TLEPropagator.java

  1. /* Copyright 2002-2024 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.tle;

  19. import java.util.ArrayList;
  20. import java.util.Collections;
  21. import java.util.HashMap;
  22. import java.util.List;
  23. import java.util.Map;

  25. import org.hipparchus.geometry.euclidean.threed.Vector3D;
  26. import org.hipparchus.linear.RealMatrix;
  27. import org.hipparchus.util.FastMath;
  28. import org.hipparchus.util.MathUtils;
  29. import org.hipparchus.util.SinCos;
  30. import org.orekit.annotation.DefaultDataContext;
  31. import org.orekit.attitudes.Attitude;
  32. import org.orekit.attitudes.AttitudeProvider;
  33. import org.orekit.attitudes.FrameAlignedProvider;
  34. import org.orekit.data.DataContext;
  35. import org.orekit.errors.OrekitException;
  36. import org.orekit.errors.OrekitMessages;
  37. import org.orekit.frames.Frame;
  38. import org.orekit.orbits.CartesianOrbit;
  39. import org.orekit.orbits.Orbit;
  40. import org.orekit.propagation.AbstractMatricesHarvester;
  41. import org.orekit.propagation.MatricesHarvester;
  42. import org.orekit.propagation.SpacecraftState;
  43. import org.orekit.propagation.analytical.AbstractAnalyticalPropagator;
  44. import org.orekit.propagation.analytical.tle.generation.FixedPointTleGenerationAlgorithm;
  45. import org.orekit.propagation.analytical.tle.generation.TleGenerationAlgorithm;
  46. import org.orekit.time.AbsoluteDate;
  47. import org.orekit.time.TimeScale;
  48. import org.orekit.utils.DoubleArrayDictionary;
  49. import org.orekit.utils.PVCoordinates;
  50. import org.orekit.utils.ParameterDriver;
  51. import org.orekit.utils.TimeSpanMap;
  52. import org.orekit.utils.TimeSpanMap.Span;

  54. /** This class provides elements to propagate TLE's.
  55.  * <p>
  56.  * The models used are SGP4 and SDP4, initially proposed by NORAD as the unique convenient
  57.  * propagator for TLE's. Inputs and outputs of this propagator are only suited for
  58.  * NORAD two lines elements sets, since it uses estimations and mean values appropriate
  59.  * for TLE's only.
  60.  * </p>
  61.  * <p>
  62.  * Deep- or near- space propagator is selected internally according to NORAD recommendations
  63.  * so that the user has not to worry about the used computation methods. One instance is created
  64.  * for each TLE (this instance can only be get using {@link #selectExtrapolator(TLE)} method,
  65.  * and can compute {@link PVCoordinates position and velocity coordinates} at any
  66.  * time. Maximum accuracy is guaranteed in a 24h range period before and after the provided
  67.  * TLE epoch (of course this accuracy is not really measurable nor predictable: according to
  68.  * <a href="https://www.celestrak.com/">CelesTrak</a>, the precision is close to one kilometer
  69.  * and error won't probably rise above 2 km).
  70.  * </p>
  71.  * <p>This implementation is largely inspired from the paper and source code <a
  72.  * href="https://www.celestrak.com/publications/AIAA/2006-6753/">Revisiting Spacetrack
  73.  * Report #3</a> and is fully compliant with its results and tests cases.</p>
  74.  * @author Felix R. Hoots, Ronald L. Roehrich, December 1980 (original fortran)
  75.  * @author David A. Vallado, Paul Crawford, Richard Hujsak, T.S. Kelso (C++ translation and improvements)
  76.  * @author Fabien Maussion (java translation)
  77.  * @see TLE
  78.  */
  79. public abstract class TLEPropagator extends AbstractAnalyticalPropagator {

  81.     // CHECKSTYLE: stop VisibilityModifier check

  83.     /** Initial state. */
  84.     protected TLE tle;

  86.     /** UTC time scale. */
  87.     protected final TimeScale utc;

  89.     /** final RAAN. */
  90.     protected double xnode;

  92.     /** final semi major axis. */
  93.     protected double a;

  95.     /** final eccentricity. */
  96.     protected double e;

  98.     /** final inclination. */
  99.     protected double i;

