FieldGnssPropagator.java
/* Copyright 2022-2025 Luc Maisonobe
* Licensed to CS GROUP (CS) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* CS licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
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package org.orekit.propagation.analytical.gnss;
import org.hipparchus.CalculusFieldElement;
import org.hipparchus.Field;
import org.hipparchus.analysis.differentiation.FieldGradient;
import org.hipparchus.analysis.differentiation.FieldUnivariateDerivative2;
import org.hipparchus.geometry.euclidean.threed.FieldVector3D;
import org.hipparchus.geometry.euclidean.threed.Vector3D;
import org.hipparchus.linear.FieldMatrix;
import org.hipparchus.linear.FieldQRDecomposition;
import org.hipparchus.linear.FieldVector;
import org.hipparchus.linear.MatrixUtils;
import org.hipparchus.util.FastMath;
import org.hipparchus.util.FieldSinCos;
import org.hipparchus.util.MathArrays;
import org.orekit.attitudes.AttitudeProvider;
import org.orekit.attitudes.FieldAttitude;
import org.orekit.frames.Frame;
import org.orekit.orbits.FieldCartesianOrbit;
import org.orekit.orbits.FieldKeplerianAnomalyUtility;
import org.orekit.orbits.FieldKeplerianOrbit;
import org.orekit.orbits.FieldOrbit;
import org.orekit.orbits.PositionAngleType;
import org.orekit.propagation.FieldSpacecraftState;
import org.orekit.propagation.analytical.FieldAbstractAnalyticalPropagator;
import org.orekit.propagation.analytical.gnss.data.FieldGnssOrbitalElements;
import org.orekit.propagation.analytical.gnss.data.GNSSOrbitalElements;
import org.orekit.time.FieldAbsoluteDate;
import org.orekit.utils.FieldPVCoordinates;
import org.orekit.utils.ParameterDriver;
import java.util.List;
/** Common handling of {@link FieldAbstractAnalyticalPropagator} methods for GNSS propagators.
* <p>
* This class allows to provide easily a subset of {@link FieldAbstractAnalyticalPropagator} methods
* for specific GNSS propagators.
* </p>
* @author Pascal Parraud
* @author Luc Maisonobe
* @param <T> type of the field elements
* @since 13.0
*/
public class FieldGnssPropagator<T extends CalculusFieldElement<T>> extends FieldAbstractAnalyticalPropagator<T> {
/** Maximum number of iterations for internal loops. */
private static final int MAX_ITER = 100;
/** Tolerance on position for rebuilding orbital elements from initial state. */
private static final double TOL_P = 1.0e-6;
/** Tolerance on velocity for rebuilding orbital elements from initial state. */
private static final double TOL_V = 1.0e-9;
/** Number of free parameters for orbital elements. */
private static final int FREE_PARAMETERS = 6;
/** Convergence parameter. */
private static final double EPS = 1.0e-12;
/** The GNSS propagation model used. */
private FieldGnssOrbitalElements<T, ?> orbitalElements;
/** The ECI frame used for GNSS propagation. */
private final Frame eci;
/** The ECEF frame used for GNSS propagation. */
private final Frame ecef;
/**
* Build a new instance.
* @param orbitalElements GNSS orbital elements
* @param eci Earth Centered Inertial frame
* @param ecef Earth Centered Earth Fixed frame
* @param provider Attitude provider
* @param mass Satellite mass (kg)
*/
public FieldGnssPropagator(final FieldGnssOrbitalElements<T, ?> orbitalElements,
final Frame eci, final Frame ecef,
final AttitudeProvider provider, final T mass) {
super(orbitalElements.getDate().getField(), provider);
// Stores the GNSS orbital elements
this.orbitalElements = orbitalElements;
// Sets the Earth Centered Inertial frame
this.eci = eci;
// Sets the Earth Centered Earth Fixed frame
this.ecef = ecef;
// Sets initial state
final FieldOrbit<T> orbit = propagateOrbit(orbitalElements.getDate(), defaultParameters());
final FieldAttitude<T> attitude = provider.getAttitude(orbit, orbit.getDate(), orbit.getFrame());
// calling the method from base class because the one overridden below recomputes the orbital elements
super.resetInitialState(new FieldSpacecraftState<>(orbit, attitude).withMass(mass));
}
/**
* Build a new instance from an initial state.
