GNSSPropagator.java
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* Unless required by applicable law or agreed to in writing, software
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package org.orekit.propagation.analytical.gnss;
import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
import org.hipparchus.analysis.differentiation.Gradient;
import org.hipparchus.analysis.differentiation.GradientField;
import org.hipparchus.analysis.differentiation.UnivariateDerivative2;
import org.hipparchus.geometry.euclidean.threed.FieldVector3D;
import org.hipparchus.geometry.euclidean.threed.Vector3D;
import org.hipparchus.linear.MatrixUtils;
import org.hipparchus.linear.QRDecomposition;
import org.hipparchus.linear.RealMatrix;
import org.hipparchus.linear.RealVector;
import org.hipparchus.util.FastMath;
import org.hipparchus.util.FieldSinCos;
import org.hipparchus.util.SinCos;
import org.orekit.attitudes.Attitude;
import org.orekit.attitudes.AttitudeProvider;
import org.orekit.attitudes.FrameAlignedProvider;
import org.orekit.frames.Frame;
import org.orekit.orbits.FieldKeplerianAnomalyUtility;
import org.orekit.orbits.FieldKeplerianOrbit;
import org.orekit.orbits.FieldKeplerianParameters;
import org.orekit.orbits.KeplerianAnomalyUtility;
import org.orekit.orbits.KeplerianOrbit;
import org.orekit.orbits.Orbit;
import org.orekit.orbits.PositionAngleType;
import org.orekit.propagation.AbstractMatricesHarvester;
import org.orekit.propagation.Propagator;
import org.orekit.propagation.SpacecraftState;
import org.orekit.propagation.analytical.AbstractAnalyticalPropagator;
import org.orekit.propagation.analytical.gnss.data.FieldGnssOrbitalElements;
import org.orekit.propagation.analytical.gnss.data.GNSSOrbitalElements;
import org.orekit.propagation.analytical.gnss.data.GNSSOrbitalElementsFactory;
import org.orekit.propagation.analytical.gnss.data.NonKeplerianDriversFactory;
import org.orekit.time.AbsoluteDate;
import org.orekit.time.FieldAbsoluteDate;
import org.orekit.time.GNSSDate;
import org.orekit.utils.DoubleArrayDictionary;
import org.orekit.utils.FieldPVCoordinates;
import org.orekit.utils.PVCoordinates;
import org.orekit.utils.ParameterDriver;
import org.orekit.utils.ParameterDriversProvider;
import org.orekit.utils.TimeSpanMap.Span;
/** Common handling of {@link AbstractAnalyticalPropagator} methods for GNSS propagators.
* <p>
* This class allows to provide easily a subset of {@link AbstractAnalyticalPropagator} methods
* for specific GNSS propagators.
* </p>
* @param <O> type of the orbital elements
* @author Pascal Parraud
*/
public class GNSSPropagator<O extends GNSSOrbitalElements<O>>
extends AbstractAnalyticalPropagator implements ParameterDriversProvider {
/** Maximum number of iterations for internal loops.
* @since 13.0
*/
private static final int MAX_ITER = 100;
/** Tolerance on position for rebuilding orbital elements from initial state.
* @since 13.0
*/
private static final double TOL_P = 1.0e-6;
/** Tolerance on velocity for rebuilding orbital elements from initial state.
* @since 13.0
*/
private static final double TOL_V = 1.0e-9;
/** Number of free parameters for orbital elements.
* @since 13.0
*/
private static final int FREE_PARAMETERS = 6;
/** Convergence parameter.
* @since 13.0
*/
private static final double EPS = 1.0e-12;
/** The GNSS propagation model used. */
private O orbitalElements;
/** Factory for non-Keplerian elements drivers.
* @since 14.0
*/
private final NonKeplerianDriversFactory driversFactory;
/** 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.
* <p>
* Beware that since GNSS orbital elements refer to an Earth frame frozen at a specific date
* to become an inertial frame, the factory date <em>must</em> have been initialized properly
* (by calling {@link GNSSOrbitalElementsFactory#setTimeOfEphemeris(GNSSDate)}). Setting the date
* allows the frozen frame to be set properly, otherwise a null pointer exception will be thrown
* when the propagator builder attempts to use the frame.
* </p>
* <p>
* The attitude provider is set by default to be aligned with the provided inertial frame.
* This can be changed (typically to {@link org.orekit.gnss.attitude.GenericGNSS}) after
* construction by calling {@link #setAttitudeProvider(org.orekit.attitudes.AttitudeProvider)
* setAttitudeProvider}
* </p>
* <p>
* The mass is set to the {@link org.orekit.propagation.Propagator#DEFAULT_MASS DEFAULT_MASS}.
