Examples with AbsoluteDate org.orekit.time.AbsoluteDate used on opensource projects

Example 71 with AbsoluteDate

use of org.orekit.time.AbsoluteDate in project Orekit by CS-SI.

the class PVTest method testPVWithCovarianceMatrix.

/**
 * Test the PV constructor with one 6x6 covariance matrix as input.
 * @throws OrekitException
 */
@Test
public void testPVWithCovarianceMatrix() throws OrekitException {
    // Context
    Context context = EstimationTestUtils.eccentricContext("regular-data:potential:tides");
    // Dummy P, V, T
    final Vector3D position = context.initialOrbit.getPVCoordinates().getPosition();
    final Vector3D velocity = context.initialOrbit.getPVCoordinates().getVelocity();
    final AbsoluteDate date = context.initialOrbit.getDate();
    // Initialize standard deviations, weight and corr coeff
    final double[] sigmaPV = { 10., 20., 30., 0.1, 0.2, 0.3 };
    final double baseWeight = 0.5;
    final double[][] corrCoefRef = new double[6][6];
    for (int i = 0; i < 6; i++) {
        for (int j = 0; j < 6; j++) {
            if (i == j) {
                corrCoefRef[i][i] = 1.;
            } else {
                corrCoefRef[i][j] = i + j + 1;
            }
        }
    }
    // Reference covariance matrix
    final double[][] Pref = new double[6][6];
    for (int i = 0; i < 6; i++) {
        for (int j = 0; j < 6; j++) {
            Pref[i][j] = corrCoefRef[i][j] * sigmaPV[i] * sigmaPV[j];
        }
    }
    // Reference propagator numbers
    final int[] propNumRef = { 0, 2 };
    // Create PV measurements
    final PV[] pvs = new PV[2];
    pvs[0] = new PV(date, position, velocity, Pref, baseWeight);
    pvs[1] = new PV(date, position, velocity, Pref, baseWeight, propNumRef[1]);
    // Tolerance
    // tolerance
    final double eps = 1.8e-15;
    // Check data
    for (int k = 0; k < pvs.length; k++) {
        final PV pv = pvs[k];
        // Propagator numbers
        assertEquals(propNumRef[k], pv.getPropagatorsIndices().get(0), eps);
        // Weights
        for (int i = 0; i < 6; i++) {
            assertEquals(baseWeight, pv.getBaseWeight()[i], eps);
        }
        // Sigmas
        for (int i = 0; i < 6; i++) {
            assertEquals(sigmaPV[i], pv.getTheoreticalStandardDeviation()[i], eps);
        }
        // Covariances
        final double[][] P = pv.getCovarianceMatrix();
        // Substract with ref and get the norm
        final double normP = MatrixUtils.createRealMatrix(P).subtract(MatrixUtils.createRealMatrix(Pref)).getNorm();
        assertEquals(0., normP, eps);
        // Correlation coef
        final double[][] corrCoef = pv.getCorrelationCoefficientsMatrix();
        // Substract with ref and get the norm
        final double normCorrCoef = MatrixUtils.createRealMatrix(corrCoef).subtract(MatrixUtils.createRealMatrix(corrCoefRef)).getNorm();
        assertEquals(0., normCorrCoef, eps);
    }
}

Example 72 with AbsoluteDate

use of org.orekit.time.AbsoluteDate in project Orekit by CS-SI.

the class PVTest method testExceptions.