* <p>
* The Keplerian elements already present in the {@code nonKeplerianElements} argument
* will be ignored as it is the {@code initialState} argument that will be used to
* build the complete orbital elements of the propagator
* </p>
* @param initialState initial state
* @param nonKeplerianElements non-Keplerian orbital elements (the Keplerian orbital elements will be ignored)
* @param ecef Earth Centered Earth Fixed frame
* @param provider attitude provider
* @param mass spacecraft mass
*/
public FieldGnssPropagator(final FieldSpacecraftState<T> initialState,
final FieldGnssOrbitalElements<T, ?> nonKeplerianElements,
final Frame ecef, final AttitudeProvider provider, final T mass) {
this(buildOrbitalElements(initialState, nonKeplerianElements, ecef, provider, mass),
initialState.getFrame(), ecef, provider, initialState.getMass());
}
/** Build default parameters.
* @return default parameters
*/
private T[] defaultParameters() {
final T[] parameters = MathArrays.buildArray(orbitalElements.getDate().getField(), GNSSOrbitalElements.SIZE);
parameters[GNSSOrbitalElements.TIME_INDEX] = getMU().newInstance(orbitalElements.getTime());
parameters[GNSSOrbitalElements.A_DOT_INDEX] = getMU().newInstance(orbitalElements.getADot());
parameters[GNSSOrbitalElements.DELTA_N0_INDEX] = getMU().newInstance(orbitalElements.getDeltaN0());
parameters[GNSSOrbitalElements.DELTA_N0_DOT_INDEX] = getMU().newInstance(orbitalElements.getDeltaN0Dot());
parameters[GNSSOrbitalElements.I_DOT_INDEX] = getMU().newInstance(orbitalElements.getIDot());
parameters[GNSSOrbitalElements.OMEGA_DOT_INDEX] = getMU().newInstance(orbitalElements.getOmegaDot());
parameters[GNSSOrbitalElements.CUC_INDEX] = getMU().newInstance(orbitalElements.getCuc());
parameters[GNSSOrbitalElements.CUS_INDEX] = getMU().newInstance(orbitalElements.getCus());
parameters[GNSSOrbitalElements.CRC_INDEX] = getMU().newInstance(orbitalElements.getCrc());
parameters[GNSSOrbitalElements.CRS_INDEX] = getMU().newInstance(orbitalElements.getCrs());
parameters[GNSSOrbitalElements.CIC_INDEX] = getMU().newInstance(orbitalElements.getCic());
parameters[GNSSOrbitalElements.CIS_INDEX] = getMU().newInstance(orbitalElements.getCis());
return parameters;
}
/** {@inheritDoc} */
@Override
public List<ParameterDriver> getParametersDrivers() {
return orbitalElements.getParametersDrivers();
}
/**
* Gets the Earth Centered Inertial frame used to propagate the orbit.
*
* @return the ECI frame
*/
public Frame getECI() {
return eci;
}
/**
* Gets the Earth Centered Earth Fixed frame used to propagate GNSS orbits according to the
* Interface Control Document.
*
* @return the ECEF frame
*/
public Frame getECEF() {
return ecef;
}
/**
* Gets the Earth gravity coefficient used for GNSS propagation.
*
* @return the Earth gravity coefficient.
*/
public T getMU() {
return orbitalElements.getMu();
}
/** {@inheritDoc} */
@Override
public FieldOrbit<T> propagateOrbit(final FieldAbsoluteDate<T> date,
final T[] parameters) {
// Gets the PVCoordinates in ECEF frame
final FieldPVCoordinates<T> pvaInECEF = propagateInEcef(date, parameters);
// Transforms the PVCoordinates to ECI frame
final FieldPVCoordinates<T> pvaInECI = ecef.getTransformTo(eci, date).transformPVCoordinates(pvaInECEF);
// Returns the Cartesian orbit
return new FieldCartesianOrbit<>(pvaInECI, eci, date, getMU());
}
/**
* Gets the PVCoordinates of the GNSS SV in {@link #getECEF() ECEF frame}.
