Examples with FieldTransform org.orekit.frames.FieldTransform used on opensource projects

Example 1 with FieldTransform

use of org.orekit.frames.FieldTransform in project Orekit by CS-SI.

the class TurnAroundRangeAnalytic method theoreticalEvaluationValidation.

/**
 * Added for validation
 * @param iteration
 * @param evaluation
 * @param state
 * @return
 * @throws OrekitException
 */
protected EstimatedMeasurement<TurnAroundRange> theoreticalEvaluationValidation(final int iteration, final int evaluation, final SpacecraftState state) throws OrekitException {
    // Stations & DSFactory attributes from parent TurnArounsRange class
    final GroundStation masterGroundStation = getMasterStation();
    final GroundStation slaveGroundStation = getSlaveStation();
    int nbParams = 6;
    final Map<String, Integer> indices = new HashMap<>();
    for (ParameterDriver driver : getParametersDrivers()) {
        // as one set only (they are combined together by the estimation engine)
        if (driver.isSelected() && !indices.containsKey(driver.getName())) {
            indices.put(driver.getName(), nbParams++);
        }
    }
    final DSFactory dsFactory = new DSFactory(nbParams, 1);
    final Field<DerivativeStructure> field = dsFactory.getDerivativeField();
    final FieldVector3D<DerivativeStructure> zero = FieldVector3D.getZero(field);
    // Coordinates of the spacecraft expressed as a derivative structure
    final TimeStampedFieldPVCoordinates<DerivativeStructure> pvaDS = getCoordinates(state, 0, dsFactory);
    // The path of the signal is divided in two legs.
    // Leg1: Emission from master station to satellite in masterTauU seconds
    // + Reflection from satellite to slave station in slaveTauD seconds
    // Leg2: Reflection from slave station to satellite in slaveTauU seconds
    // + Reflection from satellite to master station in masterTaudD seconds
    // The measurement is considered to be time stamped at reception on ground
    // by the master station. All times are therefore computed as backward offsets
    // with respect to this reception time.
    // 
    // Two intermediate spacecraft states are defined:
    // - transitStateLeg2: State of the satellite when it bounced back the signal
    // from slave station to master station during the 2nd leg
    // - transitStateLeg1: State of the satellite when it bounced back the signal
    // from master station to slave station during the 1st leg
    // Compute propagation time for the 2nd leg of the signal path
    // --
    // Time difference between t (date of the measurement) and t' (date tagged in spacecraft state)
    // (if state has already been set up to pre-compensate propagation delay,
    // we will have delta = masterTauD + slaveTauU)
    final AbsoluteDate measurementDate = getDate();
    final FieldAbsoluteDate<DerivativeStructure> measurementDateDS = new FieldAbsoluteDate<>(field, measurementDate);
    final double delta = measurementDate.durationFrom(state.getDate());
    // transform between master station topocentric frame (east-north-zenith) and inertial frame expressed as DerivativeStructures
    // The components of master station's position in offset frame are the 3 third derivative parameters
    final FieldTransform<DerivativeStructure> masterToInert = masterGroundStation.getOffsetToInertial(state.getFrame(), measurementDateDS, dsFactory, indices);
    // Master station PV in inertial frame at measurement date
    final FieldVector3D<DerivativeStructure> QMaster = masterToInert.transformPosition(zero);
    // Compute propagation times
    final DerivativeStructure masterTauD = signalTimeOfFlight(pvaDS, QMaster, measurementDateDS);
    // Elapsed time between state date t' and signal arrival to the transit state of the 2nd leg
    final DerivativeStructure dtLeg2 = masterTauD.negate().add(delta);
    // Transit state where the satellite reflected the signal from slave to master station
    final SpacecraftState transitStateLeg2 = state.shiftedBy(dtLeg2.getValue());
    // Transit state pv of leg2 (re)computed with derivative structures
    final TimeStampedFieldPVCoordinates<DerivativeStructure> transitStateLeg2PV = pvaDS.shiftedBy(dtLeg2);
    // transform between slave station topocentric frame (east-north-zenith) and inertial frame expressed as DerivativeStructures
    // The components of slave station's position in offset frame are the 3 last derivative parameters
    final FieldAbsoluteDate<DerivativeStructure> approxReboundDate = measurementDateDS.shiftedBy(-delta);
    final FieldTransform<DerivativeStructure> slaveToInertApprox = slaveGroundStation.getOffsetToInertial(state.getFrame(), approxReboundDate, dsFactory, indices);
    // Slave station PV in inertial frame at approximate rebound date on slave station
    final TimeStampedFieldPVCoordinates<DerivativeStructure> QSlaveApprox = slaveToInertApprox.transformPVCoordinates(new TimeStampedFieldPVCoordinates<>(approxReboundDate, zero, zero, zero));
    // Uplink time of flight from slave station to transit state of leg2
    final DerivativeStructure slaveTauU = signalTimeOfFlight(QSlaveApprox, transitStateLeg2PV.getPosition(), transitStateLeg2PV.getDate());
    // Total time of flight for leg 2
    final DerivativeStructure tauLeg2 = masterTauD.add(slaveTauU);
    // Compute propagation time for the 1st leg of the signal path
    // --
    // Absolute date of rebound of the signal to slave station
    final FieldAbsoluteDate<DerivativeStructure> reboundDateDS = measurementDateDS.shiftedBy(tauLeg2.negate());
    final FieldTransform<DerivativeStructure> slaveToInert = slaveGroundStation.getOffsetToInertial(state.getFrame(), reboundDateDS, dsFactory, indices);
    // Slave station PV in inertial frame at rebound date on slave station
    final FieldVector3D<DerivativeStructure> QSlave = slaveToInert.transformPosition(zero);
    // Downlink time of flight from transitStateLeg1 to slave station at rebound date
    final DerivativeStructure slaveTauD = signalTimeOfFlight(transitStateLeg2PV, QSlave, reboundDateDS);
    // Elapsed time between state date t' and signal arrival to the transit state of the 1st leg
    final DerivativeStructure dtLeg1 = dtLeg2.subtract(slaveTauU).subtract(slaveTauD);
    // Transit state pv of leg2 (re)computed with derivative structures
    final TimeStampedFieldPVCoordinates<DerivativeStructure> transitStateLeg1PV = pvaDS.shiftedBy(dtLeg1);
    // transform between master station topocentric frame (east-north-zenith) and inertial frame expressed as DerivativeStructures
    // The components of master station's position in offset frame are the 3 third derivative parameters
    final FieldAbsoluteDate<DerivativeStructure> approxEmissionDate = measurementDateDS.shiftedBy(-2 * (slaveTauU.getValue() + masterTauD.getValue()));
    final FieldTransform<DerivativeStructure> masterToInertApprox = masterGroundStation.getOffsetToInertial(state.getFrame(), approxEmissionDate, dsFactory, indices);
    // Master station PV in inertial frame at approximate emission date
    final TimeStampedFieldPVCoordinates<DerivativeStructure> QMasterApprox = masterToInertApprox.transformPVCoordinates(new TimeStampedFieldPVCoordinates<>(approxEmissionDate, zero, zero, zero));
    // Uplink time of flight from master station to transit state of leg1
    final DerivativeStructure masterTauU = signalTimeOfFlight(QMasterApprox, transitStateLeg1PV.getPosition(), transitStateLeg1PV.getDate());
    // Total time of flight for leg 1
    final DerivativeStructure tauLeg1 = slaveTauD.add(masterTauU);
    // --
    // Evaluate the turn-around range value and its derivatives
    // --------------------------------------------------------
    // The state we use to define the estimated measurement is a middle ground between the two transit states
    // This is done to avoid calling "SpacecraftState.shiftedBy" function on long duration
    // Thus we define the state at the date t" = date of rebound of the signal at the slave station
    // Or t" = t -masterTauD -slaveTauU
    // The iterative process in the estimation ensures that, after several iterations, the date stamped in the
    // state S in input of this function will be close to t"
    // Therefore we will shift state S by:
    // - +slaveTauU to get transitStateLeg2
    // - -slaveTauD to get transitStateLeg1
    final EstimatedMeasurement<TurnAroundRange> estimated = new EstimatedMeasurement<>(this, iteration, evaluation, new SpacecraftState[] { transitStateLeg2.shiftedBy(-slaveTauU.getValue()) }, null);
    // Turn-around range value = Total time of flight for the 2 legs divided by 2 and multiplied by c
    final double cOver2 = 0.5 * Constants.SPEED_OF_LIGHT;
    final DerivativeStructure turnAroundRange = (tauLeg2.add(tauLeg1)).multiply(cOver2);
    estimated.setEstimatedValue(turnAroundRange.getValue());
    // Turn-around range partial derivatives with respect to state
    final double[] derivatives = turnAroundRange.getAllDerivatives();
    estimated.setStateDerivatives(0, Arrays.copyOfRange(derivatives, 1, 7));
    // (beware element at index 0 is the value, not a derivative)
    for (final ParameterDriver driver : getParametersDrivers()) {
        final Integer index = indices.get(driver.getName());
        if (index != null) {
            estimated.setParameterDerivatives(driver, derivatives[index + 1]);
        }
    }
    // ----------
    // VALIDATION: Using analytical version to compare
    // -----------
    // Computation of the value without DS
    // ----------------------------------
    // Time difference between t (date of the measurement) and t' (date tagged in spacecraft state)
    // (if state has already been set up to pre-compensate propagation delay,
    // we will have delta = masterTauD + slaveTauU)
    // Master station PV at measurement date
    final Transform masterTopoToInert = masterGroundStation.getOffsetToInertial(state.getFrame(), measurementDate);
    final TimeStampedPVCoordinates QMt = masterTopoToInert.transformPVCoordinates(new TimeStampedPVCoordinates(measurementDate, PVCoordinates.ZERO));
    // Slave station PV at measurement date
    final Transform slaveTopoToInert = slaveGroundStation.getOffsetToInertial(state.getFrame(), measurementDate);
    final TimeStampedPVCoordinates QSt = slaveTopoToInert.transformPVCoordinates(new TimeStampedPVCoordinates(measurementDate, PVCoordinates.ZERO));
    // Downlink time of flight from master station at t to spacecraft at t'
    final double tMd = signalTimeOfFlight(state.getPVCoordinates(), QMt.getPosition(), measurementDate);
    // Transit state from which the satellite reflected the signal from slave to master station
