GLONASSAnalyticalPropagator.java
/* Copyright 2002-2023 CS GROUP
* 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
* limitations under the License.
*/
package org.orekit.propagation.analytical.gnss;
import org.hipparchus.analysis.differentiation.UnivariateDerivative2;
import org.hipparchus.geometry.euclidean.threed.FieldVector3D;
import org.hipparchus.geometry.euclidean.threed.Vector3D;
import org.hipparchus.util.FastMath;
import org.hipparchus.util.FieldSinCos;
import org.hipparchus.util.MathArrays;
import org.hipparchus.util.MathUtils;
import org.hipparchus.util.Precision;
import org.orekit.attitudes.Attitude;
import org.orekit.attitudes.AttitudeProvider;
import org.orekit.data.DataContext;
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.propagation.analytical.gnss.data.GLONASSAlmanac;
import org.orekit.propagation.analytical.gnss.data.GLONASSNavigationMessage;
import org.orekit.propagation.analytical.gnss.data.GLONASSOrbitalElements;
import org.orekit.propagation.analytical.gnss.data.GNSSConstants;
import org.orekit.time.AbsoluteDate;
import org.orekit.time.GLONASSDate;
import org.orekit.time.TimeScale;
import org.orekit.utils.PVCoordinates;
/**
* This class aims at propagating a GLONASS orbit from {@link GLONASSOrbitalElements}.
* <p>
* <b>Caution:</b> The Glonass analytical propagator can only be used with {@link GLONASSAlmanac}.
* Using this propagator with a {@link GLONASSNavigationMessage} is prone to error.
* </p>
*
* @see <a href="http://russianspacesystems.ru/wp-content/uploads/2016/08/ICD-GLONASS-CDMA-General.-Edition-1.0-2016.pdf">
* GLONASS Interface Control Document</a>
*
* @author Bryan Cazabonne
* @since 10.0
*
*/
public class GLONASSAnalyticalPropagator extends AbstractAnalyticalPropagator {
// Constants
/** Constant 7.0 / 3.0. */
private static final double SEVEN_THIRD = 7.0 / 3.0;
/** Constant 7.0 / 6.0. */
private static final double SEVEN_SIXTH = 7.0 / 6.0;
/** Constant 7.0 / 24.0. */
private static final double SEVEN_24TH = 7.0 / 24.0;
/** Constant 49.0 / 72.0. */
private static final double FN_72TH = 49.0 / 72.0;
/** Value of the earth's rotation rate in rad/s. */
private static final double GLONASS_AV = 7.2921150e-5;
/** Mean value of inclination for Glonass orbit is equal to 63°. */
private static final double GLONASS_MEAN_INCLINATION = 64.8;
/** Mean value of Draconian period for Glonass orbit is equal to 40544s : 11 hours 15 minutes 44 seconds. */
private static final double GLONASS_MEAN_DRACONIAN_PERIOD = 40544;
/** Second degree zonal coefficient of normal potential. */
private static final double GLONASS_J20 = 1.08262575e-3;
/** Equatorial radius of Earth (m). */
private static final double GLONASS_EARTH_EQUATORIAL_RADIUS = 6378136;
// 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 GLONASS orbital elements used. */
private final GLONASSOrbitalElements glonassOrbit;
/** The spacecraft mass (kg). */
private final double mass;
/** The ECI frame used for GLONASS propagation. */
private final Frame eci;
/** The ECEF frame used for GLONASS propagation. */
private final Frame ecef;
/** Data context for propagation. */
private final DataContext dataContext;
/**
* Private constructor.
* @param glonassOrbit Glonass orbital elements
* @param eci Earth Centered Inertial frame
* @param ecef Earth Centered Earth Fixed frame
* @param provider Attitude provider
* @param mass Satellite mass (kg)
* @param context Data context
*/
GLONASSAnalyticalPropagator(final GLONASSOrbitalElements glonassOrbit, final Frame eci,
final Frame ecef, final AttitudeProvider provider,
final double mass, final DataContext context) {
super(provider);
this.dataContext = context;
// Stores the GLONASS orbital elements
this.glonassOrbit = glonassOrbit;
// Sets the start date as the date of the orbital elements
setStartDate(glonassOrbit.getDate());
// Sets the mass
this.mass = mass;
// 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(getStartDate());
final Attitude attitude = provider.getAttitude(orbit, orbit.getDate(), orbit.getFrame());
super.resetInitialState(new SpacecraftState(orbit, attitude, mass));
}
/**
* Gets the PVCoordinates of the GLONASS SV in {@link #getECEF() ECEF frame}.