/**
 * Test exceptions raised if the covariance matrix does not have the proper size.
 */
@Test
public void testExceptions() throws OrekitException {
    // Context
    Context context = EstimationTestUtils.eccentricContext("regular-data:potential:tides");
    // Dummy P, V, T
    final Vector3D position = context.initialOrbit.getPVCoordinates().getPosition();
    final Vector3D velocity = context.initialOrbit.getPVCoordinates().getVelocity();
    final AbsoluteDate date = context.initialOrbit.getDate();
    final double weight = 1.;
    // Build with two 3-sized vectors
    try {
        new PV(date, position, velocity, new double[] { 0., 0., 0. }, new double[] { 1. }, weight);
        Assert.fail("An OrekitException should have been thrown");
    } catch (OrekitException e) {
    // An exception should indeed be raised here
    }
    // Build with one 6-sized vector
    try {
        new PV(date, position, velocity, new double[] { 0., 0., 0. }, weight);
        Assert.fail("An OrekitException should have been thrown");
    } catch (OrekitException e) {
    // An exception should indeed be raised here
    }
    // Build with two 3x3 matrices
    try {
        new PV(date, position, velocity, new double[][] { { 0., 0. }, { 0., 0. } }, new double[][] { { 0., 0. }, { 0., 0. } }, weight);
        Assert.fail("An OrekitException should have been thrown");
    } catch (OrekitException e) {
    // An exception should indeed be raised here
    }
    // Build with one 6x6 matrix
    try {
        new PV(date, position, velocity, new double[][] { { 0., 0. }, { 0., 0. } }, weight);
        Assert.fail("An OrekitException should have been thrown");
    } catch (OrekitException e) {
    // An exception should indeed be raised here
    }
}

Example 73 with AbsoluteDate

use of org.orekit.time.AbsoluteDate in project Orekit by CS-SI.

the class RangeAnalytic method theoreticalEvaluationAnalytic.

