AbstractGNSSPropagator.java

  1. /* Copyright 2002-2020 CS GROUP
  2.  * Licensed to CS GROUP (CS) under one or more
  3.  * contributor license agreements.  See the NOTICE file distributed with
  4.  * this work for additional information regarding copyright ownership.
  5.  * CS licenses this file to You under the Apache License, Version 2.0
  6.  * (the "License"); you may not use this file except in compliance with
  7.  * the License.  You may obtain a copy of the License at
  8.  *
  9.  *   http://www.apache.org/licenses/LICENSE-2.0
  10.  *
  11.  * Unless required by applicable law or agreed to in writing, software
  12.  * distributed under the License is distributed on an "AS IS" BASIS,
  13.  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  14.  * See the License for the specific language governing permissions and
  15.  * limitations under the License.
  16.  */
  17. package org.orekit.propagation.analytical.gnss;

  19. import org.hipparchus.analysis.differentiation.UnivariateDerivative2;
  20. import org.hipparchus.geometry.euclidean.threed.FieldVector3D;
  21. import org.hipparchus.geometry.euclidean.threed.Vector3D;
  22. import org.hipparchus.util.FastMath;
  23. import org.hipparchus.util.MathUtils;
  24. import org.hipparchus.util.Precision;
  25. import org.orekit.attitudes.AttitudeProvider;
  26. import org.orekit.errors.OrekitException;
  27. import org.orekit.errors.OrekitMessages;
  28. import org.orekit.frames.Frame;
  29. import org.orekit.orbits.CartesianOrbit;
  30. import org.orekit.orbits.Orbit;
  31. import org.orekit.propagation.SpacecraftState;
  32. import org.orekit.propagation.analytical.AbstractAnalyticalPropagator;
  33. import org.orekit.time.AbsoluteDate;
  34. import org.orekit.utils.PVCoordinates;

  36. /** Common handling of {@link AbstractAnalyticalPropagator} methods for GNSS propagators.
  37.  * <p>
  38.  * This abstract class allows to provide easily a subset of {@link AbstractAnalyticalPropagator} methods
  39.  * for specific GNSS propagators.
  40.  * </p>
  41.  * @author Pascal Parraud
  42.  */
  43. public abstract class AbstractGNSSPropagator extends AbstractAnalyticalPropagator {

  45.     // Data used to solve Kepler's equation
  46.     /** First coefficient to compute Kepler equation solver starter. */
  47.     private static final double A;

  49.     /** Second coefficient to compute Kepler equation solver starter. */
  50.     private static final double B;

  52.     static {
  53.         final double k1 = 3 * FastMath.PI + 2;
  54.         final double k2 = FastMath.PI - 1;
  55.         final double k3 = 6 * FastMath.PI - 1;
  56.         A  = 3 * k2 * k2 / k1;
  57.         B  = k3 * k3 / (6 * k1);
  58.     }

  60.     /** The GNSS orbital elements used. */
  61.     private final GNSSOrbitalElements gnssOrbit;

  63.     /** Mean angular velocity of the Earth. */
  64.     private final double av;

  66.     /** Duration of the GNSS cycle in seconds. */
  67.     private final double cycleDuration;

  69.     /** The spacecraft mass (kg). */
  70.     private final double mass;

  72.     /** The Earth gravity coefficient used for GNSS propagation. */
  73.     private final double mu;

  75.     /** The ECI frame used for GNSS propagation. */
  76.     private final Frame eci;

  78.     /** The ECEF frame used for GNSS propagation. */
  79.     private final Frame ecef;

  81.     /** Build a new instance.
  82.      * @param gnssOrbit the common GNSS orbital elements to be used by the Abstract GNSS propagator
  83.      * @param attitudeProvider provider for attitude computation
  84.      * @param eci the ECI frame used for GNSS propagation
  85.      * @param ecef the ECEF frame used for GNSS propagation
  86.      * @param mass the spacecraft mass (kg)
  87.      * @param av mean angular velocity of the Earth (rad/s)
  88.      * @param cycleDuration duration of the GNSS cycle in seconds
  89.      * @param mu the Earth gravity coefficient used for GNSS propagation
  90.      */
  91.     protected AbstractGNSSPropagator(final GNSSOrbitalElements gnssOrbit, final AttitudeProvider attitudeProvider,
  92.                                      final Frame eci, final Frame ecef, final double mass,
  93.                                      final double av, final double cycleDuration, final double mu) {
  94.         super(attitudeProvider);
  95.         this.gnssOrbit     = gnssOrbit;
  96.         this.av            = av;
  97.         this.cycleDuration = cycleDuration;
  98.         this.mass          = mass;
  99.         this.mu            = mu;
  100.         // Sets the Earth Centered Inertial frame
  101.         this.eci  = eci;
  102.         // Sets the Earth Centered Earth Fixed frame
  103.         this.ecef = ecef;
  104.         // Sets the start date as the date of the orbital elements
  105.         setStartDate(gnssOrbit.getDate());
  106.     }