    final SpacecraftState state2 = state.shiftedBy(delta - tMd);
    final AbsoluteDate transitDateLeg2 = transitStateLeg2.getDate();
    // Slave station PV at transit state leg2 date
    final Transform slaveTopoToInertTransitLeg2 = slaveGroundStation.getOffsetToInertial(state.getFrame(), transitDateLeg2);
    final TimeStampedPVCoordinates QSdate2PV = slaveTopoToInertTransitLeg2.transformPVCoordinates(new TimeStampedPVCoordinates(transitDateLeg2, PVCoordinates.ZERO));
    // Uplink time of flight from slave station to transit state leg2
    final double tSu = signalTimeOfFlight(QSdate2PV, state2.getPVCoordinates().getPosition(), transitDateLeg2);
    // Total time of flight for leg 2
    final double t2 = tMd + tSu;
    // Compute propagation time for the 1st leg of the signal path
    // --
    // Absolute date of arrival of the signal to slave station
    final AbsoluteDate tQSA = measurementDate.shiftedBy(-t2);
    // Slave station position in inertial frame at date tQSA
    final Transform slaveTopoToInertArrivalDate = slaveGroundStation.getOffsetToInertial(state.getFrame(), tQSA);
    final Vector3D QSA = slaveTopoToInertArrivalDate.transformPosition(Vector3D.ZERO);
    // Dowlink time of flight from transitStateLeg1 to slave station at slaveStationArrivalDate
    final double tSd = signalTimeOfFlight(state2.getPVCoordinates(), QSA, tQSA);
    // Transit state from which the satellite reflected the signal from master to slave station
    final SpacecraftState state1 = state.shiftedBy(delta - tMd - tSu - tSd);
    final AbsoluteDate transitDateLeg1 = transitStateLeg1PV.getDate().toAbsoluteDate();
    // Master station PV at transit state date of leg1
    final Transform masterTopoToInertTransitLeg1 = masterGroundStation.getOffsetToInertial(state.getFrame(), transitDateLeg1);
    final TimeStampedPVCoordinates QMdate1PV = masterTopoToInertTransitLeg1.transformPVCoordinates(new TimeStampedPVCoordinates(transitDateLeg1, PVCoordinates.ZERO));
    // Uplink time of flight from master station to transit state leg1
    final double tMu = signalTimeOfFlight(QMdate1PV, state1.getPVCoordinates().getPosition(), transitDateLeg1);
    // Total time of flight for leg 1
    final double t1 = tSd + tMu;
    // Total time of flight
    final double t = t1 + t2;
    // Turn-around range value
    final double TAR = t * cOver2;
    // Diff with DS
    final double dTAR = turnAroundRange.getValue() - TAR;
    // tMd derivatives / state
    // -----------------------
    // QMt_PV = Master station PV at tmeas = t = signal arrival at master station
    final Vector3D vel = state.getPVCoordinates().getVelocity();
    final PVCoordinates QMt_PV = masterTopoToInert.transformPVCoordinates(PVCoordinates.ZERO);
    final Vector3D QMt_V = QMt_PV.getVelocity();
    final Vector3D pos2 = state2.getPVCoordinates().getPosition();
    final Vector3D P2_QMt = QMt_PV.getPosition().subtract(pos2);
    final double dMDown = Constants.SPEED_OF_LIGHT * Constants.SPEED_OF_LIGHT * tMd - Vector3D.dotProduct(P2_QMt, vel);
    // derivatives of the downlink time of flight
    final double dtMddPx = -P2_QMt.getX() / dMDown;
    final double dtMddPy = -P2_QMt.getY() / dMDown;
    final double dtMddPz = -P2_QMt.getZ() / dMDown;
    final double dt = delta - tMd;
    final double dtMddVx = dtMddPx * dt;
    final double dtMddVy = dtMddPy * dt;
    final double dtMddVz = dtMddPz * dt;
    // From the DS
    final double dtMddPxDS = masterTauD.getPartialDerivative(1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
    final double dtMddPyDS = masterTauD.getPartialDerivative(0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
    final double dtMddPzDS = masterTauD.getPartialDerivative(0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0);
    final double dtMddVxDS = masterTauD.getPartialDerivative(0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0);
    final double dtMddVyDS = masterTauD.getPartialDerivative(0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0);
    final double dtMddVzDS = masterTauD.getPartialDerivative(0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0);
    // Difference
    final double d_dtMddPx = dtMddPxDS - dtMddPx;
    final double d_dtMddPy = dtMddPyDS - dtMddPy;
    final double d_dtMddPz = dtMddPzDS - dtMddPz;
    final double d_dtMddVx = dtMddVxDS - dtMddVx;
    final double d_dtMddVy = dtMddVyDS - dtMddVy;
    final double d_dtMddVz = dtMddVzDS - dtMddVz;
    // tSu derivatives / state
    // -----------------------
    // QSt = slave station PV at tmeas = t = signal arrival at master station
    // final Transform FSt     = slaveStation.getOffsetFrame().getTransformTo(state.getFrame(), measurementDate);
    // final PVCoordinates QSt = FSt.transformPVCoordinates(PVCoordinates.ZERO);
    final Vector3D QSt_V = QSt.getVelocity();
    // QSt2 = slave station PV at t-t2 = signal arrival at slave station
    final PVCoordinates QSt2 = slaveTopoToInertArrivalDate.transformPVCoordinates(PVCoordinates.ZERO);
    final Vector3D QSt2_P2 = pos2.subtract(QSt2.getPosition());
    final double dSUp = Constants.SPEED_OF_LIGHT * Constants.SPEED_OF_LIGHT * tSu - Vector3D.dotProduct(QSt2_P2, QSt_V);
    final double alphaSu = 1. / dSUp * QSt2_P2.dotProduct(QSt_V.subtract(vel));
    final double dtSudPx = 1. / dSUp * QSt2_P2.getX() + alphaSu * dtMddPx;
    final double dtSudPy = 1. / dSUp * QSt2_P2.getY() + alphaSu * dtMddPy;
    final double dtSudPz = 1. / dSUp * QSt2_P2.getZ() + alphaSu * dtMddPz;
    final double dtSudVx = dtSudPx * dt;
    final double dtSudVy = dtSudPy * dt;
    final double dtSudVz = dtSudPz * dt;
    // From the DS
    final double dtSudPxDS = slaveTauU.getPartialDerivative(1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
    final double dtSudPyDS = slaveTauU.getPartialDerivative(0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
    final double dtSudPzDS = slaveTauU.getPartialDerivative(0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0);
    final double dtSudVxDS = slaveTauU.getPartialDerivative(0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0);
    final double dtSudVyDS = slaveTauU.getPartialDerivative(0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0);
    final double dtSudVzDS = slaveTauU.getPartialDerivative(0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0);
    // Difference
    final double d_dtSudPx = dtSudPxDS - dtSudPx;
    final double d_dtSudPy = dtSudPyDS - dtSudPy;
    final double d_dtSudPz = dtSudPzDS - dtSudPz;
    final double d_dtSudVx = dtSudVxDS - dtSudVx;
    final double d_dtSudVy = dtSudVyDS - dtSudVy;
    final double d_dtSudVz = dtSudVzDS - dtSudVz;
    // t2 derivatives / state
    // -----------------------
    // t2 = Time leg 2
    double dt2dPx = dtSudPx + dtMddPx;
    double dt2dPy = dtSudPy + dtMddPy;
    double dt2dPz = dtSudPz + dtMddPz;
    double dt2dVx = dtSudVx + dtMddVx;
    double dt2dVy = dtSudVy + dtMddVy;
    double dt2dVz = dtSudVz + dtMddVz;
    // With DS
    double dt2dPxDS = tauLeg2.getPartialDerivative(1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
    double dt2dPyDS = tauLeg2.getPartialDerivative(0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
    double dt2dPzDS = tauLeg2.getPartialDerivative(0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0);
    double dt2dVxDS = tauLeg2.getPartialDerivative(0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0);
    double dt2dVyDS = tauLeg2.getPartialDerivative(0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0);
    double dt2dVzDS = tauLeg2.getPartialDerivative(0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0);
    // Diff
    final double d_dt2dPx = dt2dPxDS - dt2dPx;
    final double d_dt2dPy = dt2dPyDS - dt2dPy;
    final double d_dt2dPz = dt2dPzDS - dt2dPz;
    final double d_dt2dVx = dt2dVxDS - dt2dVx;
    final double d_dt2dVy = dt2dVyDS - dt2dVy;
    final double d_dt2dVz = dt2dVzDS - dt2dVz;
    // tSd derivatives / state
    // -----------------------
    final Vector3D pos1 = state1.getPVCoordinates().getPosition();
    final Vector3D P1_QSt2 = QSt2.getPosition().subtract(pos1);
    final double dSDown = Constants.SPEED_OF_LIGHT * Constants.SPEED_OF_LIGHT * tSd - Vector3D.dotProduct(P1_QSt2, vel);
    // derivatives w/r to state
    final double alphaSd = 1. / dSDown * P1_QSt2.dotProduct(vel.subtract(QSt_V));
    final double dtSddPx = -1. / dSDown * P1_QSt2.getX() + alphaSd * dt2dPx;
    final double dtSddPy = -1. / dSDown * P1_QSt2.getY() + alphaSd * dt2dPy;
    final double dtSddPz = -1. / dSDown * P1_QSt2.getZ() + alphaSd * dt2dPz;
    final double dt2 = delta - t2 - tSd;
    final double dtSddVx = -dt2 / dSDown * P1_QSt2.getX() + alphaSd * dt2dVx;
    final double dtSddVy = -dt2 / dSDown * P1_QSt2.getY() + alphaSd * dt2dVy;
    final double dtSddVz = -dt2 / dSDown * P1_QSt2.getZ() + alphaSd * dt2dVz;
    // From the DS
    final double dtSddPxDS = slaveTauD.getPartialDerivative(1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
    final double dtSddPyDS = slaveTauD.getPartialDerivative(0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
    final double dtSddPzDS = slaveTauD.getPartialDerivative(0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0);
    final double dtSddVxDS = slaveTauD.getPartialDerivative(0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0);
    final double dtSddVyDS = slaveTauD.getPartialDerivative(0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0);
    final double dtSddVzDS = slaveTauD.getPartialDerivative(0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0);
    // Difference
    final double d_dtSddPx = dtSddPxDS - dtSddPx;
    final double d_dtSddPy = dtSddPyDS - dtSddPy;
    final double d_dtSddPz = dtSddPzDS - dtSddPz;
    final double d_dtSddVx = dtSddVxDS - dtSddVx;
    final double d_dtSddVy = dtSddVyDS - dtSddVy;
    final double d_dtSddVz = dtSddVzDS - dtSddVz;
    // tMu derivatives / state
    // -----------------------
    // QMt1 = Master station position at t1 = t - tau = signal departure from master station
    final Transform FMt1 = masterGroundStation.getOffsetToInertial(state.getFrame(), measurementDate.shiftedBy(-t1 - t2));
    final PVCoordinates QMt1 = FMt1.transformPVCoordinates(PVCoordinates.ZERO);
    final Vector3D QMt1_P1 = pos1.subtract(QMt1.getPosition());
    final double dMUp = Constants.SPEED_OF_LIGHT * Constants.SPEED_OF_LIGHT * tMu - Vector3D.dotProduct(QMt1_P1, QMt_V);
    // derivatives w/r to state
    final double alphaMu = 1. / dMUp * QMt1_P1.dotProduct(QMt_V.subtract(vel));
    final double dtMudPx = 1. / dMUp * QMt1_P1.getX() + alphaMu * (dt2dPx + dtSddPx);
    final double dtMudPy = 1. / dMUp * QMt1_P1.getY() + alphaMu * (dt2dPy + dtSddPy);