*
* <p>The algorithm is defined at Appendix M.1 from GLONASS Interface Control Document,
* with automatic differentiation added to compute velocity and
* acceleration.</p>
*
* @param date the computation date
* @return the GLONASS SV PVCoordinates in {@link #getECEF() ECEF frame}
*/
public PVCoordinates propagateInEcef(final AbsoluteDate date) {
// Interval of prediction dTpr
final UnivariateDerivative2 dTpr = getdTpr(date);
// Zero
final UnivariateDerivative2 zero = dTpr.getField().getZero();
// The number of whole orbits "w" on a prediction interval
final UnivariateDerivative2 w = FastMath.floor(dTpr.divide(GLONASS_MEAN_DRACONIAN_PERIOD + glonassOrbit.getDeltaT()));
// Current inclination
final UnivariateDerivative2 i = zero.add(GLONASS_MEAN_INCLINATION / 180 * GNSSConstants.GLONASS_PI + glonassOrbit.getDeltaI());
// Eccentricity
final UnivariateDerivative2 e = zero.add(glonassOrbit.getE());
// Mean draconique period in orbite w+1 and mean motion
final UnivariateDerivative2 tDR = w.multiply(2.0).add(1.0).multiply(glonassOrbit.getDeltaTDot()).
add(glonassOrbit.getDeltaT()).
add(GLONASS_MEAN_DRACONIAN_PERIOD);
final UnivariateDerivative2 n = tDR.divide(2.0 * GNSSConstants.GLONASS_PI).reciprocal();
// Semi-major axis : computed by successive approximation
final UnivariateDerivative2 sma = computeSma(tDR, i, e);
// (ae / p)^2 term
final UnivariateDerivative2 p = sma.multiply(e.multiply(e).negate().add(1.0));
final UnivariateDerivative2 aeop = p.divide(GLONASS_EARTH_EQUATORIAL_RADIUS).reciprocal();
final UnivariateDerivative2 aeop2 = aeop.multiply(aeop);
// Current longitude of the ascending node
final UnivariateDerivative2 lambda = computeLambda(dTpr, n, aeop2, i);
// Current argument of perigee
final UnivariateDerivative2 pa = computePA(dTpr, n, aeop2, i);
// Mean longitude at the instant the spacecraft passes the current ascending node
final UnivariateDerivative2 tanPAo2 = FastMath.tan(pa.divide(2.0));
final UnivariateDerivative2 coef = tanPAo2.multiply(FastMath.sqrt(e.negate().add(1.0).divide(e.add(1.0))));
final UnivariateDerivative2 e0 = FastMath.atan(coef).multiply(2.0).negate();
final UnivariateDerivative2 m1 = pa.add(e0).subtract(FastMath.sin(e0).multiply(e));
// Current mean longitude
final UnivariateDerivative2 correction = dTpr.
subtract(w.multiply(GLONASS_MEAN_DRACONIAN_PERIOD + glonassOrbit.getDeltaT())).