  108.     /** Get the duration from GNSS Reference epoch.
  109.      * <p>This takes the GNSS week roll-over into account.</p>
  110.      * @param date the considered date
  111.      * @return the duration from GNSS orbit Reference epoch (s)
  112.      */
  113.     private double getTk(final AbsoluteDate date) {
  114.         // Time from ephemeris reference epoch
  115.         double tk = date.durationFrom(gnssOrbit.getDate());
  116.         // Adjusts the time to take roll over week into account
  117.         while (tk > 0.5 * cycleDuration) {
  118.             tk -= cycleDuration;
  119.         }
  120.         while (tk < -0.5 * cycleDuration) {
  121.             tk += cycleDuration;
  122.         }
  123.         // Returns the time from ephemeris reference epoch
  124.         return tk;
  125.     }

  127.     /**
  128.      * Gets the PVCoordinates of the GNSS SV in {@link #getECEF() ECEF frame}.
  129.      *
  130.      * <p>The algorithm uses automatic differentiation to compute velocity and
  131.      * acceleration.</p>
  132.      *
  133.      * @param date the computation date
  134.      * @return the GNSS SV PVCoordinates in {@link #getECEF() ECEF frame}
  135.      */
  136.     public PVCoordinates propagateInEcef(final AbsoluteDate date) {
  137.         // Duration from GNSS ephemeris Reference date
  138.         final UnivariateDerivative2 tk = new UnivariateDerivative2(getTk(date), 1.0, 0.0);
  139.         // Mean anomaly
  140.         final UnivariateDerivative2 mk = tk.multiply(gnssOrbit.getMeanMotion()).add(gnssOrbit.getM0());
  141.         // Eccentric Anomaly
  142.         final UnivariateDerivative2 ek = getEccentricAnomaly(mk);
  143.         // True Anomaly
  144.         final UnivariateDerivative2 vk =  getTrueAnomaly(ek);
  145.         // Argument of Latitude
  146.         final UnivariateDerivative2 phik    = vk.add(gnssOrbit.getPa());
  147.         final UnivariateDerivative2 twoPhik = phik.multiply(2);
  148.         final UnivariateDerivative2 c2phi   = twoPhik.cos();
  149.         final UnivariateDerivative2 s2phi   = twoPhik.sin();
  150.         // Argument of Latitude Correction
  151.         final UnivariateDerivative2 dphik = c2phi.multiply(gnssOrbit.getCuc()).add(s2phi.multiply(gnssOrbit.getCus()));
  152.         // Radius Correction
  153.         final UnivariateDerivative2 drk = c2phi.multiply(gnssOrbit.getCrc()).add(s2phi.multiply(gnssOrbit.getCrs()));
  154.         // Inclination Correction
  155.         final UnivariateDerivative2 dik = c2phi.multiply(gnssOrbit.getCic()).add(s2phi.multiply(gnssOrbit.getCis()));
  156.         // Corrected Argument of Latitude
  157.         final UnivariateDerivative2 uk = phik.add(dphik);
  158.         // Corrected Radius
  159.         final UnivariateDerivative2 rk = ek.cos().multiply(-gnssOrbit.getE()).add(1).multiply(gnssOrbit.getSma()).add(drk);
  160.         // Corrected Inclination
  161.         final UnivariateDerivative2 ik  = tk.multiply(gnssOrbit.getIDot()).add(gnssOrbit.getI0()).add(dik);
  162.         final UnivariateDerivative2 cik = ik.cos();
  163.         // Positions in orbital plane
  164.         final UnivariateDerivative2 xk = uk.cos().multiply(rk);
  165.         final UnivariateDerivative2 yk = uk.sin().multiply(rk);
  166.         // Corrected longitude of ascending node
  167.         final UnivariateDerivative2 omk = tk.multiply(gnssOrbit.getOmegaDot() - av).
  168.                                         add(gnssOrbit.getOmega0() - av * gnssOrbit.getTime());
  169.         final UnivariateDerivative2 comk = omk.cos();
  170.         final UnivariateDerivative2 somk = omk.sin();
  171.         // returns the Earth-fixed coordinates
  172.         final FieldVector3D<UnivariateDerivative2> positionwithDerivatives =
  173.                         new FieldVector3D<>(xk.multiply(comk).subtract(yk.multiply(somk).multiply(cik)),
  174.                                             xk.multiply(somk).add(yk.multiply(comk).multiply(cik)),
  175.                                             yk.multiply(ik.sin()));
  176.         return new PVCoordinates(new Vector3D(positionwithDerivatives.getX().getValue(),
  177.                                               positionwithDerivatives.getY().getValue(),
  178.                                               positionwithDerivatives.getZ().getValue()),
  179.                                  new Vector3D(positionwithDerivatives.getX().getFirstDerivative(),
  180.                                               positionwithDerivatives.getY().getFirstDerivative(),
  181.                                               positionwithDerivatives.getZ().getFirstDerivative()),
  182.                                  new Vector3D(positionwithDerivatives.getX().getSecondDerivative(),
  183.                                               positionwithDerivatives.getY().getSecondDerivative(),
  184.                                               positionwithDerivatives.getZ().getSecondDerivative()));
  185.     }