    final double dtMudPz = 1. / dMUp * QMt1_P1.getZ() + alphaMu * (dt2dPz + dtSddPz);
    final double dtMudVx = dt2 / dMUp * QMt1_P1.getX() + alphaMu * (dt2dVx + dtSddVx);
    final double dtMudVy = dt2 / dMUp * QMt1_P1.getY() + alphaMu * (dt2dVy + dtSddVy);
    final double dtMudVz = dt2 / dMUp * QMt1_P1.getZ() + alphaMu * (dt2dVz + dtSddVz);
    // From the DS
    final double dtMudPxDS = masterTauU.getPartialDerivative(1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
    final double dtMudPyDS = masterTauU.getPartialDerivative(0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
    final double dtMudPzDS = masterTauU.getPartialDerivative(0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0);
    final double dtMudVxDS = masterTauU.getPartialDerivative(0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0);
    final double dtMudVyDS = masterTauU.getPartialDerivative(0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0);
    final double dtMudVzDS = masterTauU.getPartialDerivative(0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0);
    // Difference
    final double d_dtMudPx = dtMudPxDS - dtMudPx;
    final double d_dtMudPy = dtMudPyDS - dtMudPy;
    final double d_dtMudPz = dtMudPzDS - dtMudPz;
    final double d_dtMudVx = dtMudVxDS - dtMudVx;
    final double d_dtMudVy = dtMudVyDS - dtMudVy;
    final double d_dtMudVz = dtMudVzDS - dtMudVz;
    // t1 derivatives / state
    // -----------------------
    // t1 = Time leg 1
    double dt1dPx = dtSddPx + dtMudPx;
    double dt1dPy = dtSddPy + dtMudPy;
    double dt1dPz = dtSddPz + dtMudPz;
    double dt1dVx = dtSddVx + dtMudVx;
    double dt1dVy = dtSddVy + dtMudVy;
    double dt1dVz = dtSddVz + dtMudVz;
    // With DS
    double dt1dPxDS = tauLeg1.getPartialDerivative(1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
    double dt1dPyDS = tauLeg1.getPartialDerivative(0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
    double dt1dPzDS = tauLeg1.getPartialDerivative(0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0);
    double dt1dVxDS = tauLeg1.getPartialDerivative(0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0);
    double dt1dVyDS = tauLeg1.getPartialDerivative(0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0);
    double dt1dVzDS = tauLeg1.getPartialDerivative(0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0);
    // Diff
    final double d_dt1dPx = dt1dPxDS - dt1dPx;
    final double d_dt1dPy = dt1dPyDS - dt1dPy;
    final double d_dt1dPz = dt1dPzDS - dt1dPz;
    final double d_dt1dVx = dt1dVxDS - dt1dVx;
    final double d_dt1dVy = dt1dVyDS - dt1dVy;
    final double d_dt1dVz = dt1dVzDS - dt1dVz;
    // TAR derivatives / state
    // -----------------------
    // R = TAR
    double dRdPx = (dt1dPx + dt2dPx) * cOver2;
    double dRdPy = (dt1dPy + dt2dPy) * cOver2;
    double dRdPz = (dt1dPz + dt2dPz) * cOver2;
    double dRdVx = (dt1dVx + dt2dVx) * cOver2;
    double dRdVy = (dt1dVy + dt2dVy) * cOver2;
    double dRdVz = (dt1dVz + dt2dVz) * cOver2;
    // With DS
    double dRdPxDS = turnAroundRange.getPartialDerivative(1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
    double dRdPyDS = turnAroundRange.getPartialDerivative(0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
    double dRdPzDS = turnAroundRange.getPartialDerivative(0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0);
    double dRdVxDS = turnAroundRange.getPartialDerivative(0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0);
    double dRdVyDS = turnAroundRange.getPartialDerivative(0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0);
    double dRdVzDS = turnAroundRange.getPartialDerivative(0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0);
    // Diff
    final double d_dRdPx = dRdPxDS - dRdPx;
    final double d_dRdPy = dRdPyDS - dRdPy;
    final double d_dRdPz = dRdPzDS - dRdPz;
    final double d_dRdVx = dRdVxDS - dRdVx;
    final double d_dRdVy = dRdVyDS - dRdVy;
    final double d_dRdVz = dRdVzDS - dRdVz;
    // tMd derivatives / stations
    // --------------------------
    // Master station rotation and angular speed at tmeas
    final AngularCoordinates acM = masterTopoToInert.getAngular().revert();
    final Rotation rotationMasterTopoToInert = acM.getRotation();
    final Vector3D OmegaM = acM.getRotationRate();
    // Slave station rotation and angular speed at tmeas
    final AngularCoordinates acS = slaveTopoToInert.getAngular().revert();
    final Rotation rotationSlaveTopoToInert = acS.getRotation();
    final Vector3D OmegaS = acS.getRotationRate();
    // Master station - Inertial frame
    final double dtMddQMx_I = P2_QMt.getX() / dMDown;
    final double dtMddQMy_I = P2_QMt.getY() / dMDown;
    final double dtMddQMz_I = P2_QMt.getZ() / dMDown;
    // Slave station - Inertial frame
    final double dtMddQSx_I = 0.;
    final double dtMddQSy_I = 0.;
    final double dtMddQSz_I = 0.;
    // Topo frames
    final Vector3D dtMddQM = rotationMasterTopoToInert.applyTo(new Vector3D(dtMddQMx_I, dtMddQMy_I, dtMddQMz_I));
    final Vector3D dtMddQS = rotationSlaveTopoToInert.applyTo(new Vector3D(dtMddQSx_I, dtMddQSy_I, dtMddQSz_I));
    // With DS
    double dtMddQMx_DS = masterTauD.getPartialDerivative(0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0);
    double dtMddQMy_DS = masterTauD.getPartialDerivative(0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0);
    double dtMddQMz_DS = masterTauD.getPartialDerivative(0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0);
    double dtMddQSx_DS = masterTauD.getPartialDerivative(0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0);
    double dtMddQSy_DS = masterTauD.getPartialDerivative(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0);
    double dtMddQSz_DS = masterTauD.getPartialDerivative(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1);
    // Diff
    final double d_dtMddQMx = dtMddQMx_DS - dtMddQM.getX();
    final double d_dtMddQMy = dtMddQMy_DS - dtMddQM.getY();
    final double d_dtMddQMz = dtMddQMz_DS - dtMddQM.getZ();
    final double d_dtMddQSx = dtMddQSx_DS - dtMddQS.getX();
    final double d_dtMddQSy = dtMddQSy_DS - dtMddQS.getY();
    final double d_dtMddQSz = dtMddQSz_DS - dtMddQS.getZ();
    // tSu derivatives / stations
    // --------------------------
    // Master station - Inertial frame
    final double dtSudQMx_I = dtMddQMx_I * alphaSu;
    final double dtSudQMy_I = dtMddQMy_I * alphaSu;
    final double dtSudQMz_I = dtMddQMz_I * alphaSu;
    // Slave station - Inertial frame
    final double dtSudQSx_I = 1. / dSUp * QSt2_P2.dotProduct(Vector3D.MINUS_I.add(OmegaS.crossProduct(Vector3D.PLUS_I).scalarMultiply(t2)));
    final double dtSudQSy_I = 1. / dSUp * QSt2_P2.dotProduct(Vector3D.MINUS_J.add(OmegaS.crossProduct(Vector3D.PLUS_J).scalarMultiply(t2)));
    final double dtSudQSz_I = 1. / dSUp * QSt2_P2.dotProduct(Vector3D.MINUS_K.add(OmegaS.crossProduct(Vector3D.PLUS_K).scalarMultiply(t2)));
    // Topo frames
    final Vector3D dtSudQM = rotationMasterTopoToInert.applyTo(new Vector3D(dtSudQMx_I, dtSudQMy_I, dtSudQMz_I));
    final Vector3D dtSudQS = rotationSlaveTopoToInert.applyTo(new Vector3D(dtSudQSx_I, dtSudQSy_I, dtSudQSz_I));
    // With DS
    double dtSudQMx_DS = slaveTauU.getPartialDerivative(0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0);
    double dtSudQMy_DS = slaveTauU.getPartialDerivative(0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0);
    double dtSudQMz_DS = slaveTauU.getPartialDerivative(0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0);
    double dtSudQSx_DS = slaveTauU.getPartialDerivative(0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0);
    double dtSudQSy_DS = slaveTauU.getPartialDerivative(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0);
    double dtSudQSz_DS = slaveTauU.getPartialDerivative(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1);
    // Diff
    final double d_dtSudQMx = dtSudQMx_DS - dtSudQM.getX();
    final double d_dtSudQMy = dtSudQMy_DS - dtSudQM.getY();
    final double d_dtSudQMz = dtSudQMz_DS - dtSudQM.getZ();
    final double d_dtSudQSx = dtSudQSx_DS - dtSudQS.getX();
    final double d_dtSudQSy = dtSudQSy_DS - dtSudQS.getY();
    final double d_dtSudQSz = dtSudQSz_DS - dtSudQS.getZ();
    // t2 derivatives / stations
    // --------------------------
    final double dt2dQMx_I = dtMddQMx_I + dtSudQMx_I;
    final double dt2dQMy_I = dtMddQMy_I + dtSudQMy_I;
    final double dt2dQMz_I = dtMddQMz_I + dtSudQMz_I;
    final double dt2dQSx_I = dtMddQSx_I + dtSudQSx_I;
    final double dt2dQSy_I = dtMddQSy_I + dtSudQSy_I;
    final double dt2dQSz_I = dtMddQSz_I + dtSudQSz_I;
    final Vector3D dt2dQM = dtSudQM.add(dtMddQM);
    final Vector3D dt2dQS = dtSudQS.add(dtMddQS);
    // With DS
    double dt2dQMx_DS = tauLeg2.getPartialDerivative(0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0);
    double dt2dQMy_DS = tauLeg2.getPartialDerivative(0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0);
    double dt2dQMz_DS = tauLeg2.getPartialDerivative(0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0);
    double dt2dQSx_DS = tauLeg2.getPartialDerivative(0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0);
    double dt2dQSy_DS = tauLeg2.getPartialDerivative(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0);
    double dt2dQSz_DS = tauLeg2.getPartialDerivative(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1);
    // Diff
    final double d_dt2dQMx = dt2dQMx_DS - dt2dQM.getX();
    final double d_dt2dQMy = dt2dQMy_DS - dt2dQM.getY();
    final double d_dt2dQMz = dt2dQMz_DS - dt2dQM.getZ();
    final double d_dt2dQSx = dt2dQSx_DS - dt2dQS.getX();
    final double d_dt2dQSy = dt2dQSy_DS - dt2dQS.getY();
    final double d_dt2dQSz = dt2dQSz_DS - dt2dQS.getZ();
    // tSd derivatives / stations
    // --------------------------
    // Master station - Inertial frame
    final double dtSddQMx_I = dt2dQMx_I * alphaSd;
    final double dtSddQMy_I = dt2dQMy_I * alphaSd;
    final double dtSddQMz_I = dt2dQMz_I * alphaSd;
    // Slave station - Inertial frame
    final double dtSddQSx_I = dt2dQSx_I * alphaSd + 1. / dSDown * P1_QSt2.dotProduct(Vector3D.PLUS_I.subtract(OmegaS.crossProduct(Vector3D.PLUS_I).scalarMultiply(t2)));
    final double dtSddQSy_I = dt2dQSy_I * alphaSd + 1. / dSDown * P1_QSt2.dotProduct(Vector3D.PLUS_J.subtract(OmegaS.crossProduct(Vector3D.PLUS_J).scalarMultiply(t2)));
    final double dtSddQSz_I = dt2dQSz_I * alphaSd + 1. / dSDown * P1_QSt2.dotProduct(Vector3D.PLUS_K.subtract(OmegaS.crossProduct(Vector3D.PLUS_K).scalarMultiply(t2)));
    // Topo frames
    final Vector3D dtSddQM = rotationMasterTopoToInert.applyTo(new Vector3D(dtSddQMx_I, dtSddQMy_I, dtSddQMz_I));