/**
 * Analytical version of the theoreticalEvaluation function in Range class
 * The derivative structures are not used, an analytical computation is used instead.
 * @param iteration current LS estimator iteration
 * @param evaluation current LS estimator evaluation
 * @param state spacecraft state. At measurement date on first iteration then close to emission date on further iterations
 * @param interpolator Orekit step interpolator
 * @return
 * @throws OrekitException
 */
protected EstimatedMeasurement<Range> theoreticalEvaluationAnalytic(final int iteration, final int evaluation, final SpacecraftState state) throws OrekitException {
    // Station attribute from parent Range class
    final GroundStation groundStation = this.getStation();
    // Station position at signal arrival
    final AbsoluteDate downlinkDate = getDate();
    final Transform topoToInertDownlink = groundStation.getOffsetToInertial(state.getFrame(), downlinkDate);
    final TimeStampedPVCoordinates stationDownlink = topoToInertDownlink.transformPVCoordinates(new TimeStampedPVCoordinates(downlinkDate, PVCoordinates.ZERO));
    // Take propagation time into account
    // (if state has already been set up to pre-compensate propagation delay,
    // we will have offset == downlinkDelay and transitState will be
    // the same as state)
    // Downlink time of flight
    final double tauD = signalTimeOfFlight(state.getPVCoordinates(), stationDownlink.getPosition(), downlinkDate);
    final double delta = downlinkDate.durationFrom(state.getDate());
    final double dt = delta - tauD;
    // Transit state position
    final SpacecraftState transitState = state.shiftedBy(dt);
    final AbsoluteDate transitDate = transitState.getDate();
    final Vector3D transitP = transitState.getPVCoordinates().getPosition();
    // Station position at transit state date
    final Transform topoToInertAtTransitDate = groundStation.getOffsetToInertial(state.getFrame(), transitDate);
    final TimeStampedPVCoordinates stationAtTransitDate = topoToInertAtTransitDate.transformPVCoordinates(new TimeStampedPVCoordinates(transitDate, PVCoordinates.ZERO));
    // Uplink time of flight
    final double tauU = signalTimeOfFlight(stationAtTransitDate, transitP, transitDate);
    final double tau = tauD + tauU;
    // Real date and position of station at signal departure
    final AbsoluteDate uplinkDate = downlinkDate.shiftedBy(-tau);
    final TimeStampedPVCoordinates stationUplink = topoToInertDownlink.shiftedBy(-tau).transformPVCoordinates(new TimeStampedPVCoordinates(uplinkDate, PVCoordinates.ZERO));
    // Prepare the evaluation
    final EstimatedMeasurement<Range> estimated = new EstimatedMeasurement<Range>(this, iteration, evaluation, new SpacecraftState[] { transitState }, new TimeStampedPVCoordinates[] { stationUplink, transitState.getPVCoordinates(), stationDownlink });
    // Set range value
    final double cOver2 = 0.5 * Constants.SPEED_OF_LIGHT;
    estimated.setEstimatedValue(tau * cOver2);
    // Partial derivatives with respect to state
    // The formulas below take into account the fact the measurement is at fixed reception date.
    // When spacecraft position is changed, the downlink delay is changed, and in order
    // to still have the measurement arrive at exactly the same date on ground, we must
    // take the spacecraft-station relative velocity into account.
    final Vector3D v = state.getPVCoordinates().getVelocity();
    final Vector3D qv = stationDownlink.getVelocity();
    final Vector3D downInert = stationDownlink.getPosition().subtract(transitP);
    final double dDown = Constants.SPEED_OF_LIGHT * Constants.SPEED_OF_LIGHT * tauD - Vector3D.dotProduct(downInert, v);