  187.     /**
  188.      * Gets eccentric anomaly from mean anomaly.
  189.      * <p>The algorithm used to solve the Kepler equation has been published in:
  190.      * "Procedures for  solving Kepler's Equation", A. W. Odell and R. H. Gooding,
  191.      * Celestial Mechanics 38 (1986) 307-334</p>
  192.      * <p>It has been copied from the OREKIT library (KeplerianOrbit class).</p>
  193.      *
  194.      * @param mk the mean anomaly (rad)
  195.      * @return the eccentric anomaly (rad)
  196.      */
  197.     private UnivariateDerivative2 getEccentricAnomaly(final UnivariateDerivative2 mk) {

  199.         // reduce M to [-PI PI] interval
  200.         final UnivariateDerivative2 reducedM = new UnivariateDerivative2(MathUtils.normalizeAngle(mk.getValue(), 0.0),
  201.                                                                          mk.getFirstDerivative(),
  202.                                                                          mk.getSecondDerivative());

  204.         // compute start value according to A. W. Odell and R. H. Gooding S12 starter
  205.         UnivariateDerivative2 ek;
  206.         if (FastMath.abs(reducedM.getValue()) < 1.0 / 6.0) {
  207.             if (FastMath.abs(reducedM.getValue()) < Precision.SAFE_MIN) {
  208.                 // this is an Orekit change to the S12 starter.
  209.                 // If reducedM is 0.0, the derivative of cbrt is infinite which induces NaN appearing later in
  210.                 // the computation. As in this case E and M are almost equal, we initialize ek with reducedM
  211.                 ek = reducedM;
  212.             } else {
  213.                 // this is the standard S12 starter
  214.                 ek = reducedM.add(reducedM.multiply(6).cbrt().subtract(reducedM).multiply(gnssOrbit.getE()));
  215.             }
  216.         } else {
  217.             if (reducedM.getValue() < 0) {
  218.                 final UnivariateDerivative2 w = reducedM.add(FastMath.PI);
  219.                 ek = reducedM.add(w.multiply(-A).divide(w.subtract(B)).subtract(FastMath.PI).subtract(reducedM).multiply(gnssOrbit.getE()));
  220.             } else {
  221.                 final UnivariateDerivative2 minusW = reducedM.subtract(FastMath.PI);
  222.                 ek = reducedM.add(minusW.multiply(A).divide(minusW.add(B)).add(FastMath.PI).subtract(reducedM).multiply(gnssOrbit.getE()));
  223.             }
  224.         }

  226.         final double e1 = 1 - gnssOrbit.getE();
  227.         final boolean noCancellationRisk = (e1 + ek.getValue() * ek.getValue() / 6) >= 0.1;

  229.         // perform two iterations, each consisting of one Halley step and one Newton-Raphson step
  230.         for (int j = 0; j < 2; ++j) {
  231.             final UnivariateDerivative2 f;
  232.             UnivariateDerivative2 fd;
  233.             final UnivariateDerivative2 fdd  = ek.sin().multiply(gnssOrbit.getE());
  234.             final UnivariateDerivative2 fddd = ek.cos().multiply(gnssOrbit.getE());
  235.             if (noCancellationRisk) {
  236.                 f  = ek.subtract(fdd).subtract(reducedM);
  237.                 fd = fddd.subtract(1).negate();
  238.             } else {
  239.                 f  = eMeSinE(ek).subtract(reducedM);
  240.                 final UnivariateDerivative2 s = ek.multiply(0.5).sin();
  241.                 fd = s.multiply(s).multiply(2 * gnssOrbit.getE()).add(e1);
  242.             }
  243.             final UnivariateDerivative2 dee = f.multiply(fd).divide(f.multiply(0.5).multiply(fdd).subtract(fd.multiply(fd)));

