GNSSPropagator.java
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package org.orekit.propagation.analytical.gnss;
import org.hipparchus.Field;
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.frames.Frame;
import org.orekit.orbits.CartesianOrbit;
import org.orekit.orbits.FieldKeplerianAnomalyUtility;
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.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.time.AbsoluteDate;
import org.orekit.utils.DoubleArrayDictionary;
import org.orekit.utils.FieldPVCoordinates;
import org.orekit.utils.PVCoordinates;
import org.orekit.utils.ParameterDriver;
import org.orekit.utils.TimeSpanMap.Span;
import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
/** 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>
* @author Pascal Parraud
*/
public class GNSSPropagator extends AbstractAnalyticalPropagator {
/** 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 GNSSOrbitalElements<?> 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)
*/
GNSSPropagator(final GNSSOrbitalElements<?> orbitalElements, final Frame eci,
final Frame ecef, final AttitudeProvider provider, final double mass) {
super(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 Orbit orbit = propagateOrbit(orbitalElements.getDate());
final Attitude 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 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
*/
GNSSPropagator(final SpacecraftState initialState, final GNSSOrbitalElements<?> nonKeplerianElements,
final Frame ecef, final AttitudeProvider provider, final double mass) {
this(buildOrbitalElements(initialState, nonKeplerianElements, ecef, provider, mass),
initialState.getFrame(), ecef, provider, initialState.getMass());
}
/**
* 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.getMu();
}
/** Get the underlying GNSS propagation orbital elements.
* @return the underlying GNSS orbital elements
* @since 13.0
*/
public GNSSOrbitalElements<?> 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 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 : orbitalElements.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) {
// Gets the PVCoordinates in ECEF frame
final PVCoordinates pvaInECEF = propagateInEcef(date);
// Transforms the PVCoordinates to ECI frame
final PVCoordinates pvaInECI = ecef.getTransformTo(eci, date).transformPVCoordinates(pvaInECEF);
// Returns the Cartesian orbit
return new CartesianOrbit(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) {
// 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(orbitalElements.getSma());
// Mean motion
final UnivariateDerivative2 nA = tk.multiply(orbitalElements.getDeltaN0Dot() * 0.5).
add(orbitalElements.getDeltaN0()).
add(orbitalElements.getMeanMotion0());
// Mean anomaly
final UnivariateDerivative2 mk = tk.multiply(nA).add(orbitalElements.getM0());
// Eccentric Anomaly
final UnivariateDerivative2 e = tk.newInstance(orbitalElements.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(orbitalElements.getPa());
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(-orbitalElements.getE()).add(1).multiply(ak).add(drk);
// Corrected Inclination
final UnivariateDerivative2 ik = tk.multiply(orbitalElements.getIDot()).add(orbitalElements.getI0()).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 FieldSinCos<UnivariateDerivative2> csomk =
FastMath.sinCos(tk.multiply(orbitalElements.getOmegaDot() - thetaDot).
add(orbitalElements.getOmega0() - thetaDot * orbitalElements.getTime()));
// 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, 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 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
* @since 13.0
*/
private static GNSSOrbitalElements<?> buildOrbitalElements(final SpacecraftState initialState,
final GNSSOrbitalElements<?> nonKeplerianElements,
final Frame ecef, final AttitudeProvider provider,
final double mass) {
// get approximate initial orbit
final Frame frozenEcef = ecef.getFrozenFrame(initialState.getFrame(), initialState.getDate(), "frozen");
final KeplerianOrbit orbit = approximateInitialOrbit(initialState, nonKeplerianElements, frozenEcef);
// refine orbit using simple differential correction to reach target PV
final PVCoordinates targetPV = initialState.getPVCoordinates();
final FieldGnssOrbitalElements<Gradient, ?> gElements = convert(nonKeplerianElements, orbit);
for (int i = 0; i < MAX_ITER; ++i) {
// get position-velocity derivatives with respect to initial orbit
final FieldGnssPropagator<Gradient> gPropagator =
new FieldGnssPropagator<>(gElements, initialState.getFrame(), ecef, provider,
gElements.getMu().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());
// linear correction to get closer to target PV
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());
final RealVector correction = new QRDecomposition(jacobian, 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) * 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;
}
}
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.getTime();
// recover eccentricity and anomaly
final double mu = initialState.getOrbit().getMu();
final double rV2OMu = rk * v.getNormSq() / 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,
PositionAngleType.MEAN, frozenEcef,
initialState.getDate(), mu);
}
/** Convert orbital elements to gradient.
* @param elements primitive double elements
* @param orbit Keplerian orbit
* @return converted elements, set up as gradient relative to Keplerian orbit
* @since 13.0
*/
private static FieldGnssOrbitalElements<Gradient, ?> convert(final GNSSOrbitalElements<?> elements,
final KeplerianOrbit orbit) {
final Field<Gradient> field = GradientField.getField(FREE_PARAMETERS);
final FieldGnssOrbitalElements<Gradient, ?> gElements = elements.toField(field);
// Keplerian parameters
gElements.setSma(Gradient.variable(FREE_PARAMETERS, 0, orbit.getA()));
gElements.setE(Gradient.variable(FREE_PARAMETERS, 1, orbit.getE()));
gElements.setI0(Gradient.variable(FREE_PARAMETERS, 2, orbit.getI()));
gElements.setPa(Gradient.variable(FREE_PARAMETERS, 3, orbit.getPerigeeArgument()));
gElements.setOmega0(Gradient.variable(FREE_PARAMETERS, 4, orbit.getRightAscensionOfAscendingNode()));
gElements.setM0(Gradient.variable(FREE_PARAMETERS, 5, orbit.getMeanAnomaly()));
return gElements;
}
}