* </p>
* @param factory factory for the elements and frames
* @since 14.0
*/
public GNSSPropagator(final GNSSOrbitalElementsFactory<O> factory) {
this(factory.createFromDrivers(), factory.getInertial(), factory.getBodyFixed(),
FrameAlignedProvider.of(factory.getInertial()),
Propagator.DEFAULT_MASS);
}
/** 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 GNSSPropagator(final O orbitalElements, final Frame eci, final Frame ecef,
final AttitudeProvider provider, final double mass) {
super(provider);
// Stores the GNSS orbital elements
this.orbitalElements = orbitalElements;
this.driversFactory = new NonKeplerianDriversFactory();
driversFactory.reset(orbitalElements);
// Sets the Earth Centered Inertial frame
this.eci = eci;
// Sets the Earth Centered Earth Fixed frame
this.ecef = ecef;
// Sets initial state
final Orbit orbit = propagateOrbit(orbitalElements.getDate());
final Attitude attitude = provider.getAttitude(orbit, orbit.getDate(), orbit.getFrame());
// calling the method from constructor because the one overridden below recomputes the orbital elements
super.resetInitialState(new SpacecraftState(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
* @since 13.0
*/
public GNSSPropagator(final SpacecraftState initialState, final O nonKeplerianElements,
final Frame ecef, final AttitudeProvider provider, final double mass) {
this(buildOrbitalElements(initialState, nonKeplerianElements, new NonKeplerianDriversFactory(),
ecef, provider, mass),
initialState.getFrame(), ecef, provider, initialState.getMass());
}
/** {@inheritDoc} */
@Override
public List<ParameterDriver> getParametersDrivers() {
return driversFactory.getParametersDrivers();
}
/** Get the factory for non-Keplerian elements drivers.
* @return factory for non-Keplerian elements drivers
*/
public NonKeplerianDriversFactory getDriversFactory() {
return driversFactory;
}
/**
* 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 double getMU() {
return orbitalElements.getOrbit().getMu();
}
/** Get the underlying GNSS propagation orbital elements.
* @return the underlying GNSS orbital elements
* @since 13.0
*/
public O getOrbitalElements() {
return orbitalElements;
}
/** {@inheritDoc}
* @since 13.0
*/
@Override
protected AbstractMatricesHarvester createHarvester(final String stmName, final RealMatrix initialStm,
final DoubleArrayDictionary initialJacobianColumns) {
// Create the harvester
final GnssHarvester<O> harvester = new GnssHarvester<>(this, stmName, initialStm, initialJacobianColumns);
// Update the list of additional state provider
addAdditionalDataProvider(harvester);
// Return the configured harvester
return harvester;
}
/** {@inheritDoc}
* @since 13.0
*/
@Override
protected List<String> getJacobiansColumnsNames() {
final List<String> columnsNames = new ArrayList<>();
for (final ParameterDriver driver : getParametersDrivers()) {
if (driver.isSelected() && !columnsNames.contains(driver.getNamesSpanMap().getFirstSpan().getData())) {
// As driver with same name should have same NamesSpanMap we only check if the first span is present,
// if not we add all span names to columnsNames
for (Span<String> span = driver.getNamesSpanMap().getFirstSpan(); span != null; span = span.next()) {
columnsNames.add(span.getData());
}
}
}
Collections.sort(columnsNames);
return columnsNames;
}
/** {@inheritDoc} */
@Override
public Orbit propagateOrbit(final AbsoluteDate date) {
// Get the PVCoordinates in ECEF frame
final PVCoordinates pvaInECEF = propagateInEcef(date);
// Transform the PVCoordinates to ECI frame
final PVCoordinates pvaInECI = ecef.getTransformTo(eci, date).transformPVCoordinates(pvaInECEF);
// Return the Keplerian orbit
return new KeplerianOrbit(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
* @return the GNSS SV PVCoordinates in {@link #getECEF() ECEF frame}
*/
public PVCoordinates propagateInEcef(final AbsoluteDate date) {
final KeplerianOrbit orbit = orbitalElements.getOrbit();
// Duration from GNSS ephemeris Reference date
final UnivariateDerivative2 tk = new UnivariateDerivative2(getTk(date), 1.0, 0.0);
// Semi-major axis
final UnivariateDerivative2 ak = tk.multiply(orbitalElements.getADot()).add(orbit.getA());
// Mean motion
final UnivariateDerivative2 nA = tk.multiply(orbitalElements.getDeltaN0Dot() * 0.5).