  245.             // update eccentric anomaly, using expressions that limit underflow problems
  246.             final UnivariateDerivative2 w = fd.add(dee.multiply(0.5).multiply(fdd.add(dee.multiply(fdd).divide(3))));
  247.             fd = fd.add(dee.multiply(fdd.add(dee.multiply(0.5).multiply(fdd))));
  248.             ek = ek.subtract(f.subtract(dee.multiply(fd.subtract(w))).divide(fd));
  249.         }

  251.         // expand the result back to original range
  252.         ek = ek.add(mk.getValue() - reducedM.getValue());

  254.         // Returns the eccentric anomaly
  255.         return ek;
  256.     }

  258.     /**
  259.      * Accurate computation of E - e sin(E).
  260.      *
  261.      * @param E eccentric anomaly
  262.      * @return E - e sin(E)
  263.      */
  264.     private UnivariateDerivative2 eMeSinE(final UnivariateDerivative2 E) {
  265.         UnivariateDerivative2 x = E.sin().multiply(1 - gnssOrbit.getE());
  266.         final UnivariateDerivative2 mE2 = E.negate().multiply(E);
  267.         UnivariateDerivative2 term = E;
  268.         UnivariateDerivative2 d    = E.getField().getZero();
  269.         // the inequality test below IS intentional and should NOT be replaced by a check with a small tolerance
  270.         for (UnivariateDerivative2 x0 = d.add(Double.NaN); !Double.valueOf(x.getValue()).equals(Double.valueOf(x0.getValue()));) {
  271.             d = d.add(2);
  272.             term = term.multiply(mE2.divide(d.multiply(d.add(1))));
  273.             x0 = x;
  274.             x = x.subtract(term);
  275.         }
  276.         return x;
  277.     }

  279.     /** Gets true anomaly from eccentric anomaly.
  280.      *
  281.      * @param ek the eccentric anomaly (rad)
  282.      * @return the true anomaly (rad)
  283.      */
  284.     private UnivariateDerivative2 getTrueAnomaly(final UnivariateDerivative2 ek) {
  285.         final UnivariateDerivative2 svk = ek.sin().multiply(FastMath.sqrt(1. - gnssOrbit.getE() * gnssOrbit.getE()));
  286.         final UnivariateDerivative2 cvk = ek.cos().subtract(gnssOrbit.getE());
  287.         return svk.atan2(cvk);
  288.     }

  290.     /** {@inheritDoc} */
  291.     protected Orbit propagateOrbit(final AbsoluteDate date) {
  292.         // Gets the PVCoordinates in ECEF frame
  293.         final PVCoordinates pvaInECEF = propagateInEcef(date);
  294.         // Transforms the PVCoordinates to ECI frame
  295.         final PVCoordinates pvaInECI = ecef.getTransformTo(eci, date).transformPVCoordinates(pvaInECEF);
  296.         // Returns the Cartesian orbit
  297.         return new CartesianOrbit(pvaInECI, eci, date, mu);
  298.     }

  300.     /**
  301.      * Get the Earth gravity coefficient used for GNSS propagation.
  302.      * @return the Earth gravity coefficient.
  303.      */
  304.     public double getMU() {
  305.         return mu;
  306.     }

  308.     /** {@inheritDoc} */
  309.     public Frame getFrame() {
  310.         return eci;
  311.     }

  313.     /** {@inheritDoc} */
  314.     protected double getMass(final AbsoluteDate date) {
  315.         return mass;
  316.     }

  318.     /** {@inheritDoc} */
  319.     public void resetInitialState(final SpacecraftState state) {
  320.         throw new OrekitException(OrekitMessages.NON_RESETABLE_STATE);
  321.     }

  323.     /** {@inheritDoc} */
  324.     protected void resetIntermediateState(final SpacecraftState state, final boolean forward) {
  325.         throw new OrekitException(OrekitMessages.NON_RESETABLE_STATE);
  326.     }

  328.     /**
  329.      * Gets the Earth Centered Inertial frame used to propagate the orbit.
  330.      *
  331.      * @return the ECI frame
  332.      */
  333.     public Frame getECI() {
  334.         return eci;
  335.     }

  337.     /**
  338.      * Gets the Earth Centered Earth Fixed frame used to propagate GNSS orbits according to the
  339.      * Interface Control Document.
  340.      *
  341.      * @return the ECEF frame
  342.      */
  343.     public Frame getECEF() {
  344.         return ecef;
  345.     }

  347. }
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