subtract(w.multiply(w).multiply(glonassOrbit.getDeltaTDot()));
final UnivariateDerivative2 m = m1.add(n.multiply(correction));
// Take into consideration the periodic perturbations
final FieldSinCos<UnivariateDerivative2> scPa = FastMath.sinCos(pa);
final UnivariateDerivative2 h = e.multiply(scPa.sin());
final UnivariateDerivative2 l = e.multiply(scPa.cos());
// δa1
final UnivariateDerivative2[] d1 = getParameterDifferentials(sma, i, h, l, m1);
// δa2
final UnivariateDerivative2[] d2 = getParameterDifferentials(sma, i, h, l, m);
// Apply corrections
final UnivariateDerivative2 smaCorr = sma.add(d2[0]).subtract(d1[0]);
final UnivariateDerivative2 hCorr = h.add(d2[1]).subtract(d1[1]);
final UnivariateDerivative2 lCorr = l.add(d2[2]).subtract(d1[2]);
final UnivariateDerivative2 lambdaCorr = lambda.add(d2[3]).subtract(d1[3]);
final UnivariateDerivative2 iCorr = i.add(d2[4]).subtract(d1[4]);
final UnivariateDerivative2 mCorr = m.add(d2[5]).subtract(d1[5]);
final UnivariateDerivative2 eCorr = FastMath.sqrt(hCorr.multiply(hCorr).add(lCorr.multiply(lCorr)));
final UnivariateDerivative2 paCorr;
if (eCorr.getValue() == 0.) {
paCorr = zero;
} else {
if (lCorr.getValue() == eCorr.getValue()) {
paCorr = zero.add(0.5 * GNSSConstants.GLONASS_PI);
} else if (lCorr.getValue() == -eCorr.getValue()) {
paCorr = zero.add(-0.5 * GNSSConstants.GLONASS_PI);
} else {
paCorr = FastMath.atan2(hCorr, lCorr);
}
}
// Eccentric Anomaly
final UnivariateDerivative2 mk = mCorr.subtract(paCorr);
final UnivariateDerivative2 ek = getEccentricAnomaly(mk, eCorr);
// True Anomaly
final UnivariateDerivative2 vk = getTrueAnomaly(ek, eCorr);
// Argument of Latitude
final UnivariateDerivative2 phik = vk.add(paCorr);
// Corrected Radius
final UnivariateDerivative2 pCorr = smaCorr.multiply(eCorr.multiply(eCorr).negate().add(1.0));
final UnivariateDerivative2 rk = pCorr.divide(eCorr.multiply(FastMath.cos(vk)).add(1.0));
// Positions in orbital plane
final FieldSinCos<UnivariateDerivative2> scPhik = FastMath.sinCos(phik);
final UnivariateDerivative2 xk = scPhik.cos().multiply(rk);
final UnivariateDerivative2 yk = scPhik.sin().multiply(rk);
// Coordinates of position
final FieldSinCos<UnivariateDerivative2> scL = FastMath.sinCos(lambdaCorr);
final FieldSinCos<UnivariateDerivative2> scI = FastMath.sinCos(iCorr);
final FieldVector3D<UnivariateDerivative2> positionwithDerivatives =
new FieldVector3D<>(xk.multiply(scL.cos()).subtract(yk.multiply(scL.sin()).multiply(scI.cos())),
xk.multiply(scL.sin()).add(yk.multiply(scL.cos()).multiply(scI.cos())),
yk.multiply(scI.sin()));
return new PVCoordinates(new Vector3D(positionwithDerivatives.getX().getValue(),
positionwithDerivatives.getY().getValue(),
positionwithDerivatives.getZ().getValue()),
new Vector3D(positionwithDerivatives.getX().getFirstDerivative(),
positionwithDerivatives.getY().getFirstDerivative(),
positionwithDerivatives.getZ().getFirstDerivative()),
new Vector3D(positionwithDerivatives.getX().getSecondDerivative(),
positionwithDerivatives.getY().getSecondDerivative(),
positionwithDerivatives.getZ().getSecondDerivative()));
}
/**
* 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)
* @param e the eccentricity
* @return the eccentric anomaly (rad)
*/
private UnivariateDerivative2 getEccentricAnomaly(final UnivariateDerivative2 mk, final UnivariateDerivative2 e) {
// reduce M to [-PI PI] interval
final UnivariateDerivative2 reducedM = new UnivariateDerivative2(MathUtils.normalizeAngle(mk.getValue(), 0.0),
mk.getFirstDerivative(),
mk.getSecondDerivative());
// compute start value according to A. W. Odell and R. H. Gooding S12 starter