    final Vector3D dtSddQS = rotationSlaveTopoToInert.applyTo(new Vector3D(dtSddQSx_I, dtSddQSy_I, dtSddQSz_I));
    // With DS
    double dtSddQMx_DS = slaveTauD.getPartialDerivative(0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0);
    double dtSddQMy_DS = slaveTauD.getPartialDerivative(0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0);
    double dtSddQMz_DS = slaveTauD.getPartialDerivative(0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0);
    double dtSddQSx_DS = slaveTauD.getPartialDerivative(0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0);
    double dtSddQSy_DS = slaveTauD.getPartialDerivative(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0);
    double dtSddQSz_DS = slaveTauD.getPartialDerivative(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1);
    // Diff
    final double d_dtSddQMx = dtSddQMx_DS - dtSddQM.getX();
    final double d_dtSddQMy = dtSddQMy_DS - dtSddQM.getY();
    final double d_dtSddQMz = dtSddQMz_DS - dtSddQM.getZ();
    final double d_dtSddQSx = dtSddQSx_DS - dtSddQS.getX();
    final double d_dtSddQSy = dtSddQSy_DS - dtSddQS.getY();
    final double d_dtSddQSz = dtSddQSz_DS - dtSddQS.getZ();
    // tMu derivatives / stations
    // --------------------------
    // Master station - Inertial frame
    final double dtMudQMx_I = -QMt1_P1.getX() / dMUp + alphaMu * (dt2dQMx_I + dtSddQMx_I) + t / dMUp * QMt1_P1.dotProduct(OmegaM.crossProduct(Vector3D.PLUS_I));
    final double dtMudQMy_I = -QMt1_P1.getY() / dMUp + alphaMu * (dt2dQMy_I + dtSddQMy_I) + t / dMUp * QMt1_P1.dotProduct(OmegaM.crossProduct(Vector3D.PLUS_J));
    final double dtMudQMz_I = -QMt1_P1.getZ() / dMUp + alphaMu * (dt2dQMz_I + dtSddQMz_I) + t / dMUp * QMt1_P1.dotProduct(OmegaM.crossProduct(Vector3D.PLUS_K));
    // Slave station - Inertial frame
    final double dtMudQSx_I = alphaMu * (dt2dQSx_I + dtSddQSx_I);
    final double dtMudQSy_I = alphaMu * (dt2dQSy_I + dtSddQSy_I);
    final double dtMudQSz_I = alphaMu * (dt2dQSz_I + dtSddQSz_I);
    // Topo frames
    final Vector3D dtMudQM = rotationMasterTopoToInert.applyTo(new Vector3D(dtMudQMx_I, dtMudQMy_I, dtMudQMz_I));
    final Vector3D dtMudQS = rotationSlaveTopoToInert.applyTo(new Vector3D(dtMudQSx_I, dtMudQSy_I, dtMudQSz_I));
    // With DS
    double dtMudQMx_DS = masterTauU.getPartialDerivative(0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0);
    double dtMudQMy_DS = masterTauU.getPartialDerivative(0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0);
    double dtMudQMz_DS = masterTauU.getPartialDerivative(0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0);
    double dtMudQSx_DS = masterTauU.getPartialDerivative(0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0);
    double dtMudQSy_DS = masterTauU.getPartialDerivative(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0);
    double dtMudQSz_DS = masterTauU.getPartialDerivative(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1);
    // Diff
    final double d_dtMudQMx = dtMudQMx_DS - dtMudQM.getX();
    final double d_dtMudQMy = dtMudQMy_DS - dtMudQM.getY();
    final double d_dtMudQMz = dtMudQMz_DS - dtMudQM.getZ();
    final double d_dtMudQSx = dtMudQSx_DS - dtMudQS.getX();
    final double d_dtMudQSy = dtMudQSy_DS - dtMudQS.getY();
    final double d_dtMudQSz = dtMudQSz_DS - dtMudQS.getZ();
    // t1 derivatives / stations
    // --------------------------
    final Vector3D dt1dQM = dtMudQM.add(dtSddQM);
    final Vector3D dt1dQS = dtMudQS.add(dtSddQS);
    // With DS
    double dt1dQMx_DS = tauLeg1.getPartialDerivative(0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0);
    double dt1dQMy_DS = tauLeg1.getPartialDerivative(0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0);
    double dt1dQMz_DS = tauLeg1.getPartialDerivative(0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0);
    double dt1dQSx_DS = tauLeg1.getPartialDerivative(0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0);
    double dt1dQSy_DS = tauLeg1.getPartialDerivative(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0);
    double dt1dQSz_DS = tauLeg1.getPartialDerivative(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1);
    // Diff
    final double d_dt1dQMx = dt1dQMx_DS - dt1dQM.getX();
    final double d_dt1dQMy = dt1dQMy_DS - dt1dQM.getY();
    final double d_dt1dQMz = dt1dQMz_DS - dt1dQM.getZ();
    final double d_dt1dQSx = dt1dQSx_DS - dt1dQS.getX();
    final double d_dt1dQSy = dt1dQSy_DS - dt1dQS.getY();
    final double d_dt1dQSz = dt1dQSz_DS - dt1dQS.getZ();
    // TAR derivatives / stations
    // --------------------------
    final Vector3D dRdQM = (dt1dQM.add(dt2dQM)).scalarMultiply(cOver2);
    final Vector3D dRdQS = (dt1dQS.add(dt2dQS)).scalarMultiply(cOver2);
    // With DS
    double dRdQMx_DS = turnAroundRange.getPartialDerivative(0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0);
    double dRdQMy_DS = turnAroundRange.getPartialDerivative(0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0);
    double dRdQMz_DS = turnAroundRange.getPartialDerivative(0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0);
    double dRdQSx_DS = turnAroundRange.getPartialDerivative(0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0);
    double dRdQSy_DS = turnAroundRange.getPartialDerivative(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0);
    double dRdQSz_DS = turnAroundRange.getPartialDerivative(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1);
    // Diff
    final double d_dRdQMx = dRdQMx_DS - dRdQM.getX();
    final double d_dRdQMy = dRdQMy_DS - dRdQM.getY();
    final double d_dRdQMz = dRdQMz_DS - dRdQM.getZ();
    final double d_dRdQSx = dRdQSx_DS - dRdQS.getX();
    final double d_dRdQSy = dRdQSy_DS - dRdQS.getY();
    final double d_dRdQSz = dRdQSz_DS - dRdQS.getZ();
    // Print results to avoid warning
    final boolean printResults = false;
    if (printResults) {
        System.out.println("dTAR = " + dTAR);
        System.out.println("d_dtMddPx = " + d_dtMddPx);
        System.out.println("d_dtMddPy = " + d_dtMddPy);
        System.out.println("d_dtMddPz = " + d_dtMddPz);
        System.out.println("d_dtMddVx = " + d_dtMddVx);
        System.out.println("d_dtMddVy = " + d_dtMddVy);
        System.out.println("d_dtMddVz = " + d_dtMddVz);
        System.out.println("d_dtSudPx = " + d_dtSudPx);
        System.out.println("d_dtSudPy = " + d_dtSudPy);
        System.out.println("d_dtSudPz = " + d_dtSudPz);
        System.out.println("d_dtSudVx = " + d_dtSudVx);
        System.out.println("d_dtSudVy = " + d_dtSudVy);
        System.out.println("d_dtSudVz = " + d_dtSudVz);
        System.out.println("d_dt2dPx = " + d_dt2dPx);
        System.out.println("d_dt2dPy = " + d_dt2dPy);
        System.out.println("d_dt2dPz = " + d_dt2dPz);
        System.out.println("d_dt2dVx = " + d_dt2dVx);
        System.out.println("d_dt2dVy = " + d_dt2dVy);
        System.out.println("d_dt2dVz = " + d_dt2dVz);
        System.out.println("d_dtSddPx = " + d_dtSddPx);
        System.out.println("d_dtSddPy = " + d_dtSddPy);
        System.out.println("d_dtSddPz = " + d_dtSddPz);
        System.out.println("d_dtSddVx = " + d_dtSddVx);
        System.out.println("d_dtSddVy = " + d_dtSddVy);
        System.out.println("d_dtSddVz = " + d_dtSddVz);
        System.out.println("d_dtMudPx = " + d_dtMudPx);
        System.out.println("d_dtMudPy = " + d_dtMudPy);
        System.out.println("d_dtMudPz = " + d_dtMudPz);
        System.out.println("d_dtMudVx = " + d_dtMudVx);
        System.out.println("d_dtMudVy = " + d_dtMudVy);
        System.out.println("d_dtMudVz = " + d_dtMudVz);
        System.out.println("d_dt1dPx = " + d_dt1dPx);
        System.out.println("d_dt1dPy = " + d_dt1dPy);
        System.out.println("d_dt1dPz = " + d_dt1dPz);
        System.out.println("d_dt1dVx = " + d_dt1dVx);
        System.out.println("d_dt1dVy = " + d_dt1dVy);
        System.out.println("d_dt1dVz = " + d_dt1dVz);
        System.out.println("d_dRdPx = " + d_dRdPx);
        System.out.println("d_dRdPy = " + d_dRdPy);
        System.out.println("d_dRdPz = " + d_dRdPz);
        System.out.println("d_dRdVx = " + d_dRdVx);
        System.out.println("d_dRdVy = " + d_dRdVy);
        System.out.println("d_dRdVz = " + d_dRdVz);
        System.out.println("d_dtMddQMx = " + d_dtMddQMx);
        System.out.println("d_dtMddQMy = " + d_dtMddQMy);
        System.out.println("d_dtMddQMz = " + d_dtMddQMz);
        System.out.println("d_dtMddQSx = " + d_dtMddQSx);
        System.out.println("d_dtMddQSy = " + d_dtMddQSy);
        System.out.println("d_dtMddQSz = " + d_dtMddQSz);
        System.out.println("d_dtSudQMx = " + d_dtSudQMx);
        System.out.println("d_dtSudQMy = " + d_dtSudQMy);
        System.out.println("d_dtSudQMz = " + d_dtSudQMz);
        System.out.println("d_dtSudQSx = " + d_dtSudQSx);
        System.out.println("d_dtSudQSy = " + d_dtSudQSy);
        System.out.println("d_dtSudQSz = " + d_dtSudQSz);
        System.out.println("d_dt2dQMx = " + d_dt2dQMx);
        System.out.println("d_dt2dQMy = " + d_dt2dQMy);
        System.out.println("d_dt2dQMz = " + d_dt2dQMz);
        System.out.println("d_dt2dQSx = " + d_dt2dQSx);
        System.out.println("d_dt2dQSy = " + d_dt2dQSy);
        System.out.println("d_dt2dQSz = " + d_dt2dQSz);
        System.out.println("d_dtSddQMx = " + d_dtSddQMx);
        System.out.println("d_dtSddQMy = " + d_dtSddQMy);
        System.out.println("d_dtSddQMz = " + d_dtSddQMz);
        System.out.println("d_dtSddQSx = " + d_dtSddQSx);
        System.out.println("d_dtSddQSy = " + d_dtSddQSy);
        System.out.println("d_dtSddQSz = " + d_dtSddQSz);
        System.out.println("d_dtMudQMx = " + d_dtMudQMx);
        System.out.println("d_dtMudQMy = " + d_dtMudQMy);
        System.out.println("d_dtMudQMz = " + d_dtMudQMz);
        System.out.println("d_dtMudQSx = " + d_dtMudQSx);
        System.out.println("d_dtMudQSy = " + d_dtMudQSy);
        System.out.println("d_dtMudQSz = " + d_dtMudQSz);
        System.out.println("d_dt1dQMx = " + d_dt1dQMx);
        System.out.println("d_dt1dQMy = " + d_dt1dQMy);
        System.out.println("d_dt1dQMz = " + d_dt1dQMz);
        System.out.println("d_dt1dQSx = " + d_dt1dQSx);
        System.out.println("d_dt1dQSy = " + d_dt1dQSy);
        System.out.println("d_dt1dQSz = " + d_dt1dQSz);
        System.out.println("d_dRdQMx = " + d_dRdQMx);
        System.out.println("d_dRdQMy = " + d_dRdQMy);
        System.out.println("d_dRdQMz = " + d_dRdQMz);
        System.out.println("d_dRdQSx = " + d_dRdQSx);
        System.out.println("d_dRdQSy = " + d_dRdQSy);
        System.out.println("d_dRdQSz = " + d_dRdQSz);
    }
    // Dummy return
    return estimated;
}

