasurementsParameters.getDrivers()) {
             nbMeasurementValuesToEstimate += driver.getNbOfValues();
         }
         return nbMeasurementValuesToEstimate;
     }
 
     /** Update the estimated parameters after the correction phase of the filter.
      * The min/max allowed values are handled by the parameter themselves.
      */
     private void updateParameters() {
         final RealVector correctedState = correctedEstimate.getState();
         int i = 0;
         // Orbital parameters
         for (final DelegatingDriver driver : getEstimatedOrbitalParameters().getDrivers()) {
             // let the parameter handle min/max clipping
             for (Span<Double> span = driver.getValueSpanMap().getFirstSpan(); span != null; span = span.next()) {
                 driver.setNormalizedValue(driver.getNormalizedValue(span.getStart()) + correctedState.getEntry(i++), span.getStart());
             }
         }
 
         // Propagation parameters
         for (final DelegatingDriver driver : getEstimatedPropagationParameters().getDrivers()) {
             // let the parameter handle min/max clipping
             // If the parameter driver contains only 1 value to estimate over the all time range
             for (Span<Double> span = driver.getValueSpanMap().getFirstSpan(); span != null; span = span.next()) {
                 driver.setNormalizedValue(driver.getNormalizedValue(span.getStart()) + correctedState.getEntry(i++), span.getStart());
             }
         }
 
         // Measurements parameters
         for (final DelegatingDriver driver : getEstimatedMeasurementsParameters().getDrivers()) {
             // let the parameter handle min/max clipping
             for (Span<Double> span = driver.getValueSpanMap().getFirstSpan(); span != null; span = span.next()) {
                 driver.setNormalizedValue(driver.getNormalizedValue(span.getStart()) + correctedState.getEntry(i++), span.getStart());
             }
         }
     }
 
 }