*
* <p>The algorithm uses automatic differentiation to compute velocity and
* acceleration.</p>
*
* @param date the computation date
* @param parameters propagation parameters
* @return the GNSS SV PVCoordinates in {@link #getECEF() ECEF frame}
*/
public FieldPVCoordinates<T> propagateInEcef(final FieldAbsoluteDate<T> date, final T[] parameters) {
// Duration from GNSS ephemeris Reference date
final FieldUnivariateDerivative2<T> tk = new FieldUnivariateDerivative2<>(getTk(date),
date.getField().getOne(),
date.getField().getZero());
// Semi-major axis
final FieldUnivariateDerivative2<T> ak = tk.multiply(parameters[GNSSOrbitalElements.A_DOT_INDEX]).
add(orbitalElements.getSma());
// Mean motion
final FieldUnivariateDerivative2<T> nA = tk.multiply(parameters[GNSSOrbitalElements.DELTA_N0_DOT_INDEX].multiply(0.5)).
add(parameters[GNSSOrbitalElements.DELTA_N0_INDEX]).
add(orbitalElements.getMeanMotion0());
// Mean anomaly
final FieldUnivariateDerivative2<T> mk = tk.multiply(nA).add(orbitalElements.getM0());
// Eccentric Anomaly
final FieldUnivariateDerivative2<T> e = tk.newInstance(orbitalElements.getE());
final FieldUnivariateDerivative2<T> ek = FieldKeplerianAnomalyUtility.ellipticMeanToEccentric(e, mk);
// True Anomaly
final FieldUnivariateDerivative2<T> vk = FieldKeplerianAnomalyUtility.ellipticEccentricToTrue(e, ek);
// Argument of Latitude
final FieldUnivariateDerivative2<T> phik = vk.add(orbitalElements.getPa());
final FieldSinCos<FieldUnivariateDerivative2<T>> cs2phi = FastMath.sinCos(phik.multiply(2));
// Argument of Latitude Correction
final FieldUnivariateDerivative2<T> dphik = cs2phi.cos().multiply(parameters[GNSSOrbitalElements.CUC_INDEX]).
add(cs2phi.sin().multiply(parameters[GNSSOrbitalElements.CUS_INDEX]));
// Radius Correction
final FieldUnivariateDerivative2<T> drk = cs2phi.cos().multiply(parameters[GNSSOrbitalElements.CRC_INDEX]).
add(cs2phi.sin().multiply(parameters[GNSSOrbitalElements.CRS_INDEX]));
// Inclination Correction
final FieldUnivariateDerivative2<T> dik = cs2phi.cos().multiply(parameters[GNSSOrbitalElements.CIC_INDEX]).
add(cs2phi.sin().multiply(parameters[GNSSOrbitalElements.CIS_INDEX]));
// Corrected Argument of Latitude
final FieldSinCos<FieldUnivariateDerivative2<T>> csuk = FastMath.sinCos(phik.add(dphik));
// Corrected Radius
final FieldUnivariateDerivative2<T> rk = ek.cos().multiply(e.negate()).add(1).multiply(ak).add(drk);
// Corrected Inclination
final FieldUnivariateDerivative2<T> ik = tk.multiply(parameters[GNSSOrbitalElements.I_DOT_INDEX]).
add(orbitalElements.getI0()).add(dik);
final FieldSinCos<FieldUnivariateDerivative2<T>> csik = FastMath.sinCos(ik);
// Positions in orbital plane
final FieldUnivariateDerivative2<T> xk = csuk.cos().multiply(rk);
final FieldUnivariateDerivative2<T> yk = csuk.sin().multiply(rk);
// Corrected longitude of ascending node
final FieldSinCos<FieldUnivariateDerivative2<T>> csomk =
FastMath.sinCos(tk.multiply(parameters[GNSSOrbitalElements.OMEGA_DOT_INDEX].
subtract(orbitalElements.getAngularVelocity())).
add(orbitalElements.getOmega0()).
