AbstractGNSSPropagator.java
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package org.orekit.propagation.analytical.gnss;
import org.hipparchus.analysis.differentiation.DSFactory;
import org.hipparchus.analysis.differentiation.DerivativeStructure;
import org.hipparchus.geometry.euclidean.threed.FieldVector3D;
import org.hipparchus.util.FastMath;
import org.hipparchus.util.MathUtils;
import org.hipparchus.util.Precision;
import org.orekit.attitudes.AttitudeProvider;
import org.orekit.errors.OrekitException;
import org.orekit.errors.OrekitMessages;
import org.orekit.frames.Frame;
import org.orekit.orbits.CartesianOrbit;
import org.orekit.orbits.Orbit;
import org.orekit.propagation.SpacecraftState;
import org.orekit.propagation.analytical.AbstractAnalyticalPropagator;
import org.orekit.time.AbsoluteDate;
import org.orekit.utils.PVCoordinates;
/** Common handling of {@link AbstractAnalyticalPropagator} methods for GNSS propagators.
* <p>
* This abstract class allows to provide easily a subset of {@link AbstractAnalyticalPropagator} methods
* for specific GNSS propagators.
* </p>
* @author Pascal Parraud
*/
public abstract class AbstractGNSSPropagator extends AbstractAnalyticalPropagator {
// Data used to solve Kepler's equation
/** First coefficient to compute Kepler equation solver starter. */
private static final double A;
/** Second coefficient to compute Kepler equation solver starter. */
private static final double B;
static {
final double k1 = 3 * FastMath.PI + 2;
final double k2 = FastMath.PI - 1;
final double k3 = 6 * FastMath.PI - 1;
A = 3 * k2 * k2 / k1;
B = k3 * k3 / (6 * k1);
}
/** The GNSS orbital elements used. */
private final GNSSOrbitalElements gnssOrbit;
/** Mean angular velocity of the Earth. */
private final double av;
/** Duration of the GNSS cycle in seconds. */
private final double cycleDuration;
/** The spacecraft mass (kg). */
private final double mass;
/** The Earth gravity coefficient used for GNSS propagation. */
private final double mu;
/** The ECI frame used for GNSS propagation. */
private final Frame eci;
/** The ECEF frame used for GNSS propagation. */
private final Frame ecef;
/** Factory for the DerivativeStructure instances. */
private final DSFactory factory;
/** Build a new instance.
* @param gnssOrbit the common GNSS orbital elements to be used by the Abstract GNSS propagator
* @param attitudeProvider provider for attitude computation
* @param eci the ECI frame used for GNSS propagation
* @param ecef the ECEF frame used for GNSS propagation
* @param mass the spacecraft mass (kg)
* @param av mean angular velocity of the Earth (rad/s)
* @param cycleDuration duration of the GNSS cycle in seconds
* @param mu the Earth gravity coefficient used for GNSS propagation
*/
protected AbstractGNSSPropagator(final GNSSOrbitalElements gnssOrbit, final AttitudeProvider attitudeProvider,
final Frame eci, final Frame ecef, final double mass,
final double av, final double cycleDuration, final double mu) {
super(attitudeProvider);
this.gnssOrbit = gnssOrbit;
this.av = av;
this.cycleDuration = cycleDuration;
this.mass = mass;
this.mu = mu;
this.factory = new DSFactory(1, 2);
// Sets the Earth Centered Inertial frame
this.eci = eci;
// Sets the Earth Centered Earth Fixed frame
this.ecef = ecef;
// Sets the start date as the date of the orbital elements
