TDOA.java
/* Copyright 2002-2024 CS GROUP
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* this work for additional information regarding copyright ownership.
* CS licenses this file to You under the Apache License, Version 2.0
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* Unless required by applicable law or agreed to in writing, software
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package org.orekit.estimation.measurements;
import java.util.Arrays;
import org.hipparchus.CalculusFieldElement;
import org.hipparchus.analysis.differentiation.Gradient;
import org.hipparchus.geometry.euclidean.threed.FieldVector3D;
import org.hipparchus.geometry.euclidean.threed.Vector3D;
import org.hipparchus.util.FastMath;
import org.orekit.frames.FieldTransform;
import org.orekit.frames.Transform;
import org.orekit.propagation.SpacecraftState;
import org.orekit.time.AbsoluteDate;
import org.orekit.time.FieldAbsoluteDate;
import org.orekit.utils.Constants;
import org.orekit.utils.ParameterDriver;
import org.orekit.utils.TimeSpanMap.Span;
import org.orekit.utils.TimeStampedFieldPVCoordinates;
import org.orekit.utils.TimeStampedPVCoordinates;
/** Class modeling a Time Difference of Arrival measurement with a satellite as emitter
* and two ground stations as receivers.
* <p>
* TDOA measures the difference in signal arrival time between the emitter and receivers,
* corresponding to a difference in ranges from the two receivers to the emitter.
* </p><p>
* The date of the measurement corresponds to the reception of the signal by the prime station.
* The measurement corresponds to the date of the measurement minus
* the date of reception of the signal by the second station:
* <code>tdoa = tr<sub>1</sub> - tr<sub>2</sub></code>
* </p><p>
* The motion of the stations and the satellite during the signal flight time are taken into account.
* </p>
* @author Pascal Parraud
* @since 11.2
*/
public class TDOA extends GroundReceiverMeasurement<TDOA> {
/** Type of the measurement. */
public static final String MEASUREMENT_TYPE = "TDOA";
/** Second ground station, the one that gives the measurement, i.e. the delay. */
private final GroundStation secondStation;
/** Simple constructor.
* @param primeStation ground station that gives the date of the measurement
* @param secondStation ground station that gives the measurement
* @param date date of the measurement
* @param tdoa observed value (s)
* @param sigma theoretical standard deviation
* @param baseWeight base weight
* @param satellite satellite related to this measurement
*/
public TDOA(final GroundStation primeStation, final GroundStation secondStation,
final AbsoluteDate date, final double tdoa, final double sigma,
final double baseWeight, final ObservableSatellite satellite) {
super(primeStation, false, date, tdoa, sigma, baseWeight, satellite);
// add parameter drivers for the secondary station
addParameterDriver(secondStation.getClockOffsetDriver());
addParameterDriver(secondStation.getEastOffsetDriver());
addParameterDriver(secondStation.getNorthOffsetDriver());
addParameterDriver(secondStation.getZenithOffsetDriver());
addParameterDriver(secondStation.getPrimeMeridianOffsetDriver());
addParameterDriver(secondStation.getPrimeMeridianDriftDriver());
addParameterDriver(secondStation.getPolarOffsetXDriver());
addParameterDriver(secondStation.getPolarDriftXDriver());
addParameterDriver(secondStation.getPolarOffsetYDriver());
addParameterDriver(secondStation.getPolarDriftYDriver());
this.secondStation = secondStation;
}
/** Get the prime ground station, the one that gives the date of the measurement.
* @return prime ground station
*/
public GroundStation getPrimeStation() {
return getStation();
}
/** Get the second ground station, the one that gives the measurement.