    final Vector3D upInert = transitP.subtract(stationUplink.getPosition());
    // test
    // final double   dUp       = Constants.SPEED_OF_LIGHT * Constants.SPEED_OF_LIGHT * tauU -
    // Vector3D.dotProduct(upInert, qv);
    // test
    final double dUp = Constants.SPEED_OF_LIGHT * Constants.SPEED_OF_LIGHT * tauU - Vector3D.dotProduct(upInert, stationUplink.getVelocity());
    // derivatives of the downlink time of flight
    final double dTauDdPx = -downInert.getX() / dDown;
    final double dTauDdPy = -downInert.getY() / dDown;
    final double dTauDdPz = -downInert.getZ() / dDown;
    // Derivatives of the uplink time of flight
    final double dTauUdPx = 1. / dUp * upInert.dotProduct(Vector3D.PLUS_I.add((qv.subtract(v)).scalarMultiply(dTauDdPx)));
    final double dTauUdPy = 1. / dUp * upInert.dotProduct(Vector3D.PLUS_J.add((qv.subtract(v)).scalarMultiply(dTauDdPy)));
    final double dTauUdPz = 1. / dUp * upInert.dotProduct(Vector3D.PLUS_K.add((qv.subtract(v)).scalarMultiply(dTauDdPz)));
    // derivatives of the range measurement
    final double dRdPx = (dTauDdPx + dTauUdPx) * cOver2;
    final double dRdPy = (dTauDdPy + dTauUdPy) * cOver2;
    final double dRdPz = (dTauDdPz + dTauUdPz) * cOver2;
    estimated.setStateDerivatives(0, new double[] { dRdPx, dRdPy, dRdPz, dRdPx * dt, dRdPy * dt, dRdPz * dt });
    if (groundStation.getEastOffsetDriver().isSelected() || groundStation.getNorthOffsetDriver().isSelected() || groundStation.getZenithOffsetDriver().isSelected()) {
        // Downlink tme of flight derivatives / station position in topocentric frame
        final AngularCoordinates ac = topoToInertDownlink.getAngular().revert();
        // final Rotation rotTopoToInert = ac.getRotation();
        final Vector3D omega = ac.getRotationRate();
        // Inertial frame
        final double dTauDdQIx = downInert.getX() / dDown;
        final double dTauDdQIy = downInert.getY() / dDown;
        final double dTauDdQIz = downInert.getZ() / dDown;
        // Uplink tme of flight derivatives / station position in topocentric frame
        // Inertial frame
        final double dTauUdQIx = 1 / dUp * upInert.dotProduct(Vector3D.MINUS_I.add((qv.subtract(v)).scalarMultiply(dTauDdQIx)).subtract(Vector3D.PLUS_I.crossProduct(omega).scalarMultiply(tau)));
        final double dTauUdQIy = 1 / dUp * upInert.dotProduct(Vector3D.MINUS_J.add((qv.subtract(v)).scalarMultiply(dTauDdQIy)).subtract(Vector3D.PLUS_J.crossProduct(omega).scalarMultiply(tau)));
        final double dTauUdQIz = 1 / dUp * upInert.dotProduct(Vector3D.MINUS_K.add((qv.subtract(v)).scalarMultiply(dTauDdQIz)).subtract(Vector3D.PLUS_K.crossProduct(omega).scalarMultiply(tau)));
        // Range partial derivatives
        // with respect to station position in inertial frame
        final Vector3D dRdQI = new Vector3D((dTauDdQIx + dTauUdQIx) * cOver2, (dTauDdQIy + dTauUdQIy) * cOver2, (dTauDdQIz + dTauUdQIz) * cOver2);
        // convert to topocentric frame, as the station position
        // offset parameter is expressed in this frame
        final Vector3D dRdQT = ac.getRotation().applyTo(dRdQI);
        if (groundStation.getEastOffsetDriver().isSelected()) {
            estimated.setParameterDerivatives(groundStation.getEastOffsetDriver(), dRdQT.getX());
        }
        if (groundStation.getNorthOffsetDriver().isSelected()) {
            estimated.setParameterDerivatives(groundStation.getNorthOffsetDriver(), dRdQT.getY());
        }
        if (groundStation.getZenithOffsetDriver().isSelected()) {
            estimated.setParameterDerivatives(groundStation.getZenithOffsetDriver(), dRdQT.getZ());
        }
    }
    return estimated;
}