UnivariateDerivative2 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(e));
}
} else {
if (reducedM.getValue() < 0) {
final UnivariateDerivative2 w = reducedM.add(FastMath.PI);
ek = reducedM.add(w.multiply(-A).divide(w.subtract(B)).subtract(FastMath.PI).subtract(reducedM).multiply(e));
} else {
final UnivariateDerivative2 minusW = reducedM.subtract(FastMath.PI);
ek = reducedM.add(minusW.multiply(A).divide(minusW.add(B)).add(FastMath.PI).subtract(reducedM).multiply(e));
}
}
final UnivariateDerivative2 e1 = e.negate().add(1.0);
final boolean noCancellationRisk = (e1.getValue() + 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 UnivariateDerivative2 f;
UnivariateDerivative2 fd;
final UnivariateDerivative2 fdd = ek.sin().multiply(e);
final UnivariateDerivative2 fddd = ek.cos().multiply(e);
if (noCancellationRisk) {
f = ek.subtract(fdd).subtract(reducedM);
fd = fddd.subtract(1).negate();
} else {
f = eMeSinE(ek, e).subtract(reducedM);
final UnivariateDerivative2 s = ek.multiply(0.5).sin();
fd = s.multiply(s).multiply(e.multiply(2.0)).add(e1);
}
final UnivariateDerivative2 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 UnivariateDerivative2 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
* @param ecc the eccentricity
* @return E - e sin(E)
*/
private UnivariateDerivative2 eMeSinE(final UnivariateDerivative2 E, final UnivariateDerivative2 ecc) {
UnivariateDerivative2 x = E.sin().multiply(ecc.negate().add(1.0));
final UnivariateDerivative2 mE2 = E.negate().multiply(E);
UnivariateDerivative2 term = E;
UnivariateDerivative2 d = E.getField().getZero();
// the inequality test below IS intentional and should NOT be replaced by a check with a small tolerance
for (UnivariateDerivative2 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)
* @param ecc the eccentricity
* @return the true anomaly (rad)
*/
private UnivariateDerivative2 getTrueAnomaly(final UnivariateDerivative2 ek, final UnivariateDerivative2 ecc) {
final UnivariateDerivative2 svk = ek.sin().multiply(FastMath.sqrt( ecc.multiply(ecc).negate().add(1.0)));
final UnivariateDerivative2 cvk = ek.cos().subtract(ecc);
return svk.atan2(cvk);
}
/**
* Get the interval of prediction.
*
* @param date the considered date
* @return the duration from GLONASS orbit Reference epoch (s)
*/
private UnivariateDerivative2 getdTpr(final AbsoluteDate date) {
final TimeScale glonass = dataContext.getTimeScales().getGLONASS();
final GLONASSDate tEnd = new GLONASSDate(date, glonass);
final GLONASSDate tSta = new GLONASSDate(glonassOrbit.getDate(), glonass);
final int n = tEnd.getDayNumber();
final int na = tSta.getDayNumber();
final int deltaN;
if (na == 27) {
deltaN = n - na - FastMath.round((float) (n - na) / 1460) * 1460;
} else {
deltaN = n - na - FastMath.round((float) (n - na) / 1461) * 1461;
}
final UnivariateDerivative2 ti = new UnivariateDerivative2(tEnd.getSecInDay(), 1.0, 0.0);
return ti.subtract(glonassOrbit.getTime()).add(86400 * deltaN);
}
/**
* Computes the semi-major axis of orbit using technique of successive approximations.
* @param tDR mean draconique period (s)
* @param i current inclination (rad)
* @param e eccentricity
* @return the semi-major axis (m).
*/
private UnivariateDerivative2 computeSma(final UnivariateDerivative2 tDR,
final UnivariateDerivative2 i,
final UnivariateDerivative2 e) {
// Zero
final UnivariateDerivative2 zero = tDR.getField().getZero();
// If one of the input parameter is equal to Double.NaN, an infinite loop can occur.
// In that case, we do not compute the value of the semi major axis.
// We decided to return a Double.NaN value instead.