setStartDate(gnssOrbit.getDate());
}
/** Get 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) {
// Time from ephemeris reference epoch
double tk = date.durationFrom(gnssOrbit.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;
}
/**
* 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 DerivativeStructure tk = factory.variable(0, getTk(date));
// Mean anomaly
final DerivativeStructure mk = tk.multiply(gnssOrbit.getMeanMotion()).add(gnssOrbit.getM0());
// Eccentric Anomaly
final DerivativeStructure ek = getEccentricAnomaly(mk);
// True Anomaly
final DerivativeStructure vk = getTrueAnomaly(ek);
// Argument of Latitude
final DerivativeStructure phik = vk.add(gnssOrbit.getPa());
final DerivativeStructure twoPhik = phik.multiply(2);
final DerivativeStructure c2phi = twoPhik.cos();
final DerivativeStructure s2phi = twoPhik.sin();
// Argument of Latitude Correction
final DerivativeStructure dphik = c2phi.multiply(gnssOrbit.getCuc()).add(s2phi.multiply(gnssOrbit.getCus()));
// Radius Correction
final DerivativeStructure drk = c2phi.multiply(gnssOrbit.getCrc()).add(s2phi.multiply(gnssOrbit.getCrs()));
// Inclination Correction
final DerivativeStructure dik = c2phi.multiply(gnssOrbit.getCic()).add(s2phi.multiply(gnssOrbit.getCis()));
// Corrected Argument of Latitude
final DerivativeStructure uk = phik.add(dphik);
// Corrected Radius
final DerivativeStructure rk = ek.cos().multiply(-gnssOrbit.getE()).add(1).multiply(gnssOrbit.getSma()).add(drk);
// Corrected Inclination
final DerivativeStructure ik = tk.multiply(gnssOrbit.getIDot()).add(gnssOrbit.getI0()).add(dik);
final DerivativeStructure cik = ik.cos();
// Positions in orbital plane
final DerivativeStructure xk = uk.cos().multiply(rk);
final DerivativeStructure yk = uk.sin().multiply(rk);
// Corrected longitude of ascending node
final DerivativeStructure omk = tk.multiply(gnssOrbit.getOmegaDot() - av).
add(gnssOrbit.getOmega0() - av * gnssOrbit.getTime());
final DerivativeStructure comk = omk.cos();
final DerivativeStructure somk = omk.sin();
// returns the Earth-fixed coordinates
final FieldVector3D<DerivativeStructure> positionwithDerivatives =
new FieldVector3D<>(xk.multiply(comk).subtract(yk.multiply(somk).multiply(cik)),
xk.multiply(somk).add(yk.multiply(comk).multiply(cik)),
yk.multiply(ik.sin()));
return new PVCoordinates(positionwithDerivatives);
}
/**
* Gets eccentric anomaly from mean anomaly.
* <p>The algorithm used to solve the Kepler equation has been published in:
* "Procedures for solving Kepler's Equation", A. W. Odell and R. H. Gooding,
* Celestial Mechanics 38 (1986) 307-334</p>
* <p>It has been copied from the OREKIT library (KeplerianOrbit class).</p>
*
* @param mk the mean anomaly (rad)
* @return the eccentric anomaly (rad)
*/
private DerivativeStructure getEccentricAnomaly(final DerivativeStructure mk) {
// reduce M to [-PI PI] interval
final double[] mlDerivatives = mk.getAllDerivatives();
mlDerivatives[0] = MathUtils.normalizeAngle(mlDerivatives[0], 0.0);
final DerivativeStructure reducedM = mk.getFactory().build(mlDerivatives);
// compute start value according to A. W. Odell and R. H. Gooding S12 starter
DerivativeStructure ek;
if (FastMath.abs(reducedM.getValue()) < 1.0 / 6.0) {
if (FastMath.abs(reducedM.getValue()) < Precision.SAFE_MIN) {
// this is an Orekit change to the S12 starter.