  101.     /** final perigee argument. */
  102.     protected double omega;

  104.     /** L from SPTRCK #3. */
  105.     protected double xl;

  107.     /** original recovered semi major axis. */
  108.     protected double a0dp;

  110.     /** original recovered mean motion. */
  111.     protected double xn0dp;

  113.     /** cosinus original inclination. */
  114.     protected double cosi0;

  116.     /** cos io squared. */
  117.     protected double theta2;

  119.     /** sinus original inclination. */
  120.     protected double sini0;

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

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

  128.     /** common parameter for raan (OMEGA) computation. */
  129.     protected double xnodot;

  131.     /** original eccentricity squared. */
  132.     protected double e0sq;
  133.     /** 1 - e2. */
  134.     protected double beta02;

  136.     /** sqrt (1 - e2). */
  137.     protected double beta0;

  139.     /** perigee, expressed in KM and ALTITUDE. */
  140.     protected double perige;

  142.     /** eta squared. */
  143.     protected double etasq;

  145.     /** original eccentricity * eta. */
  146.     protected double eeta;

  148.     /** s* new value for the contant s. */
  149.     protected double s4;

  151.     /** tsi from SPTRCK #3. */
  152.     protected double tsi;

  154.     /** eta from SPTRCK #3. */
  155.     protected double eta;

  157.     /** coef for SGP C3 computation. */
  158.     protected double coef;

  160.     /** coef for SGP C5 computation. */
  161.     protected double coef1;

  163.     /** C1 from SPTRCK #3. */
  164.     protected double c1;

  166.     /** C2 from SPTRCK #3. */
  167.     protected double c2;

  169.     /** C4 from SPTRCK #3. */
  170.     protected double c4;

  172.     /** common parameter for raan (OMEGA) computation. */
  173.     protected double xnodcf;

  175.     /** 3/2 * C1. */
  176.     protected double t2cof;

  178.     // CHECKSTYLE: resume VisibilityModifier check

  180.     /** TLE frame. */
  181.     private final Frame teme;

  183.     /** Spacecraft masses (kg) mapped to TLEs. */
  184.     private Map<TLE, Double> masses;

  186.     /** All TLEs. */
  187.     private TimeSpanMap<TLE> tles;

  189.     /** Protected constructor for derived classes.
  190.      *
  191.      * <p>This constructor uses the {@link DataContext#getDefault() default data context}.
  192.      *
  193.      * @param initialTLE the unique TLE to propagate
  194.      * @param attitudeProvider provider for attitude computation
  195.      * @param mass spacecraft mass (kg)
  196.      * @see #TLEPropagator(TLE, AttitudeProvider, double, Frame)
  197.      */
  198.     @DefaultDataContext
  199.     protected TLEPropagator(final TLE initialTLE, final AttitudeProvider attitudeProvider,
  200.                             final double mass) {
  201.         this(initialTLE, attitudeProvider, mass,
  202.                 DataContext.getDefault().getFrames().getTEME());
  203.     }

  205.     /** Protected constructor for derived classes.
  206.      * @param initialTLE the unique TLE to propagate
  207.      * @param attitudeProvider provider for attitude computation
  208.      * @param mass spacecraft mass (kg)
  209.      * @param teme the TEME frame to use for propagation.
  210.      * @since 10.1
  211.      */
  212.     protected TLEPropagator(final TLE initialTLE,
  213.                             final AttitudeProvider attitudeProvider,
  214.                             final double mass,
  215.                             final Frame teme) {
  216.         super(attitudeProvider);
  217.         setStartDate(initialTLE.getDate());
  218.         this.utc       = initialTLE.getUtc();
  219.         initializeTle(initialTLE);
  220.         this.teme      = teme;
  221.         this.tles      = new TimeSpanMap<>(tle);
  222.         this.masses    = new HashMap<>();
  223.         this.masses.put(tle, mass);

  225.         // set the initial state
  226.         final Orbit orbit = propagateOrbit(initialTLE.getDate());
  227.         final Attitude attitude = attitudeProvider.getAttitude(orbit, orbit.getDate(), orbit.getFrame());
  228.         super.resetInitialState(new SpacecraftState(orbit, attitude, mass));
  229.     }