Example 2 with FieldTransform

use of org.orekit.frames.FieldTransform in project Orekit by CS-SI.

the class EstimationTestUtils method geoStationnaryContext.

public static Context geoStationnaryContext(final String dataRoot) throws OrekitException {
    Utils.setDataRoot(dataRoot);
    Context context = new Context();
    context.conventions = IERSConventions.IERS_2010;
    context.utc = TimeScalesFactory.getUTC();
    context.ut1 = TimeScalesFactory.getUT1(context.conventions, true);
    context.displacements = new StationDisplacement[0];
    String Myframename = "MyEarthFrame";
    final AbsoluteDate datedef = new AbsoluteDate(2000, 1, 1, 12, 0, 0.0, context.utc);
    final double omega = Constants.WGS84_EARTH_ANGULAR_VELOCITY;
    final Vector3D rotationRate = new Vector3D(0.0, 0.0, omega);
    TransformProvider MyEarthFrame = new TransformProvider() {

        private static final long serialVersionUID = 1L;

        public Transform getTransform(final AbsoluteDate date) {
            final double rotationduration = date.durationFrom(datedef);
            final Vector3D alpharot = new Vector3D(rotationduration, rotationRate);
            final Rotation rotation = new Rotation(Vector3D.PLUS_K, -alpharot.getZ(), RotationConvention.VECTOR_OPERATOR);
            return new Transform(date, rotation, rotationRate);
        }

