TLEPropagator.java

  1. /* Copyright 2002-2013 CS Systèmes d'Information
  2.  * Licensed to CS Systèmes d'Information (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.tle;

  19. import org.apache.commons.math3.geometry.euclidean.threed.Vector3D;
  20. import org.apache.commons.math3.util.FastMath;
  21. import org.apache.commons.math3.util.MathUtils;
  22. import org.orekit.attitudes.AttitudeProvider;
  23. import org.orekit.errors.OrekitException;
  24. import org.orekit.errors.OrekitMessages;
  25. import org.orekit.errors.PropagationException;
  26. import org.orekit.frames.Frame;
  27. import org.orekit.frames.FramesFactory;
  28. import org.orekit.orbits.CartesianOrbit;
  29. import org.orekit.orbits.Orbit;
  30. import org.orekit.propagation.SpacecraftState;
  31. import org.orekit.propagation.analytical.AbstractAnalyticalPropagator;
  32. import org.orekit.time.AbsoluteDate;
  33. import org.orekit.utils.PVCoordinates;


  36. /** This class provides elements to propagate TLE's.
  37.  * <p>
  38.  * The models used are SGP4 and SDP4, initially proposed by NORAD as the unique convenient
  39.  * propagator for TLE's. Inputs and outputs of this propagator are only suited for
  40.  * NORAD two lines elements sets, since it uses estimations and mean values appropriate
  41.  * for TLE's only.
  42.  * </p>
  43.  * <p>
  44.  * Deep- or near- space propagator is selected internally according to NORAD recommendations
  45.  * so that the user has not to worry about the used computation methods. One instance is created
  46.  * for each TLE (this instance can only be get using {@link #selectExtrapolator(TLE)} method,
  47.  * and can compute {@link PVCoordinates position and velocity coordinates} at any
  48.  * time. Maximum accuracy is guaranteed in a 24h range period before and after the provided
  49.  * TLE epoch (of course this accuracy is not really measurable nor predictable: according to
  50.  * <a href="http://www.celestrak.com/">CelesTrak</a>, the precision is close to one kilometer
  51.  * and error won't probably rise above 2 km).
  52.  * </p>
  53.  * <p>This implementation is largely inspired from the paper and source code <a
  54.  * href="http://www.celestrak.com/publications/AIAA/2006-6753/">Revisiting Spacetrack
  55.  * Report #3</a> and is fully compliant with its results and tests cases.</p>
  56.  * @author Felix R. Hoots, Ronald L. Roehrich, December 1980 (original fortran)
  57.  * @author David A. Vallado, Paul Crawford, Richard Hujsak, T.S. Kelso (C++ translation and improvements)
  58.  * @author Fabien Maussion (java translation)
  59.  * @see TLE
  60.  */
  61. public abstract class TLEPropagator extends AbstractAnalyticalPropagator {

  63.     // CHECKSTYLE: stop VisibilityModifierCheck

  65.     /** Initial state. */
  66.     protected final TLE tle;

  68.     /** final RAAN. */
  69.     protected double xnode;

  71.     /** final semi major axis. */
  72.     protected double a;

  74.     /** final eccentricity. */
  75.     protected double e;

  77.     /** final inclination. */
  78.     protected double i;

  80.     /** final perigee argument. */
  81.     protected double omega;

  83.     /** L from SPTRCK #3. */
  84.     protected double xl;

  86.     /** original recovered semi major axis. */
  87.     protected double a0dp;

  89.     /** original recovered mean motion. */
  90.     protected double xn0dp;

  92.     /** cosinus original inclination. */
  93.     protected double cosi0;

  95.     /** cos io squared. */
  96.     protected double theta2;

  98.     /** sinus original inclination. */
  99.     protected double sini0;

  101.     /** common parameter for mean anomaly (M) computation. */
  102.     protected double xmdot;

  104.     /** common parameter for perigee argument (omega) computation. */
  105.     protected double omgdot;