subtract(parameters[GNSSOrbitalElements.TIME_INDEX].multiply(orbitalElements.getAngularVelocity())));
// returns the Earth-fixed coordinates
final FieldVector3D<FieldUnivariateDerivative2<T>> positionWithDerivatives =
new FieldVector3D<>(xk.multiply(csomk.cos()).subtract(yk.multiply(csomk.sin()).multiply(csik.cos())),
xk.multiply(csomk.sin()).add(yk.multiply(csomk.cos()).multiply(csik.cos())),
yk.multiply(csik.sin()));
return new FieldPVCoordinates<>(positionWithDerivatives);
}
/**
* Gets the duration from GNSS Reference epoch.
* <p>This takes the GNSS week roll-over into account.</p>
* @param date the considered date
* @return the duration from GNSS orbit Reference epoch (s)
*/
private T getTk(final FieldAbsoluteDate<T> date) {
// Time from ephemeris reference epoch
T tk = date.durationFrom(orbitalElements.getDate());
// Adjusts the time to take roll over week into account
while (tk.getReal() > 0.5 * orbitalElements.getCycleDuration()) {
tk = tk.subtract(orbitalElements.getCycleDuration());
}
while (tk.getReal() < -0.5 * orbitalElements.getCycleDuration()) {
tk = tk.add(orbitalElements.getCycleDuration());
}
// Returns the time from ephemeris reference epoch
return tk;
}
/** {@inheritDoc} */
@Override
public Frame getFrame() {
return eci;
}
/** {@inheritDoc} */
@Override
protected T getMass(final FieldAbsoluteDate<T> date) {
return getInitialState().getMass();
}
/** {@inheritDoc} */
@Override
public void resetInitialState(final FieldSpacecraftState<T> state) {
orbitalElements = buildOrbitalElements(state, orbitalElements, ecef, getAttitudeProvider(), state.getMass());
final FieldOrbit<T> orbit = propagateOrbit(orbitalElements.getDate(), defaultParameters());
final FieldAttitude<T> attitude = getAttitudeProvider().getAttitude(orbit, orbit.getDate(), orbit.getFrame());
super.resetInitialState(new FieldSpacecraftState<>(orbit, attitude).withMass(state.getMass()));
}
/** {@inheritDoc} */
@Override
protected void resetIntermediateState(final FieldSpacecraftState<T> state, final boolean forward) {
resetInitialState(state);
}
/**
* Build orbital elements from initial state.
* <p>
* This method is roughly the inverse of {@link #propagateInEcef(FieldAbsoluteDate, CalculusFieldElement[])},
* except it starts from a state in inertial frame
* </p>
*
* @param <T> type of the field elements
* @param initialState initial state
* @param nonKeplerianElements non-Keplerian orbital elements (the Keplerian orbital elements will be overridden)
* @param ecef Earth Centered Earth Fixed frame
* @param provider attitude provider
* @param mass satellite mass (kg)
* @return orbital elements that generate the {@code initialState} when used with a propagator
*/
private static <T extends CalculusFieldElement<T>> FieldGnssOrbitalElements<T, ?>
buildOrbitalElements(final FieldSpacecraftState<T> initialState,
final FieldGnssOrbitalElements<T, ?> nonKeplerianElements,
final Frame ecef, final AttitudeProvider provider,
final T mass) {
final Field<T> field = initialState.getDate().getField();
// get approximate initial orbit
final Frame frozenEcef = ecef.getFrozenFrame(initialState.getFrame(),
initialState.getDate().toAbsoluteDate(),