        public <T extends RealFieldElement<T>> FieldTransform<T> getTransform(final FieldAbsoluteDate<T> date) {
            final T rotationduration = date.durationFrom(datedef);
            final FieldVector3D<T> alpharot = new FieldVector3D<>(rotationduration, rotationRate);
            final FieldRotation<T> rotation = new FieldRotation<>(FieldVector3D.getPlusK(date.getField()), alpharot.getZ().negate(), RotationConvention.VECTOR_OPERATOR);
            return new FieldTransform<>(date, rotation, new FieldVector3D<>(date.getField(), rotationRate));
        }
    };
    Frame FrameTest = new Frame(FramesFactory.getEME2000(), MyEarthFrame, Myframename, true);
    // Earth is spherical, rotating in one sidereal day
    context.earth = new OneAxisEllipsoid(Constants.WGS84_EARTH_EQUATORIAL_RADIUS, 0.0, FrameTest);
    context.sun = CelestialBodyFactory.getSun();
    context.moon = CelestialBodyFactory.getMoon();
    context.radiationSensitive = new IsotropicRadiationClassicalConvention(2.0, 0.2, 0.8);
    context.dragSensitive = new IsotropicDrag(2.0, 1.2);
    GravityFieldFactory.addPotentialCoefficientsReader(new GRGSFormatReader("grim4s4_gr", true));
    AstronomicalAmplitudeReader aaReader = new AstronomicalAmplitudeReader("hf-fes2004.dat", 5, 2, 3, 1.0);
    DataProvidersManager.getInstance().feed(aaReader.getSupportedNames(), aaReader);
    Map<Integer, Double> map = aaReader.getAstronomicalAmplitudesMap();
    GravityFieldFactory.addOceanTidesReader(new FESCHatEpsilonReader("fes2004-7x7.dat", 0.01, FastMath.toRadians(1.0), OceanLoadDeformationCoefficients.IERS_2010, map));
    context.gravity = GravityFieldFactory.getNormalizedProvider(20, 20);
    // semimajor axis for a geostationnary satellite
    double da = FastMath.cbrt(context.gravity.getMu() / (omega * omega));
    // context.stations = Arrays.asList(context.createStation(  0.0,  0.0, 0.0, "Lat0_Long0"),
    // context.createStation( 62.29639,   -7.01250,  880.0, "Slættaratindur")
    // );
    context.stations = Arrays.asList(context.createStation(0.0, 0.0, 0.0, "Lat0_Long0"));
    // Station position & velocity in EME2000
    final Vector3D geovelocity = new Vector3D(0., 0., 0.);
    // Compute the frames transformation from station frame to EME2000
    Transform topoToEME = context.stations.get(0).getBaseFrame().getTransformTo(FramesFactory.getEME2000(), new AbsoluteDate(2000, 1, 1, 12, 0, 0.0, context.utc));
    // Station position in EME2000 at reference date
    Vector3D stationPositionEME = topoToEME.transformPosition(Vector3D.ZERO);
    // Satellite position and velocity in Station Frame
    final Vector3D sat_pos = new Vector3D(0., 0., da - stationPositionEME.getNorm());
    final Vector3D acceleration = new Vector3D(-context.gravity.getMu(), sat_pos);
    final PVCoordinates pv_sat_topo = new PVCoordinates(sat_pos, geovelocity, acceleration);
    // satellite position in EME2000
    final PVCoordinates pv_sat_iner = topoToEME.transformPVCoordinates(pv_sat_topo);
    // Geo-stationary Satellite Orbit, tightly above the station (l0-L0)
    context.initialOrbit = new KeplerianOrbit(pv_sat_iner, FramesFactory.getEME2000(), new AbsoluteDate(2000, 1, 1, 12, 0, 0.0, context.utc), context.gravity.getMu());
    context.stations = Arrays.asList(context.createStation(10.0, 45.0, 0.0, "Lat10_Long45"));
    // Turn-around range stations
    // Map entry = master station
    // Map value = slave station associated
    context.TARstations = new HashMap<GroundStation, GroundStation>();
    context.TARstations.put(context.createStation(41.977, 13.600, 671.354, "Fucino"), context.createStation(43.604, 1.444, 263.0, "Toulouse"));
    context.TARstations.put(context.createStation(49.867, 8.65, 144.0, "Darmstadt"), context.createStation(-25.885, 27.707, 1566.633, "Pretoria"));
    return context;
}

Example 3 with FieldTransform

use of org.orekit.frames.FieldTransform in project Orekit by CS-SI.

the class Geoid method getIntersectionPoint.

/**
 * {@inheritDoc}
 *
 * <p> The intersection point is computed using a line search along the
 * specified line. This is accurate when the geoid is slowly varying.
 */
@Override
public <T extends RealFieldElement<T>> FieldGeodeticPoint<T> getIntersectionPoint(final FieldLine<T> lineInFrame, final FieldVector3D<T> closeInFrame, final Frame frame, final FieldAbsoluteDate<T> date) throws OrekitException {
    final Field<T> field = date.getField();
    /*
         * It is assumed that the geoid is slowly varying over it's entire
         * surface. Therefore there will one local intersection.
         */
    // transform to body frame
    final Frame bodyFrame = this.getBodyFrame();
    final FieldTransform<T> frameToBody = frame.getTransformTo(bodyFrame, date);
    final FieldVector3D<T> close = frameToBody.transformPosition(closeInFrame);
    final FieldLine<T> lineInBodyFrame = frameToBody.transformLine(lineInFrame);
    // set the line's direction so the solved for value is always positive
    final FieldLine<T> line;
    if (lineInBodyFrame.getAbscissa(close).getReal() < 0) {
        line = lineInBodyFrame.revert();
    } else {
        line = lineInBodyFrame;
    }
    final ReferenceEllipsoid ellipsoid = this.getEllipsoid();
    // calculate end points
    // distance from line to center of earth, squared
    final T d2 = line.pointAt(0.0).getNormSq();
    // the minimum abscissa, squared
    final double n = ellipsoid.getPolarRadius() + MIN_UNDULATION;
    final T minAbscissa2 = d2.negate().add(n * n);
    // smaller end point of the interval = 0.0 or intersection with
    // min_undulation sphere
    final T lowPoint = minAbscissa2.getReal() < 0 ? field.getZero() : minAbscissa2.sqrt();
    // the maximum abscissa, squared
    final double x = ellipsoid.getEquatorialRadius() + MAX_UNDULATION;
    final T maxAbscissa2 = d2.negate().add(x * x);
    // larger end point of the interval
    final T highPoint = maxAbscissa2.sqrt();
    // line search function
    final RealFieldUnivariateFunction<T> heightFunction = z -> {
        try {
            final FieldGeodeticPoint<T> geodetic = transform(line.pointAt(z), bodyFrame, date);
            return geodetic.getAltitude();
        } catch (OrekitException e) {
            // due to frame transform -> re-throw
            throw new RuntimeException(e);
        }
    };
    // compute answer
    if (maxAbscissa2.getReal() < 0) {
        // ray does not pierce bounding sphere -> no possible intersection
        return null;
    }
    // solve line search problem to find the intersection
    final FieldBracketingNthOrderBrentSolver<T> solver = new FieldBracketingNthOrderBrentSolver<>(field.getZero().add(1.0e-14), field.getZero().add(1.0e-6), field.getZero().add(1.0e-15), 5);
    try {
        final T abscissa = solver.solve(MAX_EVALUATIONS, heightFunction, lowPoint, highPoint, AllowedSolution.ANY_SIDE);
        // return intersection point
        return this.transform(line.pointAt(abscissa), bodyFrame, date);
    } catch (MathRuntimeException e) {
        // no intersection
        return null;
    }
}

Example 4 with FieldTransform

use of org.orekit.frames.FieldTransform in project Orekit by CS-SI.

the class LofOffsetPointing method getTargetPV.

/**
 * {@inheritDoc}
 */
public <T extends RealFieldElement<T>> TimeStampedFieldPVCoordinates<T> getTargetPV(final FieldPVCoordinatesProvider<T> pvProv, final FieldAbsoluteDate<T> date, final Frame frame) throws OrekitException {
    // sample intersection points in current date neighborhood
    final double h = 0.1;
    final List<TimeStampedFieldPVCoordinates<T>> sample = new ArrayList<>();
    FieldTransform<T> centralRefToBody = null;
    for (int i = -1; i < 2; ++i) {
        final FieldAbsoluteDate<T> shifted = date.shiftedBy(i * h);
        // transform from specified reference frame to spacecraft frame
        final FieldTransform<T> refToSc = new FieldTransform<>(shifted, new FieldTransform<>(shifted, pvProv.getPVCoordinates(shifted, frame).negate()), new FieldTransform<>(shifted, attitudeLaw.getAttitude(pvProv, shifted, frame).getOrientation()));
        // transform from specified reference frame to body frame
        final FieldTransform<T> refToBody = frame.getTransformTo(shape.getBodyFrame(), shifted);
        if (i == 0) {
            centralRefToBody = refToBody;
        }
        sample.add(losIntersectionWithBody(new FieldTransform<>(shifted, refToSc.getInverse(), refToBody)));
    }
    // use interpolation to compute properly the time-derivatives
    final TimeStampedFieldPVCoordinates<T> targetBody = TimeStampedFieldPVCoordinates.interpolate(date, CartesianDerivativesFilter.USE_P, sample);
    // convert back to caller specified frame
    return centralRefToBody.getInverse().transformPVCoordinates(targetBody);
}

Example 5 with FieldTransform

use of org.orekit.frames.FieldTransform in project Orekit by CS-SI.

the class RangeAnalytic method theoreticalEvaluationValidation.