  107.     /** common parameter for raan (OMEGA) computation. */
  108.     protected double xnodot;

  110.     /** original eccentricity squared. */
  111.     protected double e0sq;
  112.     /** 1 - e2. */
  113.     protected double beta02;

  115.     /** sqrt (1 - e2). */
  116.     protected double beta0;

  118.     /** perigee, expressed in KM and ALTITUDE. */
  119.     protected double perige;

  121.     /** eta squared. */
  122.     protected double etasq;

  124.     /** original eccentricity * eta. */
  125.     protected double eeta;

  127.     /** s* new value for the contant s. */
  128.     protected double s4;

  130.     /** tsi from SPTRCK #3. */
  131.     protected double tsi;

  133.     /** eta from SPTRCK #3. */
  134.     protected double eta;

  136.     /** coef for SGP C3 computation. */
  137.     protected double coef;

  139.     /** coef for SGP C5 computation. */
  140.     protected double coef1;

  142.     /** C1 from SPTRCK #3. */
  143.     protected double c1;

  145.     /** C2 from SPTRCK #3. */
  146.     protected double c2;

  148.     /** C4 from SPTRCK #3. */
  149.     protected double c4;

  151.     /** common parameter for raan (OMEGA) computation. */
  152.     protected double xnodcf;

  154.     /** 3/2 * C1. */
  155.     protected double t2cof;

  157.     // CHECKSTYLE: resume VisibilityModifierCheck

  159.     /** TLE frame. */
  160.     private final Frame teme;

  162.     /** Spacecraft mass (kg). */
  163.     private final double mass;

  165.     /** Protected constructor for derived classes.
  166.      * @param initialTLE the unique TLE to propagate
  167.      * @param attitudeProvider provider for attitude computation
  168.      * @param mass spacecraft mass (kg)
  169.      * @exception OrekitException if some specific error occurs
  170.      */
  171.     protected TLEPropagator(final TLE initialTLE, final AttitudeProvider attitudeProvider,
  172.                             final double mass)
  173.         throws OrekitException {
  174.         super(attitudeProvider);
  175.         setStartDate(initialTLE.getDate());
  176.         this.tle  = initialTLE;
  177.         this.teme = FramesFactory.getTEME();
  178.         this.mass = mass;
  179.         initializeCommons();
  180.         sxpInitialize();
  181.         // set the initial state
  182.         super.resetInitialState(new SpacecraftState(propagateOrbit(initialTLE.getDate())));
  183.     }

  185.     /** Selects the extrapolator to use with the selected TLE.
  186.      * @param tle the TLE to propagate.
  187.      * @return the correct propagator.
  188.      * @exception OrekitException if the underlying model cannot be initialized
  189.      */
  190.     public static TLEPropagator selectExtrapolator(final TLE tle) throws OrekitException {
  191.         return selectExtrapolator(tle, DEFAULT_LAW, DEFAULT_MASS);
  192.     }

  194.     /** Selects the extrapolator to use with the selected TLE.
  195.      * @param tle the TLE to propagate.
  196.      * @param attitudeProvider provider for attitude computation
  197.      * @param mass spacecraft mass (kg)
  198.      * @return the correct propagator.
  199.      * @exception OrekitException if the underlying model cannot be initialized
  200.      */
  201.     public static TLEPropagator selectExtrapolator(final TLE tle, final AttitudeProvider attitudeProvider,
  202.                                                    final double mass) throws OrekitException {

  204.         final double a1 = FastMath.pow( TLEConstants.XKE / (tle.getMeanMotion() * 60.0), TLEConstants.TWO_THIRD);
  205.         final double cosi0 = FastMath.cos(tle.getI());
  206.         final double temp = TLEConstants.CK2 * 1.5 * (3 * cosi0 * cosi0 - 1.0) *
  207.                             FastMath.pow(1.0 - tle.getE() * tle.getE(), -1.5);
  208.         final double delta1 = temp / (a1 * a1);
  209.         final double a0 = a1 * (1.0 - delta1 * (TLEConstants.ONE_THIRD + delta1 * (delta1 * 134.0 / 81.0 + 1.0)));
  210.         final double delta0 = temp / (a0 * a0);