Example 74 with AbsoluteDate

use of org.orekit.time.AbsoluteDate in project Orekit by CS-SI.

the class RangeAnalyticTest method genericTestStateDerivatives.

/**
 * Generic test function for derivatives with respect to state
 * @param isModifier Use of atmospheric modifiers
 * @param isFiniteDifferences Finite differences reference calculation if true, Range class otherwise
 * @param printResults Print the results ?
 * @throws OrekitException
 */
void genericTestStateDerivatives(final boolean isModifier, final boolean isFiniteDifferences, final boolean printResults, final double refErrorsPMedian, final double refErrorsPMean, final double refErrorsPMax, final double refErrorsVMedian, final double refErrorsVMean, final double refErrorsVMax) throws OrekitException {
    Context context = EstimationTestUtils.eccentricContext("regular-data:potential:tides");
    final NumericalPropagatorBuilder propagatorBuilder = context.createBuilder(OrbitType.KEPLERIAN, PositionAngle.TRUE, true, 1.0e-6, 60.0, 0.001);
    // Create perfect range measurements
    final Propagator propagator = EstimationTestUtils.createPropagator(context.initialOrbit, propagatorBuilder);
    final List<ObservedMeasurement<?>> measurements = EstimationTestUtils.createMeasurements(propagator, new RangeMeasurementCreator(context), 1.0, 3.0, 300.0);
    // Lists for results' storage - Used only for derivatives with respect to state
    // "final" value to be seen by "handleStep" function of the propagator
    final List<Double> errorsP = new ArrayList<Double>();
    final List<Double> errorsV = new ArrayList<Double>();
    // Set master mode
    // Use a lambda function to implement "handleStep" function
    propagator.setMasterMode((OrekitStepInterpolator interpolator, boolean isLast) -> {
        for (final ObservedMeasurement<?> measurement : measurements) {
            // Play test if the measurement date is between interpolator previous and current date
            if ((measurement.getDate().durationFrom(interpolator.getPreviousState().getDate()) > 0.) && (measurement.getDate().durationFrom(interpolator.getCurrentState().getDate()) <= 0.)) {
                // Add modifiers if test implies it
                final RangeTroposphericDelayModifier modifier = new RangeTroposphericDelayModifier(SaastamoinenModel.getStandardModel());
                if (isModifier) {
                    ((Range) measurement).addModifier(modifier);
                }
                // We intentionally propagate to a date which is close to the
                // real spacecraft state but is *not* the accurate date, by
                // compensating only part of the downlink delay. This is done
                // in order to validate the partial derivatives with respect
                // to velocity. If we had chosen the proper state date, the
                // range would have depended only on the current position but
                // not on the current velocity.
                final double meanDelay = measurement.getObservedValue()[0] / Constants.SPEED_OF_LIGHT;
                final AbsoluteDate date = measurement.getDate().shiftedBy(-0.75 * meanDelay);
                final SpacecraftState state = interpolator.getInterpolatedState(date);
                final EstimatedMeasurement<Range> range = new RangeAnalytic((Range) measurement).theoreticalEvaluationAnalytic(0, 0, state);
                if (isModifier) {
                    modifier.modify(range);
                }
                final double[][] jacobian = range.getStateDerivatives(0);
                // Jacobian reference value
                final double[][] jacobianRef;
                if (isFiniteDifferences) {
                    // Compute a reference value using finite differences
                    jacobianRef = Differentiation.differentiate(new StateFunction() {