"frozen");
final FieldKeplerianOrbit<T> orbit = approximateInitialOrbit(initialState, nonKeplerianElements, frozenEcef);
// refine orbit using simple differential correction to reach target PV
final FieldPVCoordinates<T> targetPV = initialState.getPVCoordinates();
final FieldGnssOrbitalElements<FieldGradient<T>, ?> gElements = convert(nonKeplerianElements, orbit);
for (int i = 0; i < MAX_ITER; ++i) {
// get position-velocity derivatives with respect to initial orbit
final FieldGnssPropagator<FieldGradient<T>> gPropagator =
new FieldGnssPropagator<>(gElements, initialState.getFrame(), ecef, provider,
gElements.getMu().newInstance(mass));
final FieldPVCoordinates<FieldGradient<T>> gPV = gPropagator.getInitialState().getPVCoordinates();
// compute Jacobian matrix
final FieldMatrix<T> jacobian = MatrixUtils.createFieldMatrix(field, FREE_PARAMETERS, FREE_PARAMETERS);
jacobian.setRow(0, gPV.getPosition().getX().getGradient());
jacobian.setRow(1, gPV.getPosition().getY().getGradient());
jacobian.setRow(2, gPV.getPosition().getZ().getGradient());
jacobian.setRow(3, gPV.getVelocity().getX().getGradient());
jacobian.setRow(4, gPV.getVelocity().getY().getGradient());
jacobian.setRow(5, gPV.getVelocity().getZ().getGradient());
// linear correction to get closer to target PV
final FieldVector<T> residuals = MatrixUtils.createFieldVector(field, FREE_PARAMETERS);
residuals.setEntry(0, targetPV.getPosition().getX().subtract(gPV.getPosition().getX().getValue()));
residuals.setEntry(1, targetPV.getPosition().getY().subtract(gPV.getPosition().getY().getValue()));
residuals.setEntry(2, targetPV.getPosition().getZ().subtract(gPV.getPosition().getZ().getValue()));
residuals.setEntry(3, targetPV.getVelocity().getX().subtract(gPV.getVelocity().getX().getValue()));
residuals.setEntry(4, targetPV.getVelocity().getY().subtract(gPV.getVelocity().getY().getValue()));
residuals.setEntry(5, targetPV.getVelocity().getZ().subtract(gPV.getVelocity().getZ().getValue()));
final FieldVector<T> correction = new FieldQRDecomposition<>(jacobian, field.getZero().newInstance(EPS)).
getSolver().
solve(residuals);
// update initial orbit
gElements.setSma(gElements.getSma().add(correction.getEntry(0)));
gElements.setE(gElements.getE().add(correction.getEntry(1)));
gElements.setI0(gElements.getI0().add(correction.getEntry(2)));
gElements.setPa(gElements.getPa().add(correction.getEntry(3)));
gElements.setOmega0(gElements.getOmega0().add(correction.getEntry(4)));
gElements.setM0(gElements.getM0().add(correction.getEntry(5)));
final double deltaP = FastMath.sqrt(residuals.getEntry(0).getReal() * residuals.getEntry(0).getReal() +
residuals.getEntry(1).getReal() * residuals.getEntry(1).getReal() +
residuals.getEntry(2).getReal() * residuals.getEntry(2).getReal());
final double deltaV = FastMath.sqrt(residuals.getEntry(3).getReal() * residuals.getEntry(3).getReal() +
residuals.getEntry(4).getReal() * residuals.getEntry(4).getReal() +
residuals.getEntry(5).getReal() * residuals.getEntry(5).getReal());
if (deltaP < TOL_P && deltaV < TOL_V) {
break;
}
}
return gElements.changeField(FieldGradient::getValue);
}
/** Compute approximate initial orbit.