/**
 * Added for validation
 * Compares directly numeric and analytic computations
 * @param iteration
 * @param evaluation
 * @param state
 * @return
 * @throws OrekitException
 */
protected EstimatedMeasurement<Range> theoreticalEvaluationValidation(final int iteration, final int evaluation, final SpacecraftState state) throws OrekitException {
    // Station & DSFactory attributes from parent Range class
    final GroundStation groundStation = getStation();
    // get the number of parameters used for derivation
    int nbParams = 6;
    final Map<String, Integer> indices = new HashMap<>();
    for (ParameterDriver driver : getParametersDrivers()) {
        if (driver.isSelected()) {
            indices.put(driver.getName(), nbParams++);
        }
    }
    final DSFactory dsFactory = new DSFactory(nbParams, 1);
    final Field<DerivativeStructure> field = dsFactory.getDerivativeField();
    final FieldVector3D<DerivativeStructure> zero = FieldVector3D.getZero(field);
    // Range derivatives are computed with respect to spacecraft state in inertial frame
    // and station position in station's offset frame
    // -------
    // 
    // Parameters:
    // - 0..2 - Px, Py, Pz   : Position of the spacecraft in inertial frame
    // - 3..5 - Vx, Vy, Vz   : Velocity of the spacecraft in inertial frame
    // - 6..8 - QTx, QTy, QTz: Position of the station in station's offset frame
    // Coordinates of the spacecraft expressed as a derivative structure
    final TimeStampedFieldPVCoordinates<DerivativeStructure> pvaDS = getCoordinates(state, 0, dsFactory);
    // transform between station and inertial frame, expressed as a derivative structure
    // The components of station's position in offset frame are the 3 last derivative parameters
    final AbsoluteDate downlinkDate = getDate();
    final FieldAbsoluteDate<DerivativeStructure> downlinkDateDS = new FieldAbsoluteDate<>(field, downlinkDate);
    final FieldTransform<DerivativeStructure> offsetToInertialDownlink = groundStation.getOffsetToInertial(state.getFrame(), downlinkDateDS, dsFactory, indices);
    // Station position in inertial frame at end of the downlink leg
    final TimeStampedFieldPVCoordinates<DerivativeStructure> stationDownlink = offsetToInertialDownlink.transformPVCoordinates(new TimeStampedFieldPVCoordinates<>(downlinkDateDS, zero, zero, zero));
    // Compute propagation times
    // (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 delay
    final DerivativeStructure tauD = signalTimeOfFlight(pvaDS, stationDownlink.getPosition(), downlinkDateDS);
    // Transit state
    final double delta = downlinkDate.durationFrom(state.getDate());
    final DerivativeStructure tauDMDelta = tauD.negate().add(delta);
    final SpacecraftState transitState = state.shiftedBy(tauDMDelta.getValue());
    // Transit state position (re)computed with derivative structures
    final TimeStampedFieldPVCoordinates<DerivativeStructure> transitStateDS = pvaDS.shiftedBy(tauDMDelta);
    // Station at transit state date (derivatives of tauD taken into account)
    final TimeStampedFieldPVCoordinates<DerivativeStructure> stationAtTransitDate = stationDownlink.shiftedBy(tauD.negate());
    // Uplink delay
    final DerivativeStructure tauU = signalTimeOfFlight(stationAtTransitDate, transitStateDS.getPosition(), transitStateDS.getDate());
    // Prepare the evaluation
    final EstimatedMeasurement<Range> estimated = new EstimatedMeasurement<Range>(this, iteration, evaluation, new SpacecraftState[] { transitState }, null);
    // Range value
    final DerivativeStructure tau = tauD.add(tauU);
    final double cOver2 = 0.5 * Constants.SPEED_OF_LIGHT;
    final DerivativeStructure range = tau.multiply(cOver2);
    estimated.setEstimatedValue(range.getValue());
    // Range partial derivatives with respect to state
    final double[] derivatives = range.getAllDerivatives();
    estimated.setStateDerivatives(0, Arrays.copyOfRange(derivatives, 1, 7));
    // (beware element at index 0 is the value, not a derivative)
    for (final ParameterDriver driver : getParametersDrivers()) {
        final Integer index = indices.get(driver.getName());
        if (index != null) {
            estimated.setParameterDerivatives(driver, derivatives[index + 1]);
        }
    }
    // ----------
    // VALIDATION
    // -----------
    // Computation of the value without DS
    // ----------------------------------
    // Time difference between t (date of the measurement) and t' (date tagged in spacecraft state)
    // Station position at signal arrival
    final Transform topoToInertDownlink = groundStation.getOffsetToInertial(state.getFrame(), downlinkDate);
    final PVCoordinates QDownlink = topoToInertDownlink.transformPVCoordinates(PVCoordinates.ZERO);
    // Downlink time of flight from spacecraft to station
    final double td = signalTimeOfFlight(state.getPVCoordinates(), QDownlink.getPosition(), downlinkDate);
    final double dt = delta - td;
    // Transit state position
    final AbsoluteDate transitT = state.getDate().shiftedBy(dt);
    final SpacecraftState transit = state.shiftedBy(dt);
    final Vector3D transitP = transitState.getPVCoordinates().getPosition();
    // Station position at signal departure
    // First guess
    // AbsoluteDate uplinkDate = downlinkDate.shiftedBy(-getObservedValue()[0] / cOver2);
    // final Transform topoToInertUplink =
    // station.getOffsetFrame().getTransformTo(state.getFrame(), uplinkDate);
    // TimeStampedPVCoordinates QUplink = topoToInertUplink.
    // transformPVCoordinates(new TimeStampedPVCoordinates(uplinkDate, PVCoordinates.ZERO));
    // Station position at transit state date
    final Transform topoToInertAtTransitDate = groundStation.getOffsetToInertial(state.getFrame(), transitT);
    TimeStampedPVCoordinates QAtTransitDate = topoToInertAtTransitDate.transformPVCoordinates(new TimeStampedPVCoordinates(transitT, PVCoordinates.ZERO));
    // Uplink time of flight
    final double tu = signalTimeOfFlight(QAtTransitDate, transitP, transitT);
    // Total time of flight
    final double t = td + tu;
    // Real date and position of station at signal departure
    AbsoluteDate uplinkDate = downlinkDate.shiftedBy(-t);
    TimeStampedPVCoordinates QUplink = topoToInertDownlink.shiftedBy(-t).transformPVCoordinates(new TimeStampedPVCoordinates(uplinkDate, PVCoordinates.ZERO));
    // Range value
    double r = t * cOver2;
    double dR = r - range.getValue();
    // td derivatives / state
    // -----------------------
    // Qt = Master station position at tmeas = t = signal arrival at master station
    final Vector3D vel = state.getPVCoordinates().getVelocity();
    final Vector3D Qt_V = QDownlink.getVelocity();
    final Vector3D Ptr = transit.getPVCoordinates().getPosition();
    final Vector3D Ptr_Qt = QDownlink.getPosition().subtract(Ptr);
    final double dDown = Constants.SPEED_OF_LIGHT * Constants.SPEED_OF_LIGHT * td - Vector3D.dotProduct(Ptr_Qt, vel);
    // Derivatives of the downlink time of flight
    final double dtddPx = -Ptr_Qt.getX() / dDown;
    final double dtddPy = -Ptr_Qt.getY() / dDown;
    final double dtddPz = -Ptr_Qt.getZ() / dDown;
    final double dtddVx = dtddPx * dt;
    final double dtddVy = dtddPy * dt;
    final double dtddVz = dtddPz * dt;
    // From the DS
    final double dtddPxDS = tauD.getPartialDerivative(1, 0, 0, 0, 0, 0, 0, 0, 0);
    final double dtddPyDS = tauD.getPartialDerivative(0, 1, 0, 0, 0, 0, 0, 0, 0);
    final double dtddPzDS = tauD.getPartialDerivative(0, 0, 1, 0, 0, 0, 0, 0, 0);
    final double dtddVxDS = tauD.getPartialDerivative(0, 0, 0, 1, 0, 0, 0, 0, 0);
    final double dtddVyDS = tauD.getPartialDerivative(0, 0, 0, 0, 1, 0, 0, 0, 0);
    final double dtddVzDS = tauD.getPartialDerivative(0, 0, 0, 0, 0, 1, 0, 0, 0);
    // Difference
    final double d_dtddPx = dtddPxDS - dtddPx;
    final double d_dtddPy = dtddPyDS - dtddPy;
    final double d_dtddPz = dtddPzDS - dtddPz;
    final double d_dtddVx = dtddVxDS - dtddVx;
    final double d_dtddVy = dtddVyDS - dtddVy;
    final double d_dtddVz = dtddVzDS - dtddVz;
    // tu derivatives / state
    // -----------------------
    final Vector3D Qt2_Ptr = Ptr.subtract(QUplink.getPosition());
    final double dUp = Constants.SPEED_OF_LIGHT * Constants.SPEED_OF_LIGHT * tu - Vector3D.dotProduct(Qt2_Ptr, Qt_V);
    // test
    // // Speed of the station at tmeas-t
    // // Note: Which one to use in the calculation of dUp ???