add(orbitalElements.getDeltaN0()).
add(orbit.getKeplerianMeanMotion());
// Mean anomaly
final UnivariateDerivative2 mk = tk.multiply(nA).add(orbit.getMeanAnomaly());
// Eccentric Anomaly
final UnivariateDerivative2 e = tk.newInstance(orbit.getE());
final UnivariateDerivative2 ek = FieldKeplerianAnomalyUtility.ellipticMeanToEccentric(e, mk);
// True Anomaly
final UnivariateDerivative2 vk = FieldKeplerianAnomalyUtility.ellipticEccentricToTrue(e, ek);
// Argument of Latitude
final UnivariateDerivative2 phik = vk.add(orbit.getPeriapsisArgument());
final FieldSinCos<UnivariateDerivative2> cs2phi = FastMath.sinCos(phik.multiply(2));
// Argument of Latitude Correction
final UnivariateDerivative2 dphik = cs2phi.cos().multiply(orbitalElements.getCuc()).add(cs2phi.sin().multiply(orbitalElements.getCus()));
// Radius Correction
final UnivariateDerivative2 drk = cs2phi.cos().multiply(orbitalElements.getCrc()).add(cs2phi.sin().multiply(orbitalElements.getCrs()));
// Inclination Correction
final UnivariateDerivative2 dik = cs2phi.cos().multiply(orbitalElements.getCic()).add(cs2phi.sin().multiply(orbitalElements.getCis()));
// Corrected Argument of Latitude
final FieldSinCos<UnivariateDerivative2> csuk = FastMath.sinCos(phik.add(dphik));
// Corrected Radius
final UnivariateDerivative2 rk = ek.cos().multiply(e.negate()).add(1).multiply(ak).add(drk);
// Corrected Inclination
final UnivariateDerivative2 ik = tk.multiply(orbitalElements.getIDot()).add(orbit.getI()).add(dik);
final FieldSinCos<UnivariateDerivative2> csik = FastMath.sinCos(ik);
// Positions in orbital plane
final UnivariateDerivative2 xk = csuk.cos().multiply(rk);
final UnivariateDerivative2 yk = csuk.sin().multiply(rk);
// Corrected longitude of ascending node
final double thetaDot = orbitalElements.getAngularVelocity();
final double toe = orbitalElements.getTimeOfEphemeris().getSecondsInWeek();
final FieldSinCos<UnivariateDerivative2> csomk =
FastMath.sinCos(tk.multiply(orbitalElements.getOmegaDot() - thetaDot).
add(orbit.getRightAscensionOfAscendingNode() - thetaDot * toe));
// returns the Earth-fixed coordinates
final FieldVector3D<UnivariateDerivative2> 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 PVCoordinates(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 double getTk(final AbsoluteDate date) {
final double cycleDuration = orbitalElements.getCycleDuration();
// Time from ephemeris reference epoch
double tk = date.durationFrom(orbitalElements.getDate());
// Adjusts the time to take roll over week into account
while (tk > 0.5 * cycleDuration) {
tk -= cycleDuration;
}
while (tk < -0.5 * cycleDuration) {
tk += cycleDuration;
}
// Returns the time from ephemeris reference epoch
return tk;
}
/** {@inheritDoc} */
@Override
public Frame getFrame() {
return eci;
}
/** {@inheritDoc} */
@Override
protected double getMass(final AbsoluteDate date) {
return getInitialState().getMass();
}
/** {@inheritDoc} */
@Override
public void resetInitialState(final SpacecraftState state) {
orbitalElements = buildOrbitalElements(state, orbitalElements, driversFactory,
ecef, getAttitudeProvider(), state.getMass());
final Orbit orbit = propagateOrbit(orbitalElements.getDate());
final Attitude attitude = getAttitudeProvider().getAttitude(orbit, orbit.getDate(), orbit.getFrame());
super.resetInitialState(new SpacecraftState(orbit, attitude).withMass(state.getMass()));
}
/** {@inheritDoc} */
@Override
protected void resetIntermediateState(final SpacecraftState state, final boolean forward) {
resetInitialState(state);
}
/**
* Build orbital elements from initial state.