// If reducedM is 0.0, the derivative of cbrt is infinite which induces NaN appearing later in
// the computation. As in this case E and M are almost equal, we initialize ek with reducedM
ek = reducedM;
} else {
// this is the standard S12 starter
ek = reducedM.add(reducedM.multiply(6).cbrt().subtract(reducedM).multiply(gnssOrbit.getE()));
}
} else {
if (reducedM.getValue() < 0) {
final DerivativeStructure w = reducedM.add(FastMath.PI);
ek = reducedM.add(w.multiply(-A).divide(w.subtract(B)).subtract(FastMath.PI).subtract(reducedM).multiply(gnssOrbit.getE()));
} else {
final DerivativeStructure minusW = reducedM.subtract(FastMath.PI);
ek = reducedM.add(minusW.multiply(A).divide(minusW.add(B)).add(FastMath.PI).subtract(reducedM).multiply(gnssOrbit.getE()));
}
}
final double e1 = 1 - gnssOrbit.getE();
final boolean noCancellationRisk = (e1 + ek.getValue() * ek.getValue() / 6) >= 0.1;
// perform two iterations, each consisting of one Halley step and one Newton-Raphson step
for (int j = 0; j < 2; ++j) {
final DerivativeStructure f;
DerivativeStructure fd;
final DerivativeStructure fdd = ek.sin().multiply(gnssOrbit.getE());
final DerivativeStructure fddd = ek.cos().multiply(gnssOrbit.getE());
if (noCancellationRisk) {
f = ek.subtract(fdd).subtract(reducedM);
fd = fddd.subtract(1).negate();
} else {
f = eMeSinE(ek).subtract(reducedM);
final DerivativeStructure s = ek.multiply(0.5).sin();
fd = s.multiply(s).multiply(2 * gnssOrbit.getE()).add(e1);
}
final DerivativeStructure dee = f.multiply(fd).divide(f.multiply(0.5).multiply(fdd).subtract(fd.multiply(fd)));
// update eccentric anomaly, using expressions that limit underflow problems
final DerivativeStructure w = fd.add(dee.multiply(0.5).multiply(fdd.add(dee.multiply(fdd).divide(3))));
fd = fd.add(dee.multiply(fdd.add(dee.multiply(0.5).multiply(fdd))));
ek = ek.subtract(f.subtract(dee.multiply(fd.subtract(w))).divide(fd));
}
// expand the result back to original range
ek = ek.add(mk.getValue() - reducedM.getValue());
// Returns the eccentric anomaly
return ek;
}
/**
* Accurate computation of E - e sin(E).
*
* @param E eccentric anomaly
* @return E - e sin(E)
*/
private DerivativeStructure eMeSinE(final DerivativeStructure E) {
DerivativeStructure x = E.sin().multiply(1 - gnssOrbit.getE());
final DerivativeStructure mE2 = E.negate().multiply(E);
DerivativeStructure term = E;
DerivativeStructure d = E.getField().getZero();
// the inequality test below IS intentional and should NOT be replaced by a check with a small tolerance
for (DerivativeStructure x0 = d.add(Double.NaN); !Double.valueOf(x.getValue()).equals(Double.valueOf(x0.getValue()));) {
d = d.add(2);
term = term.multiply(mE2.divide(d.multiply(d.add(1))));
x0 = x;
x = x.subtract(term);
}
return x;
}
/** Gets true anomaly from eccentric anomaly.
*
* @param ek the eccentric anomaly (rad)
* @return the true anomaly (rad)
*/
private DerivativeStructure getTrueAnomaly(final DerivativeStructure ek) {
final DerivativeStructure svk = ek.sin().multiply(FastMath.sqrt(1. - gnssOrbit.getE() * gnssOrbit.getE()));
final DerivativeStructure cvk = ek.cos().subtract(gnssOrbit.getE());
return svk.atan2(cvk);
}
/** {@inheritDoc} */
protected 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, mu);
}
/**
* Get the Earth gravity coefficient used for GNSS propagation.
* @return the Earth gravity coefficient.
*/
public double getMU() {
return mu;
}
/** {@inheritDoc} */
public Frame getFrame() {
return eci;
}
/** {@inheritDoc} */
protected double getMass(final AbsoluteDate date) {
return mass;
}
/** {@inheritDoc} */
public void resetInitialState(final SpacecraftState state) {
throw new OrekitException(OrekitMessages.NON_RESETABLE_STATE);
}
/** {@inheritDoc} */
protected void resetIntermediateState(final SpacecraftState state, final boolean forward) {
throw new OrekitException(OrekitMessages.NON_RESETABLE_STATE);
}
/**
* 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;
}
}