  212.         // recover original mean motion :
  213.         final double xn0dp = tle.getMeanMotion() * 60.0 / (delta0 + 1.0);

  215.         // Period >= 225 minutes is deep space
  216.         if (MathUtils.TWO_PI / (xn0dp * TLEConstants.MINUTES_PER_DAY) >= (1.0 / 6.4)) {
  217.             return new DeepSDP4(tle, attitudeProvider, mass);
  218.         } else {
  219.             return new SGP4(tle, attitudeProvider, mass);
  220.         }
  221.     }

  223.     /** Get the Earth gravity coefficient used for TLE propagation.
  224.      * @return the Earth gravity coefficient.
  225.      */
  226.     public static double getMU() {
  227.         return TLEConstants.MU;
  228.     }

  230.     /** Get the extrapolated position and velocity from an initial TLE.
  231.      * @param date the final date
  232.      * @return the final PVCoordinates
  233.      * @exception OrekitException if propagation cannot be performed at given date
  234.      */
  235.     public PVCoordinates getPVCoordinates(final AbsoluteDate date)
  236.         throws OrekitException {

  238.         sxpPropagate(date.durationFrom(tle.getDate()) / 60.0);

  240.         // Compute PV with previous calculated parameters
  241.         return computePVCoordinates();
  242.     }

  244.     /** Computation of the first commons parameters.
  245.      */
  246.     private void initializeCommons() {

  248.         final double a1 = FastMath.pow(TLEConstants.XKE / (tle.getMeanMotion() * 60.0), TLEConstants.TWO_THIRD);
  249.         cosi0 = FastMath.cos(tle.getI());
  250.         theta2 = cosi0 * cosi0;
  251.         final double x3thm1 = 3.0 * theta2 - 1.0;
  252.         e0sq = tle.getE() * tle.getE();
  253.         beta02 = 1.0 - e0sq;
  254.         beta0 = FastMath.sqrt(beta02);
  255.         final double tval = TLEConstants.CK2 * 1.5 * x3thm1 / (beta0 * beta02);
  256.         final double delta1 = tval / (a1 * a1);
  257.         final double a0 = a1 * (1.0 - delta1 * (TLEConstants.ONE_THIRD + delta1 * (1.0 + 134.0 / 81.0 * delta1)));
  258.         final double delta0 = tval / (a0 * a0);

  260.         // recover original mean motion and semi-major axis :
  261.         xn0dp = tle.getMeanMotion() * 60.0 / (delta0 + 1.0);
  262.         a0dp = a0 / (1.0 - delta0);

  264.         // Values of s and qms2t :
  265.         s4 = TLEConstants.S;  // unmodified value for s
  266.         double q0ms24 = TLEConstants.QOMS2T; // unmodified value for q0ms2T

  268.         perige = (a0dp * (1 - tle.getE()) - TLEConstants.NORMALIZED_EQUATORIAL_RADIUS) * TLEConstants.EARTH_RADIUS; // perige

  270.         //  For perigee below 156 km, the values of s and qoms2t are changed :
  271.         if (perige < 156.0) {
  272.             if (perige <= 98.0) {
  273.                 s4 = 20.0;
  274.             } else {
  275.                 s4 = perige - 78.0;
  276.             }
  277.             final double temp_val = (120.0 - s4) * TLEConstants.NORMALIZED_EQUATORIAL_RADIUS / TLEConstants.EARTH_RADIUS;
  278.             final double temp_val_squared = temp_val * temp_val;
  279.             q0ms24 = temp_val_squared * temp_val_squared;
  280.             s4 = s4 / TLEConstants.EARTH_RADIUS + TLEConstants.NORMALIZED_EQUATORIAL_RADIUS; // new value for q0ms2T and s
  281.         }