* <p>
* This method is roughly the inverse of {@link #propagateInEcef(AbsoluteDate)}, except it starts from a state in
* inertial frame
* </p>
*
* @param <O> type of the orbital elements (non-field version)
* @param initialState initial state
* @param nonKeplerianElements non-Keplerian orbital elements (the Keplerian orbital elements will be overridden)
* @param driversFactory factory for non-Keplerian drivers
* @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
* @since 13.0
*/
public static <O extends GNSSOrbitalElements<O>>
O buildOrbitalElements(final SpacecraftState initialState,
final O nonKeplerianElements,
final NonKeplerianDriversFactory driversFactory,
final Frame ecef, final AttitudeProvider provider,
final double mass) {
// get approximate initial orbit
final Frame frozenEcef = ecef.getFrozenFrame(initialState.getFrame(), initialState.getDate(),
GNSSOrbitalElementsFactory.FROZEN + ecef.getName());
final KeplerianOrbit orbit = approximateInitialOrbit(initialState, nonKeplerianElements, frozenEcef);
driversFactory.reset(nonKeplerianElements);
// refine orbit using simple differential correction to reach target PV
final PVCoordinates targetPV = initialState.getPVCoordinates(frozenEcef);
FieldGnssOrbitalElements<Gradient, O> gElements = toGradient(nonKeplerianElements, orbit, driversFactory);
for (int i = 0; i < MAX_ITER; ++i) {
// get position-velocity derivatives with respect to initial orbit
final FieldGnssPropagator<Gradient, O> gPropagator =
new FieldGnssPropagator<>(gElements, frozenEcef, ecef, provider,
gElements.getTgd().newInstance(mass));
final FieldPVCoordinates<Gradient> gPV = gPropagator.getInitialState().getPVCoordinates();
// compute Jacobian matrix
final RealMatrix jacobian = MatrixUtils.createRealMatrix(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());
// compute residuals
final RealVector residuals = MatrixUtils.createRealVector(FREE_PARAMETERS);
residuals.setEntry(0, targetPV.getPosition().getX() - gPV.getPosition().getX().getValue());
residuals.setEntry(1, targetPV.getPosition().getY() - gPV.getPosition().getY().getValue());
residuals.setEntry(2, targetPV.getPosition().getZ() - gPV.getPosition().getZ().getValue());
residuals.setEntry(3, targetPV.getVelocity().getX() - gPV.getVelocity().getX().getValue());
residuals.setEntry(4, targetPV.getVelocity().getY() - gPV.getVelocity().getY().getValue());
residuals.setEntry(5, targetPV.getVelocity().getZ() - gPV.getVelocity().getZ().getValue());
// check convergence
final double deltaP = FastMath.sqrt(residuals.getEntry(0) * residuals.getEntry(0) +
residuals.getEntry(1) * residuals.getEntry(1) +
residuals.getEntry(2) * residuals.getEntry(2));
final double deltaV = FastMath.sqrt(residuals.getEntry(3) * residuals.getEntry(3) +
residuals.getEntry(4) * residuals.getEntry(4) +
residuals.getEntry(5) * residuals.getEntry(5));
if (deltaP < TOL_P && deltaV < TOL_V) {
break;
}
// linear correction to get closer to target PV
final RealVector correction = new QRDecomposition(jacobian, EPS).getSolver().solve(residuals);
// prevent correction to produce invalid values
final FieldKeplerianOrbit<Gradient> previous = gElements.getOrbit();
Gradient updatedA;
Gradient updatedE;
double factor = 2;
do {
// loop until eccentricity is valid
factor *= 0.5;
updatedA = previous.getA().add(correction.getEntry(0) * factor);
updatedE = previous.getE().add(correction.getEntry(1) * factor);
} while (updatedA.getValue() < 0 || updatedE.getValue() < 0 || updatedE.getValue() >= 1);
// update initial orbit
final FieldKeplerianOrbit<Gradient> updated =
new FieldKeplerianOrbit<>(new FieldKeplerianParameters<>(updatedA,
updatedE,
previous.getI().add(correction.getEntry(2) * factor),
previous.getPeriapsisArgument().add(correction.getEntry(3) * factor),
previous.getRightAscensionOfAscendingNode().add(correction.getEntry(4) * factor),
previous.getMeanAnomaly().add(correction.getEntry(5) * factor),
PositionAngleType.MEAN),
previous.getFrame(), previous.getDate(), previous.getMu());
gElements = toGradient(nonKeplerianElements, updated.toOrbit(), driversFactory);
}
return gElements.toNonField();
}
/** Compute approximate initial orbit.