* @param <T> type of the field elements
* @param initialState initial state
* @param nonKeplerianElements non-Keplerian orbital elements (the Keplerian orbital elements will be ignored)
* @param frozenEcef inertial frame aligned with Earth Centered Earth Fixed frame at orbit date
* @return approximate initial orbit that generate a state close to {@code initialState}
*/
private static <T extends CalculusFieldElement<T>> FieldKeplerianOrbit<T>
approximateInitialOrbit(final FieldSpacecraftState<T> initialState,
final FieldGnssOrbitalElements<T, ?> nonKeplerianElements,
final Frame frozenEcef) {
// rotate the state to a frame that is inertial but aligned with Earth frame,
// as analytical model is expressed in Earth frame
final FieldPVCoordinates<T> pv = initialState.getPVCoordinates(frozenEcef);
final FieldVector3D<T> p = pv.getPosition();
final FieldVector3D<T> v = pv.getVelocity();
// compute Keplerian orbital parameters
final T rk = p.getNorm();
// compute orbital plane orientation
final FieldVector3D<T> normal = pv.getMomentum().normalize();
final T cosIk = normal.getZ();
final T ik = FieldVector3D.angle(normal, Vector3D.PLUS_K);
// compute position in orbital plane
final T q = FastMath.hypot(normal.getX(), normal.getY());
final T cos = normal.getY().negate().divide(q);
final T sin = normal.getX().divide(q);
final T xk = p.getX().multiply(cos).add(p.getY().multiply(sin));
final T yk = p.getY().multiply(cos).subtract(p.getX().multiply(sin)).divide(cosIk);
// corrected latitude argument
final T uk = FastMath.atan2(yk, xk);
// recover latitude argument before correction, using a fixed-point method
T phi = uk;
for (int i = 0; i < MAX_ITER; ++i) {
final T previous = phi;
final FieldSinCos<T> cs2Phi = FastMath.sinCos(phi.multiply(2));
phi = uk.subtract(cs2Phi.cos().multiply(nonKeplerianElements.getCuc()).add(cs2Phi.sin().multiply(nonKeplerianElements.getCus())));
if (FastMath.abs(phi.subtract(previous).getReal()) <= EPS) {
break;
}
}
final FieldSinCos<T> cs2phi = FastMath.sinCos(phi.multiply(2));
// recover plane orientation before correction
// here, we know that tk = 0 since our orbital elements will be at initial state date
final T i0 = ik.subtract(cs2phi.cos().multiply(nonKeplerianElements.getCic()).add(cs2phi.sin().multiply(nonKeplerianElements.getCis())));
final T om0 = FastMath.atan2(sin, cos).
add(nonKeplerianElements.getAngularVelocity() * nonKeplerianElements.getTime());
// recover eccentricity and anomaly
final T mu = initialState.getOrbit().getMu();
final T rV2OMu = rk.multiply(v.getNorm2Sq()).divide(mu);
final T sma = rk.divide(rV2OMu.negate().add(2));
final T eCosE = rV2OMu.subtract(1);
final T eSinE = FieldVector3D.dotProduct(p, v).divide(FastMath.sqrt(mu.multiply(sma)));
final T e = FastMath.hypot(eCosE, eSinE);
final T eccentricAnomaly = FastMath.atan2(eSinE, eCosE);
final T aop = phi.subtract(eccentricAnomaly);
final T meanAnomaly = FieldKeplerianAnomalyUtility.ellipticEccentricToMean(e, eccentricAnomaly);
return new FieldKeplerianOrbit<>(sma, e, i0, aop, om0, meanAnomaly, PositionAngleType.MEAN,
PositionAngleType.MEAN, frozenEcef,
initialState.getDate(), mu);
}
/** Convert orbital elements to gradient.
* @param <T> type of the field elements
* @param elements primitive double elements
* @param orbit Keplerian orbit
* @return converted elements, set up as gradient relative to Keplerian orbit
*/
private static <T extends CalculusFieldElement<T>> FieldGnssOrbitalElements<FieldGradient<T>, ?>
convert(final FieldGnssOrbitalElements<T, ?> elements, final FieldKeplerianOrbit<T> orbit) {
final FieldGnssOrbitalElements<FieldGradient<T>, ?> gElements =
elements.changeField(t -> FieldGradient.constant(FREE_PARAMETERS, t));
// Keplerian parameters
gElements.setSma(FieldGradient.variable(FREE_PARAMETERS, 0, orbit.getA()));
gElements.setE(FieldGradient.variable(FREE_PARAMETERS, 1, orbit.getE()));
gElements.setI0(FieldGradient.variable(FREE_PARAMETERS, 2, orbit.getI()));
gElements.setPa(FieldGradient.variable(FREE_PARAMETERS, 3, orbit.getPerigeeArgument()));
gElements.setOmega0(FieldGradient.variable(FREE_PARAMETERS, 4, orbit.getRightAscensionOfAscendingNode()));
gElements.setM0(FieldGradient.variable(FREE_PARAMETERS, 5, orbit.getMeanAnomaly()));
return gElements;
}
}