  283.         final double pinv = 1.0 / (a0dp * beta02);
  284.         final double pinvsq = pinv * pinv;
  285.         tsi = 1.0 / (a0dp - s4);
  286.         eta = a0dp * tle.getE() * tsi;
  287.         etasq = eta * eta;
  288.         eeta = tle.getE() * eta;

  290.         final double psisq = FastMath.abs(1.0 - etasq); // abs because pow 3.5 needs positive value
  291.         final double tsi_squared = tsi * tsi;
  292.         coef = q0ms24 * tsi_squared * tsi_squared;
  293.         coef1 = coef / FastMath.pow(psisq, 3.5);

  295.         // C2 and C1 coefficients computation :
  296.         c2 = coef1 * xn0dp * (a0dp * (1.0 + 1.5 * etasq + eeta * (4.0 + etasq)) +
  297.              0.75 * TLEConstants.CK2 * tsi / psisq * x3thm1 * (8.0 + 3.0 * etasq * (8.0 + etasq)));
  298.         c1 = tle.getBStar() * c2;
  299.         sini0 = FastMath.sin(tle.getI());

  301.         final double x1mth2 = 1.0 - theta2;

  303.         // C4 coefficient computation :
  304.         c4 = 2.0 * xn0dp * coef1 * a0dp * beta02 * (eta * (2.0 + 0.5 * etasq) +
  305.              tle.getE() * (0.5 + 2.0 * etasq) -
  306.              2 * TLEConstants.CK2 * tsi / (a0dp * psisq) *
  307.              (-3.0 * x3thm1 * (1.0 - 2.0 * eeta + etasq * (1.5 - 0.5 * eeta)) +
  308.               0.75 * x1mth2 * (2.0 * etasq - eeta * (1.0 + etasq)) * FastMath.cos(2.0 * tle.getPerigeeArgument())));

  310.         final double theta4 = theta2 * theta2;
  311.         final double temp1 = 3 * TLEConstants.CK2 * pinvsq * xn0dp;
  312.         final double temp2 = temp1 * TLEConstants.CK2 * pinvsq;
  313.         final double temp3 = 1.25 * TLEConstants.CK4 * pinvsq * pinvsq * xn0dp;

  315.         // atmospheric and gravitation coefs :(Mdf and OMEGAdf)
  316.         xmdot = xn0dp +
  317.                 0.5 * temp1 * beta0 * x3thm1 +
  318.                 0.0625 * temp2 * beta0 * (13.0 - 78.0 * theta2 + 137.0 * theta4);

  320.         final double x1m5th = 1.0 - 5.0 * theta2;

  322.         omgdot = -0.5 * temp1 * x1m5th +
  323.                  0.0625 * temp2 * (7.0 - 114.0 * theta2 + 395.0 * theta4) +
  324.                  temp3 * (3.0 - 36.0 * theta2 + 49.0 * theta4);

  326.         final double xhdot1 = -temp1 * cosi0;

  328.         xnodot = xhdot1 + (0.5 * temp2 * (4.0 - 19.0 * theta2) + 2.0 * temp3 * (3.0 - 7.0 * theta2)) * cosi0;
  329.         xnodcf = 3.5 * beta02 * xhdot1 * c1;
  330.         t2cof = 1.5 * c1;

  332.     }

  334.     /** Retrieves the position and velocity.
  335.      * @return the computed PVCoordinates.
  336.      * @exception OrekitException if current orbit is out of supported range
  337.      * (too large eccentricity, too low perigee ...)
  338.      */
  339.     private PVCoordinates computePVCoordinates() throws OrekitException {