                        public double[] value(final SpacecraftState state) throws OrekitException {
                            return measurement.estimate(0, 0, new SpacecraftState[] { state }).getEstimatedValue();
                        }
                    }, measurement.getDimension(), propagator.getAttitudeProvider(), OrbitType.CARTESIAN, PositionAngle.TRUE, 2.0, 3).value(state);
                } else {
                    // Compute a reference value using Range class function
                    jacobianRef = ((Range) measurement).theoreticalEvaluation(0, 0, new SpacecraftState[] { state }).getStateDerivatives(0);
                }
                // //Test: Test point by point with the debugger
                // if (!isFiniteDifferences && !isModifier) {
                // final EstimatedMeasurement<Range> test =
                // new RangeAnalytic((Range)measurement).theoreticalEvaluationValidation(0, 0, state);
                // }
                // //Test
                Assert.assertEquals(jacobianRef.length, jacobian.length);
                Assert.assertEquals(jacobianRef[0].length, jacobian[0].length);
                // Errors & relative errors on the jacobian
                double[][] dJacobian = new double[jacobian.length][jacobian[0].length];
                double[][] dJacobianRelative = new double[jacobian.length][jacobian[0].length];
                for (int i = 0; i < jacobian.length; ++i) {
                    for (int j = 0; j < jacobian[i].length; ++j) {
                        dJacobian[i][j] = jacobian[i][j] - jacobianRef[i][j];
                        dJacobianRelative[i][j] = FastMath.abs(dJacobian[i][j] / jacobianRef[i][j]);
                        if (j < 3) {
                            errorsP.add(dJacobianRelative[i][j]);
                        } else {
                            errorsV.add(dJacobianRelative[i][j]);
                        }
                    }
                }
                // Print values in console ?
                if (printResults) {
                    String stationName = ((Range) measurement).getStation().getBaseFrame().getName();
                    System.out.format(Locale.US, "%-15s  %-23s  %-23s  " + "%10.3e  %10.3e  %10.3e  " + "%10.3e  %10.3e  %10.3e  " + "%10.3e  %10.3e  %10.3e  " + "%10.3e  %10.3e  %10.3e%n", stationName, measurement.getDate(), date, dJacobian[0][0], dJacobian[0][1], dJacobian[0][2], dJacobian[0][3], dJacobian[0][4], dJacobian[0][5], dJacobianRelative[0][0], dJacobianRelative[0][1], dJacobianRelative[0][2], dJacobianRelative[0][3], dJacobianRelative[0][4], dJacobianRelative[0][5]);
                }
            }
        // End if measurement date between previous and current interpolator step
        }
    // End for loop on the measurements
    });
    // Print results on console ?
    if (printResults) {
        System.out.format(Locale.US, "%-15s  %-23s  %-23s  " + "%10s  %10s  %10s  " + "%10s  %10s  %10s  " + "%10s  %10s  %10s  " + "%10s  %10s  %10s%n", "Station", "Measurement Date", "State Date", "ΔdPx", "ΔdPy", "ΔdPz", "ΔdVx", "ΔdVy", "ΔdVz", "rel ΔdPx", "rel ΔdPy", "rel ΔdPz", "rel ΔdVx", "rel ΔdVy", "rel ΔdVz");
    }
    // Rewind the propagator to initial date
    propagator.propagate(context.initialOrbit.getDate());
    // Sort measurements chronologically
    measurements.sort(new ChronologicalComparator());
    // Propagate to final measurement's date
    propagator.propagate(measurements.get(measurements.size() - 1).getDate());
    // Convert lists to double[] and evaluate some statistics
    final double[] relErrorsP = errorsP.stream().mapToDouble(Double::doubleValue).toArray();
    final double[] relErrorsV = errorsV.stream().mapToDouble(Double::doubleValue).toArray();
    final double errorsPMedian = new Median().evaluate(relErrorsP);
    final double errorsPMean = new Mean().evaluate(relErrorsP);
    final double errorsPMax = new Max().evaluate(relErrorsP);
    final double errorsVMedian = new Median().evaluate(relErrorsV);
    final double errorsVMean = new Mean().evaluate(relErrorsV);
    final double errorsVMax = new Max().evaluate(relErrorsV);
    // Print the results on console ?
    if (printResults) {
        System.out.println();
        System.out.format(Locale.US, "Relative errors dR/dP -> Median: %6.3e / Mean: %6.3e / Max: %6.3e%n", errorsPMedian, errorsPMean, errorsPMax);
        System.out.format(Locale.US, "Relative errors dR/dV -> Median: %6.3e / Mean: %6.3e / Max: %6.3e%n", errorsVMedian, errorsVMean, errorsVMax);
    }
    // Reference comparison with Range class
    Assert.assertEquals(0.0, errorsPMedian, refErrorsPMedian);
    Assert.assertEquals(0.0, errorsPMean, refErrorsPMean);
    Assert.assertEquals(0.0, errorsPMax, refErrorsPMax);
    Assert.assertEquals(0.0, errorsVMedian, refErrorsVMedian);
    Assert.assertEquals(0.0, errorsVMean, refErrorsVMean);
    Assert.assertEquals(0.0, errorsVMax, refErrorsVMax);
}