if (Double.isNaN(tDR.getValue()) || Double.isNaN(i.getValue()) || Double.isNaN(e.getValue())) {
return zero.add(Double.NaN);
}
// Common parameters
final UnivariateDerivative2 sinI = FastMath.sin(i);
final UnivariateDerivative2 sin2I = sinI.multiply(sinI);
final UnivariateDerivative2 ome2 = e.multiply(e).negate().add(1.0);
final UnivariateDerivative2 ome2Pow3o2 = FastMath.sqrt(ome2).multiply(ome2);
final UnivariateDerivative2 pa = zero.add(glonassOrbit.getPa());
final UnivariateDerivative2 cosPA = FastMath.cos(pa);
final UnivariateDerivative2 opecosPA = e.multiply(cosPA).add(1.0);
final UnivariateDerivative2 opecosPAPow2 = opecosPA.multiply(opecosPA);
final UnivariateDerivative2 opecosPAPow3 = opecosPAPow2.multiply(opecosPA);
// Initial approximation
UnivariateDerivative2 tOCK = tDR;
// Successive approximations
// The process of approximation ends when fulfilling the following condition: |a(n+1) - a(n)| < 1cm
UnivariateDerivative2 an = zero;
UnivariateDerivative2 anp1 = zero;
boolean isLastStep = false;
while (!isLastStep) {
// a(n+1) computation
final UnivariateDerivative2 tOCKo2p = tOCK.divide(2.0 * GNSSConstants.GLONASS_PI);
final UnivariateDerivative2 tOCKo2pPow2 = tOCKo2p.multiply(tOCKo2p);
anp1 = FastMath.cbrt(tOCKo2pPow2.multiply(GNSSConstants.GLONASS_MU));
// p(n+1) computation
final UnivariateDerivative2 p = anp1.multiply(ome2);
// Tock(n+1) computation
final UnivariateDerivative2 aeop = p.divide(GLONASS_EARTH_EQUATORIAL_RADIUS).reciprocal();
final UnivariateDerivative2 aeop2 = aeop.multiply(aeop);
final UnivariateDerivative2 term1 = aeop2.multiply(GLONASS_J20).multiply(1.5);
final UnivariateDerivative2 term2 = sin2I.multiply(2.5).negate().add(2.0);
final UnivariateDerivative2 term3 = ome2Pow3o2.divide(opecosPAPow2);
final UnivariateDerivative2 term4 = opecosPAPow3.divide(ome2);
tOCK = tDR.divide(term1.multiply(term2.multiply(term3).add(term4)).negate().add(1.0));
// Check convergence
if (FastMath.abs(anp1.subtract(an).getReal()) <= 0.01) {
isLastStep = true;
}
an = anp1;
}
return an;
}
/**
* Computes the current longitude of the ascending node.
* @param dTpr interval of prediction (s)
* @param n mean motion (rad/s)
* @param aeop2 square of the ratio between the radius of the ellipsoid and p, with p = sma * (1 - ecc²)
* @param i inclination (rad)
* @return the current longitude of the ascending node (rad)
*/
private UnivariateDerivative2 computeLambda(final UnivariateDerivative2 dTpr,
final UnivariateDerivative2 n,
final UnivariateDerivative2 aeop2,
final UnivariateDerivative2 i) {
final UnivariateDerivative2 cosI = FastMath.cos(i);
final UnivariateDerivative2 precession = aeop2.multiply(n).multiply(cosI).multiply(1.5 * GLONASS_J20);
return dTpr.multiply(precession.add(GLONASS_AV)).negate().add(glonassOrbit.getLambda());
}
/**
* Computes the current argument of perigee.
* @param dTpr interval of prediction (s)
* @param n mean motion (rad/s)
* @param aeop2 square of the ratio between the radius of the ellipsoid and p, with p = sma * (1 - ecc²)
* @param i inclination (rad)
* @return the current argument of perigee (rad)
*/
private UnivariateDerivative2 computePA(final UnivariateDerivative2 dTpr,
final UnivariateDerivative2 n,
final UnivariateDerivative2 aeop2,
final UnivariateDerivative2 i) {
final UnivariateDerivative2 cosI = FastMath.cos(i);
final UnivariateDerivative2 cos2I = cosI.multiply(cosI);
final UnivariateDerivative2 precession = aeop2.multiply(n).multiply(cos2I.multiply(5.0).negate().add(1.0)).multiply(0.75 * GLONASS_J20);
return dTpr.multiply(precession).negate().add(glonassOrbit.getPa());
}
/**
* Computes the differentials δa<sub>i</sub>.