  341.         // Long period periodics
  342.         final double axn = e * FastMath.cos(omega);
  343.         double temp = 1.0 / (a * (1.0 - e * e));
  344.         final double xlcof = 0.125 * TLEConstants.A3OVK2 * sini0 * (3.0 + 5.0 * cosi0) / (1.0 + cosi0);
  345.         final double aycof = 0.25 * TLEConstants.A3OVK2 * sini0;
  346.         final double xll = temp * xlcof * axn;
  347.         final double aynl = temp * aycof;
  348.         final double xlt = xl + xll;
  349.         final double ayn = e * FastMath.sin(omega) + aynl;
  350.         final double elsq = axn * axn + ayn * ayn;
  351.         final double capu = MathUtils.normalizeAngle(xlt - xnode, FastMath.PI);
  352.         double epw = capu;
  353.         double ecosE = 0;
  354.         double esinE = 0;
  355.         double sinEPW = 0;
  356.         double cosEPW = 0;

  358.         // Dundee changes:  items dependent on cosio get recomputed:
  359.         final double cosi0Sq = cosi0 * cosi0;
  360.         final double x3thm1 = 3.0 * cosi0Sq - 1.0;
  361.         final double x1mth2 = 1.0 - cosi0Sq;
  362.         final double x7thm1 = 7.0 * cosi0Sq - 1.0;

  364.         if (e > (1 - 1e-6)) {
  365.             throw new OrekitException(OrekitMessages.TOO_LARGE_ECCENTRICITY_FOR_PROPAGATION_MODEL, e);
  366.         }

  368.         // Solve Kepler's' Equation.
  369.         final double newtonRaphsonEpsilon = 1e-12;
  370.         for (int j = 0; j < 10; j++) {

  372.             boolean doSecondOrderNewtonRaphson = true;

  374.             sinEPW = FastMath.sin( epw);
  375.             cosEPW = FastMath.cos( epw);
  376.             ecosE = axn * cosEPW + ayn * sinEPW;
  377.             esinE = axn * sinEPW - ayn * cosEPW;
  378.             final double f = capu - epw + esinE;
  379.             if (FastMath.abs(f) < newtonRaphsonEpsilon) {
  380.                 break;
  381.             }
  382.             final double fdot = 1.0 - ecosE;
  383.             double delta_epw = f / fdot;
  384.             if (j == 0) {
  385.                 final double maxNewtonRaphson = 1.25 * FastMath.abs(e);
  386.                 doSecondOrderNewtonRaphson = false;
  387.                 if (delta_epw > maxNewtonRaphson) {
  388.                     delta_epw = maxNewtonRaphson;
  389.                 } else if (delta_epw < -maxNewtonRaphson) {
  390.                     delta_epw = -maxNewtonRaphson;
  391.                 } else {
  392.                     doSecondOrderNewtonRaphson = true;
  393.                 }
  394.             }
  395.             if (doSecondOrderNewtonRaphson) {
  396.                 delta_epw = f / (fdot + 0.5 * esinE * delta_epw);
  397.             }
  398.             epw += delta_epw;
  399.         }

  401.         // Short period preliminary quantities
  402.         temp = 1.0 - elsq;
  403.         final double pl = a * temp;
  404.         final double r = a * (1.0 - ecosE);
  405.         double temp2 = a / r;
  406.         final double betal = FastMath.sqrt(temp);
  407.         temp = esinE / (1.0 + betal);
  408.         final double cosu = temp2 * (cosEPW - axn + ayn * temp);
  409.         final double sinu = temp2 * (sinEPW - ayn - axn * temp);
  410.         final double u = FastMath.atan2(sinu, cosu);
  411.         final double sin2u = 2.0 * sinu * cosu;
  412.         final double cos2u = 2.0 * cosu * cosu - 1.0;
  413.         final double temp1 = TLEConstants.CK2 / pl;
  414.         temp2 = temp1 / pl;