* @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}
* @since 13.0
*/
private static KeplerianOrbit approximateInitialOrbit(final SpacecraftState initialState,
final GNSSOrbitalElements<?> 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 PVCoordinates pv = initialState.getPVCoordinates(frozenEcef);
final Vector3D p = pv.getPosition();
final Vector3D v = pv.getVelocity();
// compute Keplerian orbital parameters
final double rk = p.getNorm();
// compute orbital plane orientation
final Vector3D normal = pv.getMomentum().normalize();
final double cosIk = normal.getZ();
final double ik = Vector3D.angle(normal, Vector3D.PLUS_K);
// compute position in orbital plane
final double q = FastMath.hypot(normal.getX(), normal.getY());
final double cos = -normal.getY() / q;
final double sin = normal.getX() / q;
final double xk = p.getX() * cos + p.getY() * sin;
final double yk = (p.getY() * cos - p.getX() * sin) / cosIk;
// corrected latitude argument
final double uk = FastMath.atan2(yk, xk);
// recover latitude argument before correction, using a fixed-point method
double phi = uk;
for (int i = 0; i < MAX_ITER; ++i) {
final double previous = phi;
final SinCos cs2Phi = FastMath.sinCos(2 * phi);
phi = uk - (cs2Phi.cos() * nonKeplerianElements.getCuc() + cs2Phi.sin() * nonKeplerianElements.getCus());
if (FastMath.abs(phi - previous) <= EPS) {
break;
}
}
final SinCos cs2phi = FastMath.sinCos(2 * phi);
// recover plane orientation before correction
// here, we know that tk = 0 since our orbital elements will be at initial state date
final double i0 = ik - (cs2phi.cos() * nonKeplerianElements.getCic() + cs2phi.sin() * nonKeplerianElements.getCis());
final double om0 = FastMath.atan2(sin, cos) +
nonKeplerianElements.getAngularVelocity() *
nonKeplerianElements.getTimeOfEphemeris().getSecondsInWeek();
// recover eccentricity and anomaly
final double mu = initialState.getOrbit().getMu();
final double rV2OMu = rk * v.getNorm2Sq() / mu;
final double sma = rk / (2 - rV2OMu);
final double eCosE = rV2OMu - 1;
final double eSinE = Vector3D.dotProduct(p, v) / FastMath.sqrt(mu * sma);
final double e = FastMath.hypot(eCosE, eSinE);
final double eccentricAnomaly = FastMath.atan2(eSinE, eCosE);
final double aop = phi - eccentricAnomaly;
final double meanAnomaly = KeplerianAnomalyUtility.ellipticEccentricToMean(e, eccentricAnomaly);
return new KeplerianOrbit(sma, e, i0, aop, om0, meanAnomaly, PositionAngleType.MEAN, frozenEcef,
initialState.getDate(), mu);
}
/** Convert orbital elements to gradient.
* @param <O> type of the orbital elements (non-field version)
* @param elements primitive double elements
* @param orbit Keplerian orbit
* @param driversFactory factory for non-Kepleria drivers
* @return converted elements, set up as gradient relative to Keplerian orbit
* @since 14.0
*/
private static <O extends GNSSOrbitalElements<O>>
FieldGnssOrbitalElements<Gradient, O> toGradient(final O elements,
final KeplerianOrbit orbit,
final NonKeplerianDriversFactory driversFactory) {
// build orbit with gradient
final Gradient aG = Gradient.variable(FREE_PARAMETERS, 0, orbit.getA());
final Gradient eG = Gradient.variable(FREE_PARAMETERS, 1, orbit.getE());
final Gradient iG = Gradient.variable(FREE_PARAMETERS, 2, orbit.getI());
final Gradient paG = Gradient.variable(FREE_PARAMETERS, 3, orbit.getPeriapsisArgument());
final Gradient raanG = Gradient.variable(FREE_PARAMETERS, 4, orbit.getRightAscensionOfAscendingNode());
final Gradient mG = Gradient.variable(FREE_PARAMETERS, 5, orbit.getMeanAnomaly());
final FieldKeplerianOrbit<Gradient> orbitG =
new FieldKeplerianOrbit<>(new FieldKeplerianParameters<>(aG, eG, iG, paG, raanG, mG,
PositionAngleType.MEAN),
orbit.getFrame(),
new FieldAbsoluteDate<>(GradientField.getField(FREE_PARAMETERS),
orbit.getDate()),
Gradient.constant(FREE_PARAMETERS, orbit.getMu()));
// convert to GNSS orbital elements
return elements.toField(orbitG,
driversFactory.toGradients(FREE_PARAMETERS),
d -> Gradient.constant(FREE_PARAMETERS, d));
}
}