* @return second ground station
*/
public GroundStation getSecondStation() {
return secondStation;
}
/** {@inheritDoc} */
@SuppressWarnings("checkstyle:WhitespaceAround")
@Override
protected EstimatedMeasurementBase<TDOA> theoreticalEvaluationWithoutDerivatives(final int iteration, final int evaluation,
final SpacecraftState[] states) {
final GroundReceiverCommonParametersWithoutDerivatives common = computeCommonParametersWithout(states[0]);
final TimeStampedPVCoordinates emitterPV = common.getTransitPV();
final AbsoluteDate emitterDate = emitterPV.getDate();
// Approximate second location at transit time
final Transform secondToInertial =
getSecondStation().getOffsetToInertial(common.getState().getFrame(), emitterDate, true);
final TimeStampedPVCoordinates secondApprox =
secondToInertial.transformPVCoordinates(new TimeStampedPVCoordinates(emitterDate,
Vector3D.ZERO, Vector3D.ZERO, Vector3D.ZERO));
// Time of flight from emitter to second station
final double tau2 = forwardSignalTimeOfFlight(secondApprox, emitterPV.getPosition(), emitterDate);
// Secondary station PV in inertial frame at receive at second station
final TimeStampedPVCoordinates secondPV = secondApprox.shiftedBy(tau2);
// The measured TDOA is (tau1 + clockOffset1) - (tau2 + clockOffset2)
final double offset1 = getPrimeStation().getClockOffsetDriver().getValue(emitterDate);
final double offset2 = getSecondStation().getClockOffsetDriver().getValue(emitterDate);
final double tdoa = (common.getTauD() + offset1) - (tau2 + offset2);
// Evaluate the TDOA value
// -------------------------------------------
final EstimatedMeasurement<TDOA> estimated =
new EstimatedMeasurement<>(this, iteration, evaluation,
new SpacecraftState[] {
common.getTransitState()
},
new TimeStampedPVCoordinates[] {
emitterPV,
tdoa > 0.0 ? secondPV : common.getStationDownlink(),
tdoa > 0.0 ? common.getStationDownlink() : secondPV
});
// set TDOA value
estimated.setEstimatedValue(tdoa);
return estimated;
}
/** {@inheritDoc} */
@Override
protected EstimatedMeasurement<TDOA> theoreticalEvaluation(final int iteration, final int evaluation,
final SpacecraftState[] states) {
final SpacecraftState state = states[0];
// TDOA derivatives are computed with respect to spacecraft state in inertial frame
// and station parameters
// ----------------------
//
// Parameters:
// - 0..2 - Position of the spacecraft in inertial frame
// - 3..5 - Velocity of the spacecraft in inertial frame
// - 6..n - measurements parameters (clock offset, station offsets, pole, prime meridian, sat clock offset...)
final GroundReceiverCommonParametersWithDerivatives common = computeCommonParametersWithDerivatives(state);
final int nbParams = common.getTauD().getFreeParameters();
final TimeStampedFieldPVCoordinates<Gradient> emitterPV = common.getTransitPV();
final FieldAbsoluteDate<Gradient> emitterDate = emitterPV.getDate();
// Approximate secondary location (at emission time)
final FieldVector3D<Gradient> zero = FieldVector3D.getZero(common.getTauD().getField());
final FieldTransform<Gradient> secondToInertial =
getSecondStation().getOffsetToInertial(state.getFrame(), emitterDate, nbParams, common.getIndices());
final TimeStampedFieldPVCoordinates<Gradient> secondApprox =
secondToInertial.transformPVCoordinates(new TimeStampedFieldPVCoordinates<>(emitterDate,
zero, zero, zero));
// Time of flight from emitter to second station
final Gradient tau2 = forwardSignalTimeOfFlight(secondApprox, emitterPV.getPosition(), emitterDate);
// Second station coordinates at receive time
final TimeStampedFieldPVCoordinates<Gradient> secondPV = secondApprox.shiftedBy(tau2);
// The measured TDOA is (tau1 + clockOffset1) - (tau2 + clockOffset2)
final Gradient offset1 = getPrimeStation().getClockOffsetDriver()
.getValue(nbParams, common.getIndices(), emitterDate.toAbsoluteDate());
final Gradient offset2 = getSecondStation().getClockOffsetDriver()
.getValue(nbParams, common.getIndices(), emitterDate.toAbsoluteDate());
final Gradient tdoaG = common.getTauD().add(offset1).subtract(tau2.add(offset2));
final double tdoa = tdoaG.getValue();
// Evaluate the TDOA value and derivatives
// -------------------------------------------
final TimeStampedPVCoordinates pv1 = common.getStationDownlink().toTimeStampedPVCoordinates();
final TimeStampedPVCoordinates pv2 = secondPV.toTimeStampedPVCoordinates();
final EstimatedMeasurement<TDOA> estimated =
new EstimatedMeasurement<>(this, iteration, evaluation,
new SpacecraftState[] {
common.getTransitState()
},
new TimeStampedPVCoordinates[] {
emitterPV.toTimeStampedPVCoordinates(),
tdoa > 0 ? pv2 : pv1,
tdoa > 0 ? pv1 : pv2
});
// set TDOA value
estimated.setEstimatedValue(tdoa);
// set partial derivatives with respect to state
final double[] derivatives = tdoaG.getGradient();
estimated.setStateDerivatives(0, Arrays.copyOfRange(derivatives, 0, 6));
// set partial derivatives with respect to parameters
for (final ParameterDriver driver : getParametersDrivers()) {
for (Span<String> span = driver.getNamesSpanMap().getFirstSpan(); span != null; span = span.next()) {
final Integer index = common.getIndices().get(span.getData());
if (index != null) {
estimated.setParameterDerivatives(driver, span.getStart(), derivatives[index]);
}
}
}
return estimated;
}
/** Compute propagation delay on a link leg (typically downlink or uplink). This differs from signalTimeOfFlight
* through <em>advancing</em> rather than delaying the emitter.