Example 75 with AbsoluteDate

use of org.orekit.time.AbsoluteDate in project Orekit by CS-SI.

the class RangeAnalyticTest method genericTestParameterDerivatives.

/**
 * Generic test function for derivatives with respect to parameters (station's position in station's topocentric frame)
 * @param isModifier Use of atmospheric modifiers
 * @param isFiniteDifferences Finite differences reference calculation if true, Range class otherwise
 * @param printResults Print the results ?
 * @throws OrekitException
 */
void genericTestParameterDerivatives(final boolean isModifier, final boolean isFiniteDifferences, final boolean printResults) throws OrekitException {
    Context context = EstimationTestUtils.eccentricContext("regular-data:potential:tides");
    final NumericalPropagatorBuilder propagatorBuilder = context.createBuilder(OrbitType.KEPLERIAN, PositionAngle.TRUE, true, 1.0e-6, 60.0, 0.001);
    // Create perfect range measurements
    for (final GroundStation station : context.stations) {
        station.getEastOffsetDriver().setSelected(true);
        station.getNorthOffsetDriver().setSelected(true);
        station.getZenithOffsetDriver().setSelected(true);
    }
    final Propagator propagator = EstimationTestUtils.createPropagator(context.initialOrbit, propagatorBuilder);
    final List<ObservedMeasurement<?>> measurements = EstimationTestUtils.createMeasurements(propagator, new RangeMeasurementCreator(context), 1.0, 3.0, 300.0);
    // List to store the results
    final List<Double> relErrorList = new ArrayList<Double>();
    // Set master mode
    // Use a lambda function to implement "handleStep" function
    propagator.setMasterMode((OrekitStepInterpolator interpolator, boolean isLast) -> {
        for (final ObservedMeasurement<?> measurement : measurements) {
            // Play test if the measurement date is between interpolator previous and current date
            if ((measurement.getDate().durationFrom(interpolator.getPreviousState().getDate()) > 0.) && (measurement.getDate().durationFrom(interpolator.getCurrentState().getDate()) <= 0.)) {
                // Add modifiers if test implies it
                final RangeTroposphericDelayModifier modifier = new RangeTroposphericDelayModifier(SaastamoinenModel.getStandardModel());
                if (isModifier) {
                    ((Range) measurement).addModifier(modifier);
                }
                // Parameter corresponding to station position offset
                final GroundStation stationParameter = ((Range) measurement).getStation();
                // We intentionally propagate to a date which is close to the
                // real spacecraft state but is *not* the accurate date, by
                // compensating only part of the downlink delay. This is done
                // in order to validate the partial derivatives with respect
                // to velocity. If we had chosen the proper state date, the
                // range would have depended only on the current position but
                // not on the current velocity.
                final double meanDelay = measurement.getObservedValue()[0] / Constants.SPEED_OF_LIGHT;
                final AbsoluteDate date = measurement.getDate().shiftedBy(-0.75 * meanDelay);
                final SpacecraftState state = interpolator.getInterpolatedState(date);
                final ParameterDriver[] drivers = new ParameterDriver[] { stationParameter.getEastOffsetDriver(), stationParameter.getNorthOffsetDriver(), stationParameter.getZenithOffsetDriver() };
                if (printResults) {
                    String stationName = ((Range) measurement).getStation().getBaseFrame().getName();
                    System.out.format(Locale.US, "%-15s  %-23s  %-23s  ", stationName, measurement.getDate(), date);
                }
                for (int i = 0; i < 3; ++i) {
                    final double[] gradient = measurement.estimate(0, 0, new SpacecraftState[] { state }).getParameterDerivatives(drivers[i]);
                    Assert.assertEquals(1, measurement.getDimension());
                    Assert.assertEquals(1, gradient.length);
                    // Compute a reference value using analytical formulas
                    final EstimatedMeasurement<Range> rangeAnalytic = new RangeAnalytic((Range) measurement).theoreticalEvaluationAnalytic(0, 0, state);
                    if (isModifier) {
                        modifier.modify(rangeAnalytic);
                    }
                    final double ref = rangeAnalytic.getParameterDerivatives(drivers[i])[0];
                    if (printResults) {
                        System.out.format(Locale.US, "%10.3e  %10.3e  ", gradient[0] - ref, FastMath.abs((gradient[0] - ref) / ref));
                    }
                    final double relError = FastMath.abs((ref - gradient[0]) / ref);
                    relErrorList.add(relError);
                // Assert.assertEquals(ref, gradient[0], 6.1e-5 * FastMath.abs(ref));
                }
                if (printResults) {
                    System.out.format(Locale.US, "%n");
                }
            }
        // End if measurement date between previous and current interpolator step
        }
    // End for loop on the measurements
    });
    // Rewind the propagator to initial date
    propagator.propagate(context.initialOrbit.getDate());
    // Sort measurements chronologically
    measurements.sort(new ChronologicalComparator());
    // Print results ? Header
    if (printResults) {
        System.out.format(Locale.US, "%-15s  %-23s  %-23s  " + "%10s  %10s  %10s  " + "%10s  %10s  %10s%n", "Station", "Measurement Date", "State Date", "ΔdQx", "rel ΔdQx", "ΔdQy", "rel ΔdQy", "ΔdQz", "rel ΔdQz");
    }
    // Propagate to final measurement's date
    propagator.propagate(measurements.get(measurements.size() - 1).getDate());
    // Convert error list to double[]
    final double[] relErrors = relErrorList.stream().mapToDouble(Double::doubleValue).toArray();
    // Compute statistics
    final double relErrorsMedian = new Median().evaluate(relErrors);
    final double relErrorsMean = new Mean().evaluate(relErrors);
    final double relErrorsMax = new Max().evaluate(relErrors);
    // Print the results on console ?
    if (printResults) {
        System.out.println();
        System.out.format(Locale.US, "Relative errors dR/dQ -> Median: %6.3e / Mean: %6.3e / Max: %6.3e%n", relErrorsMedian, relErrorsMean, relErrorsMax);
    }
    // Assert the results / max values depend on the test
    double refErrorsMedian, refErrorsMean, refErrorsMax;
    // Analytic references
    refErrorsMedian = 1.55e-06;
    refErrorsMean = 3.64e-06;
    refErrorsMax = 6.1e-05;
    Assert.assertEquals(0.0, relErrorsMedian, refErrorsMedian);
    Assert.assertEquals(0.0, relErrorsMean, refErrorsMean);
    Assert.assertEquals(0.0, relErrorsMax, refErrorsMax);
}