  416.         // Update for short periodics
  417.         final double rk = r * (1.0 - 1.5 * temp2 * betal * x3thm1) + 0.5 * temp1 * x1mth2 * cos2u;
  418.         final double uk = u - 0.25 * temp2 * x7thm1 * sin2u;
  419.         final double xnodek = xnode + 1.5 * temp2 * cosi0 * sin2u;
  420.         final double xinck = i + 1.5 * temp2 * cosi0 * sini0 * cos2u;

  422.         // Orientation vectors
  423.         final double sinuk = FastMath.sin(uk);
  424.         final double cosuk = FastMath.cos(uk);
  425.         final double sinik = FastMath.sin(xinck);
  426.         final double cosik = FastMath.cos(xinck);
  427.         final double sinnok = FastMath.sin(xnodek);
  428.         final double cosnok = FastMath.cos(xnodek);
  429.         final double xmx = -sinnok * cosik;
  430.         final double xmy = cosnok * cosik;
  431.         final double ux = xmx * sinuk + cosnok * cosuk;
  432.         final double uy = xmy * sinuk + sinnok * cosuk;
  433.         final double uz = sinik * sinuk;

  435.         // Position and velocity
  436.         final double cr = 1000 * rk * TLEConstants.EARTH_RADIUS;
  437.         final Vector3D pos = new Vector3D(cr * ux, cr * uy, cr * uz);

  439.         final double rdot   = TLEConstants.XKE * FastMath.sqrt(a) * esinE / r;
  440.         final double rfdot  = TLEConstants.XKE * FastMath.sqrt(pl) / r;
  441.         final double xn     = TLEConstants.XKE / (a * FastMath.sqrt(a));
  442.         final double rdotk  = rdot - xn * temp1 * x1mth2 * sin2u;
  443.         final double rfdotk = rfdot + xn * temp1 * (x1mth2 * cos2u + 1.5 * x3thm1);
  444.         final double vx     = xmx * cosuk - cosnok * sinuk;
  445.         final double vy     = xmy * cosuk - sinnok * sinuk;
  446.         final double vz     = sinik * cosuk;

  448.         final double cv = 1000.0 * TLEConstants.EARTH_RADIUS / 60.0;
  449.         final Vector3D vel = new Vector3D(cv * (rdotk * ux + rfdotk * vx),
  450.                                           cv * (rdotk * uy + rfdotk * vy),
  451.                                           cv * (rdotk * uz + rfdotk * vz));

  453.         return new PVCoordinates(pos, vel);

  455.     }

  457.     /** Initialization proper to each propagator (SGP or SDP).
  458.      * @exception OrekitException if some specific error occurs
  459.      */
  460.     protected abstract void sxpInitialize() throws OrekitException;

  462.     /** Propagation proper to each propagator (SGP or SDP).
  463.      * @param t the offset from initial epoch (min)
  464.      * @exception OrekitException if current state cannot be propagated
  465.      */
  466.     protected abstract void sxpPropagate(double t) throws OrekitException;

  468.     /** {@inheritDoc} */
  469.     public void resetInitialState(final SpacecraftState state)
  470.         throws PropagationException {
  471.         throw new PropagationException(OrekitMessages.NON_RESETABLE_STATE);
  472.     }

  474.     /** {@inheritDoc} */
  475.     protected double getMass(final AbsoluteDate date) {
  476.         return mass;
  477.     }

  479.     /** {@inheritDoc} */
  480.     protected Orbit propagateOrbit(final AbsoluteDate date) throws PropagationException {
  481.         try {
  482.             return new CartesianOrbit(getPVCoordinates(date), teme, date, TLEConstants.MU);
  483.         } catch (OrekitException oe) {
  484.             throw new PropagationException(oe);
  485.         }
  486.     }

  488.     /** Get the underlying TLE.
  489.      * @return underlying TLE
  490.      */
  491.     public TLE getTLE() {
  492.         return tle;
  493.     }

  495.     /** {@inheritDoc} */
  496.     public Frame getFrame() {
  497.         return teme;
  498.     }

  500. }
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