* <p>
* The value of i depends of the type of longitude (i = 2 for the current mean longitude;
* i = 1 for the mean longitude at the instant the spacecraft passes the current ascending node)
* </p>
* @param a semi-major axis (m)
* @param i inclination (rad)
* @param h x component of the eccentricity (rad)
* @param l y component of the eccentricity (rad)
* @param m longitude (current or at the ascending node instant)
* @return the differentials of the orbital parameters
*/
private UnivariateDerivative2[] getParameterDifferentials(final UnivariateDerivative2 a, final UnivariateDerivative2 i,
final UnivariateDerivative2 h, final UnivariateDerivative2 l,
final UnivariateDerivative2 m) {
// B constant
final UnivariateDerivative2 aeoa = a.divide(GLONASS_EARTH_EQUATORIAL_RADIUS).reciprocal();
final UnivariateDerivative2 aeoa2 = aeoa.multiply(aeoa);
final UnivariateDerivative2 b = aeoa2.multiply(1.5 * GLONASS_J20);
// Commons Parameters
final FieldSinCos<UnivariateDerivative2> scI = FastMath.sinCos(i);
final FieldSinCos<UnivariateDerivative2> scLk = FastMath.sinCos(m);
final FieldSinCos<UnivariateDerivative2> sc2Lk = FieldSinCos.sum(scLk, scLk);
final FieldSinCos<UnivariateDerivative2> sc3Lk = FieldSinCos.sum(scLk, sc2Lk);
final FieldSinCos<UnivariateDerivative2> sc4Lk = FieldSinCos.sum(sc2Lk, sc2Lk);
final UnivariateDerivative2 cosI = scI.cos();
final UnivariateDerivative2 sinI = scI.sin();
final UnivariateDerivative2 cosI2 = cosI.multiply(cosI);
final UnivariateDerivative2 sinI2 = sinI.multiply(sinI);
final UnivariateDerivative2 cosLk = scLk.cos();
final UnivariateDerivative2 sinLk = scLk.sin();
final UnivariateDerivative2 cos2Lk = sc2Lk.cos();
final UnivariateDerivative2 sin2Lk = sc2Lk.sin();
final UnivariateDerivative2 cos3Lk = sc3Lk.cos();
final UnivariateDerivative2 sin3Lk = sc3Lk.sin();
final UnivariateDerivative2 cos4Lk = sc4Lk.cos();
final UnivariateDerivative2 sin4Lk = sc4Lk.sin();
// h*cos(nLk), l*cos(nLk), h*sin(nLk) and l*sin(nLk)
// n = 1
final UnivariateDerivative2 hCosLk = h.multiply(cosLk);
final UnivariateDerivative2 hSinLk = h.multiply(sinLk);
final UnivariateDerivative2 lCosLk = l.multiply(cosLk);
final UnivariateDerivative2 lSinLk = l.multiply(sinLk);
// n = 2
final UnivariateDerivative2 hCos2Lk = h.multiply(cos2Lk);
final UnivariateDerivative2 hSin2Lk = h.multiply(sin2Lk);
final UnivariateDerivative2 lCos2Lk = l.multiply(cos2Lk);
final UnivariateDerivative2 lSin2Lk = l.multiply(sin2Lk);
// n = 3
final UnivariateDerivative2 hCos3Lk = h.multiply(cos3Lk);
final UnivariateDerivative2 hSin3Lk = h.multiply(sin3Lk);
final UnivariateDerivative2 lCos3Lk = l.multiply(cos3Lk);
final UnivariateDerivative2 lSin3Lk = l.multiply(sin3Lk);
// n = 4
final UnivariateDerivative2 hCos4Lk = h.multiply(cos4Lk);
final UnivariateDerivative2 hSin4Lk = h.multiply(sin4Lk);
final UnivariateDerivative2 lCos4Lk = l.multiply(cos4Lk);
final UnivariateDerivative2 lSin4Lk = l.multiply(sin4Lk);
// 1 - (3 / 2)*sin²i
final UnivariateDerivative2 om3o2xSinI2 = sinI2.multiply(1.5).negate().add(1.0);
// Compute Differentials
// δa
final UnivariateDerivative2 dakT1 = b.multiply(2.0).multiply(om3o2xSinI2).multiply(lCosLk.add(hSinLk));
final UnivariateDerivative2 dakT2 = b.multiply(sinI2).multiply(hSinLk.multiply(0.5).subtract(lCosLk.multiply(0.5)).
add(cos2Lk).add(lCos3Lk.multiply(3.5)).add(hSin3Lk.multiply(3.5)));
final UnivariateDerivative2 dak = dakT1.add(dakT2);
// δh
final UnivariateDerivative2 dhkT1 = b.multiply(om3o2xSinI2).multiply(sinLk.add(lSin2Lk.multiply(1.5)).subtract(hCos2Lk.multiply(1.5)));
final UnivariateDerivative2 dhkT2 = b.multiply(sinI2).multiply(0.25).multiply(sinLk.subtract(sin3Lk.multiply(SEVEN_THIRD)).add(lSin2Lk.multiply(5.0)).