*
* @param adjustableEmitterPV position/velocity of emitter that may be adjusted
* @param receiverPosition fixed position of receiver at {@code signalArrivalDate},
* in the same frame as {@code adjustableEmitterPV}
* @param signalArrivalDate date at which the signal arrives to receiver
* @return <em>positive</em> delay between signal emission and signal reception dates
*/
public static double forwardSignalTimeOfFlight(final TimeStampedPVCoordinates adjustableEmitterPV,
final Vector3D receiverPosition,
final AbsoluteDate signalArrivalDate) {
// initialize emission date search loop assuming the state is already correct
// this will be true for all but the first orbit determination iteration,
// and even for the first iteration the loop will converge very fast
final double offset = signalArrivalDate.durationFrom(adjustableEmitterPV.getDate());
double delay = offset;
// search signal transit date, computing the signal travel in inertial frame
final double cReciprocal = 1.0 / Constants.SPEED_OF_LIGHT;
double delta;
int count = 0;
do {
final double previous = delay;
final Vector3D transitP = adjustableEmitterPV.shiftedBy(delay - offset).getPosition();
delay = receiverPosition.distance(transitP) * cReciprocal;
delta = FastMath.abs(delay - previous);
} while (count++ < 10 && delta >= 2 * FastMath.ulp(delay));
return delay;
}
/** Compute propagation delay on a link leg (typically downlink or uplink).This differs from signalTimeOfFlight
* through <em>advancing</em> rather than delaying the emitter.
*
* @param adjustableEmitterPV position/velocity of emitter that may be adjusted
* @param receiverPosition fixed position of receiver at {@code signalArrivalDate},
* in the same frame as {@code adjustableEmitterPV}
* @param signalArrivalDate date at which the signal arrives to receiver
* @return <em>positive</em> delay between signal emission and signal reception dates
* @param <T> the type of the components
*/
public static <T extends CalculusFieldElement<T>> T forwardSignalTimeOfFlight(final TimeStampedFieldPVCoordinates<T> adjustableEmitterPV,
final FieldVector3D<T> receiverPosition,
final FieldAbsoluteDate<T> signalArrivalDate) {
// Initialize emission date search loop assuming the emitter PV is almost correct
// this will be true for all but the first orbit determination iteration,
// and even for the first iteration the loop will converge extremely fast
final T offset = signalArrivalDate.durationFrom(adjustableEmitterPV.getDate());
T delay = offset;
// search signal transit date, computing the signal travel in the frame shared by emitter and receiver
final double cReciprocal = 1.0 / Constants.SPEED_OF_LIGHT;
double delta;
int count = 0;
do {
final double previous = delay.getReal();
final FieldVector3D<T> transitP = adjustableEmitterPV.shiftedBy(delay.subtract(offset)).getPosition();
delay = receiverPosition.distance(transitP).multiply(cReciprocal);
delta = FastMath.abs(delay.getReal() - previous);
} while (count++ < 10 && delta >= 2 * FastMath.ulp(delay.getReal()));
return delay;
}
}