    // final Vector3D Qt2_V    = QUplink.getVelocity();
    // final double   dUp      = Constants.SPEED_OF_LIGHT * Constants.SPEED_OF_LIGHT * tu -
    // Vector3D.dotProduct(Qt2_Ptr, Qt2_V);
    // test
    // tu derivatives
    final double dtudPx = 1. / dUp * Qt2_Ptr.dotProduct(Vector3D.PLUS_I.add((Qt_V.subtract(vel)).scalarMultiply(dtddPx)));
    final double dtudPy = 1. / dUp * Qt2_Ptr.dotProduct(Vector3D.PLUS_J.add((Qt_V.subtract(vel)).scalarMultiply(dtddPy)));
    final double dtudPz = 1. / dUp * Qt2_Ptr.dotProduct(Vector3D.PLUS_K.add((Qt_V.subtract(vel)).scalarMultiply(dtddPz)));
    final double dtudVx = dtudPx * dt;
    final double dtudVy = dtudPy * dt;
    final double dtudVz = dtudPz * dt;
    // From the DS
    final double dtudPxDS = tauU.getPartialDerivative(1, 0, 0, 0, 0, 0, 0, 0, 0);
    final double dtudPyDS = tauU.getPartialDerivative(0, 1, 0, 0, 0, 0, 0, 0, 0);
    final double dtudPzDS = tauU.getPartialDerivative(0, 0, 1, 0, 0, 0, 0, 0, 0);
    final double dtudVxDS = tauU.getPartialDerivative(0, 0, 0, 1, 0, 0, 0, 0, 0);
    final double dtudVyDS = tauU.getPartialDerivative(0, 0, 0, 0, 1, 0, 0, 0, 0);
    final double dtudVzDS = tauU.getPartialDerivative(0, 0, 0, 0, 0, 1, 0, 0, 0);
    // Difference
    final double d_dtudPx = dtudPxDS - dtudPx;
    final double d_dtudPy = dtudPyDS - dtudPy;
    final double d_dtudPz = dtudPzDS - dtudPz;
    final double d_dtudVx = dtudVxDS - dtudVx;
    final double d_dtudVy = dtudVyDS - dtudVy;
    final double d_dtudVz = dtudVzDS - dtudVz;
    // Range derivatives / state
    // -----------------------
    // R = Range
    double dRdPx = (dtddPx + dtudPx) * cOver2;
    double dRdPy = (dtddPy + dtudPy) * cOver2;
    double dRdPz = (dtddPz + dtudPz) * cOver2;
    double dRdVx = (dtddVx + dtudVx) * cOver2;
    double dRdVy = (dtddVy + dtudVy) * cOver2;
    double dRdVz = (dtddVz + dtudVz) * cOver2;
    // With DS
    double dRdPxDS = range.getPartialDerivative(1, 0, 0, 0, 0, 0, 0, 0, 0);
    double dRdPyDS = range.getPartialDerivative(0, 1, 0, 0, 0, 0, 0, 0, 0);
    double dRdPzDS = range.getPartialDerivative(0, 0, 1, 0, 0, 0, 0, 0, 0);
    double dRdVxDS = range.getPartialDerivative(0, 0, 0, 1, 0, 0, 0, 0, 0);
    double dRdVyDS = range.getPartialDerivative(0, 0, 0, 0, 1, 0, 0, 0, 0);
    double dRdVzDS = range.getPartialDerivative(0, 0, 0, 0, 0, 1, 0, 0, 0);
    // Diff
    final double d_dRdPx = dRdPxDS - dRdPx;
    final double d_dRdPy = dRdPyDS - dRdPy;
    final double d_dRdPz = dRdPzDS - dRdPz;
    final double d_dRdVx = dRdVxDS - dRdVx;
    final double d_dRdVy = dRdVyDS - dRdVy;
    final double d_dRdVz = dRdVzDS - dRdVz;
    // td derivatives / station
    // -----------------------
    final AngularCoordinates ac = topoToInertDownlink.getAngular().revert();
    final Rotation rotTopoToInert = ac.getRotation();
    final Vector3D omega = ac.getRotationRate();
    final Vector3D dtddQI = Ptr_Qt.scalarMultiply(1. / dDown);
    final double dtddQIx = dtddQI.getX();
    final double dtddQIy = dtddQI.getY();
    final double dtddQIz = dtddQI.getZ();
    final Vector3D dtddQ = rotTopoToInert.applyTo(dtddQI);
    // With DS
    double dtddQxDS = tauD.getPartialDerivative(0, 0, 0, 0, 0, 0, 1, 0, 0);
    double dtddQyDS = tauD.getPartialDerivative(0, 0, 0, 0, 0, 0, 0, 1, 0);
    double dtddQzDS = tauD.getPartialDerivative(0, 0, 0, 0, 0, 0, 0, 0, 1);
    // Diff
    final double d_dtddQx = dtddQxDS - dtddQ.getX();
    final double d_dtddQy = dtddQyDS - dtddQ.getY();
    final double d_dtddQz = dtddQzDS - dtddQ.getZ();
    // tu derivatives / station
    // -----------------------
    // Inertial frame
    final double dtudQIx = 1 / dUp * Qt2_Ptr.dotProduct(Vector3D.MINUS_I.add((Qt_V.subtract(vel)).scalarMultiply(dtddQIx)).subtract(Vector3D.PLUS_I.crossProduct(omega).scalarMultiply(t)));
    final double dtudQIy = 1 / dUp * Qt2_Ptr.dotProduct(Vector3D.MINUS_J.add((Qt_V.subtract(vel)).scalarMultiply(dtddQIy)).subtract(Vector3D.PLUS_J.crossProduct(omega).scalarMultiply(t)));
    final double dtudQIz = 1 / dUp * Qt2_Ptr.dotProduct(Vector3D.MINUS_K.add((Qt_V.subtract(vel)).scalarMultiply(dtddQIz)).subtract(Vector3D.PLUS_K.crossProduct(omega).scalarMultiply(t)));
    // // test
    // final double dtudQIx = 1/dUp*Qt2_Ptr
    // //                        .dotProduct(Vector3D.MINUS_I);
    // //                                    .dotProduct((Qt_V.subtract(vel)).scalarMultiply(dtddQIx));
    // .dotProduct(Vector3D.MINUS_I.crossProduct(omega).scalarMultiply(t));
    // final double dtudQIy = 1/dUp*Qt2_Ptr
    // //                        .dotProduct(Vector3D.MINUS_J);
    // //                                    .dotProduct((Qt_V.subtract(vel)).scalarMultiply(dtddQIy));
    // .dotProduct(Vector3D.MINUS_J.crossProduct(omega).scalarMultiply(t));
    // final double dtudQIz = 1/dUp*Qt2_Ptr
    // //                        .dotProduct(Vector3D.MINUS_K);
    // //                                    .dotProduct((Qt_V.subtract(vel)).scalarMultiply(dtddQIz));
    // .dotProduct(Vector3D.MINUS_K.crossProduct(omega).scalarMultiply(t));
    // 
    // double dtu_dQxDS = tauU.getPartialDerivative(0, 0, 0, 0, 0, 0, 1, 0, 0);
    // double dtu_dQyDS = tauU.getPartialDerivative(0, 0, 0, 0, 0, 0, 0, 1, 0);
    // double dtu_dQzDS = tauU.getPartialDerivative(0, 0, 0, 0, 0, 0, 0, 0, 1);
    // final Vector3D dtudQDS = new Vector3D(dtu_dQxDS, dtu_dQyDS, dtu_dQzDS);
    // final Vector3D dtudQIDS = rotTopoToInert.applyInverseTo(dtudQDS);
    // double dtudQIxDS = dtudQIDS.getX();
    // double dtudQIyDS = dtudQIDS.getY();
    // double dtudQIxzS = dtudQIDS.getZ();
    // // test
    // Topocentric frame
    final Vector3D dtudQI = new Vector3D(dtudQIx, dtudQIy, dtudQIz);
    final Vector3D dtudQ = rotTopoToInert.applyTo(dtudQI);
    // With DS
    double dtudQxDS = tauU.getPartialDerivative(0, 0, 0, 0, 0, 0, 1, 0, 0);
    double dtudQyDS = tauU.getPartialDerivative(0, 0, 0, 0, 0, 0, 0, 1, 0);
    double dtudQzDS = tauU.getPartialDerivative(0, 0, 0, 0, 0, 0, 0, 0, 1);
    // Diff
    final double d_dtudQx = dtudQxDS - dtudQ.getX();
    final double d_dtudQy = dtudQyDS - dtudQ.getY();
    final double d_dtudQz = dtudQzDS - dtudQ.getZ();
    // Range derivatives / station
    // -----------------------
    double dRdQx = (dtddQ.getX() + dtudQ.getX()) * cOver2;
    double dRdQy = (dtddQ.getY() + dtudQ.getY()) * cOver2;
    double dRdQz = (dtddQ.getZ() + dtudQ.getZ()) * cOver2;
    // With DS
    double dRdQxDS = range.getPartialDerivative(0, 0, 0, 0, 0, 0, 1, 0, 0);
    double dRdQyDS = range.getPartialDerivative(0, 0, 0, 0, 0, 0, 0, 1, 0);
    double dRdQzDS = range.getPartialDerivative(0, 0, 0, 0, 0, 0, 0, 0, 1);
    // Diff
    final double d_dRdQx = dRdQxDS - dRdQx;
    final double d_dRdQy = dRdQyDS - dRdQy;
    final double d_dRdQz = dRdQzDS - dRdQz;
    // Print results to avoid warning
    final boolean printResults = false;
    if (printResults) {
        System.out.println("dR = " + dR);
        System.out.println("d_dtddPx = " + d_dtddPx);
        System.out.println("d_dtddPy = " + d_dtddPy);
        System.out.println("d_dtddPz = " + d_dtddPz);
        System.out.println("d_dtddVx = " + d_dtddVx);
        System.out.println("d_dtddVy = " + d_dtddVy);
        System.out.println("d_dtddVz = " + d_dtddVz);
        System.out.println("d_dtudPx = " + d_dtudPx);
        System.out.println("d_dtudPy = " + d_dtudPy);
        System.out.println("d_dtudPz = " + d_dtudPz);
        System.out.println("d_dtudVx = " + d_dtudVx);
        System.out.println("d_dtudVy = " + d_dtudVy);
        System.out.println("d_dtudVz = " + d_dtudVz);
        System.out.println("d_dRdPx = " + d_dRdPx);
        System.out.println("d_dRdPy = " + d_dRdPy);
        System.out.println("d_dRdPz = " + d_dRdPz);
        System.out.println("d_dRdVx = " + d_dRdVx);
        System.out.println("d_dRdVy = " + d_dRdVy);
        System.out.println("d_dRdVz = " + d_dRdVz);
        System.out.println("d_dtddQx = " + d_dtddQx);
        System.out.println("d_dtddQy = " + d_dtddQy);
        System.out.println("d_dtddQz = " + d_dtddQz);
        System.out.println("d_dtudQx = " + d_dtudQx);
        System.out.println("d_dtudQy = " + d_dtudQy);
        System.out.println("d_dtudQz = " + d_dtudQz);
        System.out.println("d_dRdQx = " + d_dRdQx);
        System.out.println("d_dRdQy = " + d_dRdQy);
        System.out.println("d_dRdQz = " + d_dRdQz);
    }
    // Dummy return
    return estimated;
}