subtract(lSin4Lk.multiply(8.5)).add(hCos4Lk.multiply(8.5)).add(hCos2Lk));
final UnivariateDerivative2 dhkT3 = lSin2Lk.multiply(cosI2).multiply(b).multiply(0.5).negate();
final UnivariateDerivative2 dhk = dhkT1.subtract(dhkT2).add(dhkT3);
// δl
final UnivariateDerivative2 dlkT1 = b.multiply(om3o2xSinI2).multiply(cosLk.add(lCos2Lk.multiply(1.5)).add(hSin2Lk.multiply(1.5)));
final UnivariateDerivative2 dlkT2 = b.multiply(sinI2).multiply(0.25).multiply(cosLk.negate().subtract(cos3Lk.multiply(SEVEN_THIRD)).subtract(hSin2Lk.multiply(5.0)).
subtract(lCos4Lk.multiply(8.5)).subtract(hSin4Lk.multiply(8.5)).add(lCos2Lk));
final UnivariateDerivative2 dlkT3 = hSin2Lk.multiply(cosI2).multiply(b).multiply(0.5);
final UnivariateDerivative2 dlk = dlkT1.subtract(dlkT2).add(dlkT3);
// δλ
final UnivariateDerivative2 dokT1 = b.negate().multiply(cosI);
final UnivariateDerivative2 dokT2 = lSinLk.multiply(3.5).subtract(hCosLk.multiply(2.5)).subtract(sin2Lk.multiply(0.5)).
subtract(lSin3Lk.multiply(SEVEN_SIXTH)).add(hCos3Lk.multiply(SEVEN_SIXTH));
final UnivariateDerivative2 dok = dokT1.multiply(dokT2);
// δi
final UnivariateDerivative2 dik = b.multiply(sinI).multiply(cosI).multiply(0.5).
multiply(lCosLk.negate().add(hSinLk).add(cos2Lk).add(lCos3Lk.multiply(SEVEN_THIRD)).add(hSin3Lk.multiply(SEVEN_THIRD)));
// δL
final UnivariateDerivative2 dLkT1 = b.multiply(2.0).multiply(om3o2xSinI2).multiply(lSinLk.multiply(1.75).subtract(hCosLk.multiply(1.75)));
final UnivariateDerivative2 dLkT2 = b.multiply(sinI2).multiply(3.0).multiply(hCosLk.multiply(SEVEN_24TH).negate().subtract(lSinLk.multiply(SEVEN_24TH)).
subtract(hCos3Lk.multiply(FN_72TH)).add(lSin3Lk.multiply(FN_72TH)).add(sin2Lk.multiply(0.25)));
final UnivariateDerivative2 dLkT3 = b.multiply(cosI2).multiply(lSinLk.multiply(3.5).subtract(hCosLk.multiply(2.5)).subtract(sin2Lk.multiply(0.5)).
subtract(lSin3Lk.multiply(SEVEN_SIXTH)).add(hCos3Lk.multiply(SEVEN_SIXTH)));
final UnivariateDerivative2 dLk = dLkT1.add(dLkT2).add(dLkT3);
// Final array
final UnivariateDerivative2[] differentials = MathArrays.buildArray(a.getField(), 6);
differentials[0] = dak.multiply(a);
differentials[1] = dhk;
differentials[2] = dlk;
differentials[3] = dok;
differentials[4] = dik;
differentials[5] = dLk;
return differentials;
}
/** {@inheritDoc} */
protected double getMass(final AbsoluteDate date) {
return mass;
}
/**
* Get the Earth gravity coefficient used for GLONASS propagation.
* @return the Earth gravity coefficient.
*/
public static double getMU() {
return GNSSConstants.GLONASS_MU;
}
/**
* Gets the underlying GLONASS orbital elements.
*
* @return the underlying GLONASS orbital elements
*/
public GLONASSOrbitalElements getGLONASSOrbitalElements() {
return glonassOrbit;
}
/**
* 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 GLONASS orbits.
* @return the ECEF frame
*/
public Frame getECEF() {
return ecef;
}
/** {@inheritDoc} */
public Frame getFrame() {
return eci;
}
/** {@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);
}
/** {@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, GNSSConstants.GLONASS_MU);
}
}