  231.     /** Selects the extrapolator to use with the selected TLE.
  232.      *
  233.      * <p>This method uses the {@link DataContext#getDefault() default data context}.
  234.      *
  235.      * @param tle the TLE to propagate.
  236.      * @return the correct propagator.
  237.      * @see #selectExtrapolator(TLE, Frame)
  238.      */
  239.     @DefaultDataContext
  240.     public static TLEPropagator selectExtrapolator(final TLE tle) {
  241.         return selectExtrapolator(tle, DataContext.getDefault().getFrames().getTEME());
  242.     }

  244.     /** Selects the extrapolator to use with the selected TLE.
  245.      * @param tle the TLE to propagate.
  246.      * @param teme TEME frame.
  247.      * @return the correct propagator.
  248.      * @since 10.1
  249.      * @see #selectExtrapolator(TLE, Frame, AttitudeProvider)
  250.      */
  251.     public static TLEPropagator selectExtrapolator(final TLE tle, final Frame teme) {
  252.         return selectExtrapolator(tle, teme, FrameAlignedProvider.of(teme));
  253.     }

  255.     /** Selects the extrapolator to use with the selected TLE.
  256.      * @param tle the TLE to propagate.
  257.      * @param teme TEME frame.
  258.      * @param attitudeProvider provider for attitude computation
  259.      * @return the correct propagator.
  260.      * @since 12.2
  261.      */
  262.     public static TLEPropagator selectExtrapolator(final TLE tle, final Frame teme, final AttitudeProvider attitudeProvider) {
  263.         return selectExtrapolator(tle, attitudeProvider, DEFAULT_MASS, teme);
  264.     }

  266.     /** Selects the extrapolator to use with the selected TLE.
  267.      *
  268.      * <p>This method uses the {@link DataContext#getDefault() default data context}.
  269.      *
  270.      * @param tle the TLE to propagate.
  271.      * @param attitudeProvider provider for attitude computation
  272.      * @param mass spacecraft mass (kg)
  273.      * @return the correct propagator.
  274.      * @see #selectExtrapolator(TLE, AttitudeProvider, double, Frame)
  275.      */
  276.     @DefaultDataContext
  277.     public static TLEPropagator selectExtrapolator(final TLE tle, final AttitudeProvider attitudeProvider,
  278.                                                    final double mass) {
  279.         return selectExtrapolator(tle, attitudeProvider, mass,
  280.                                   DataContext.getDefault().getFrames().getTEME());
  281.     }

  283.     /** Selects the extrapolator to use with the selected TLE.
  284.      * @param tle the TLE to propagate.
  285.      * @param attitudeProvider provider for attitude computation
  286.      * @param mass spacecraft mass (kg)
  287.      * @param teme the TEME frame to use for propagation.
  288.      * @return the correct propagator.
  289.      * @since 10.1
  290.      */
  291.     public static TLEPropagator selectExtrapolator(final TLE tle,
  292.                                                    final AttitudeProvider attitudeProvider,
  293.                                                    final double mass,
  294.                                                    final Frame teme) {

  296.         final double a1 = FastMath.pow( TLEConstants.XKE / (tle.getMeanMotion() * 60.0), TLEConstants.TWO_THIRD);
  297.         final double cosi0 = FastMath.cos(tle.getI());
  298.         final double temp = TLEConstants.CK2 * 1.5 * (3 * cosi0 * cosi0 - 1.0) *
  299.                             FastMath.pow(1.0 - tle.getE() * tle.getE(), -1.5);
  300.         final double delta1 = temp / (a1 * a1);
  301.         final double a0 = a1 * (1.0 - delta1 * (TLEConstants.ONE_THIRD + delta1 * (delta1 * 134.0 / 81.0 + 1.0)));
  302.         final double delta0 = temp / (a0 * a0);

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

  307.         // Period >= 225 minutes is deep space
  308.         if (MathUtils.TWO_PI / (xn0dp * TLEConstants.MINUTES_PER_DAY) >= (1.0 / 6.4)) {
  309.             return new DeepSDP4(tle, attitudeProvider, mass, teme);
  310.         } else {
  311.             return new SGP4(tle, attitudeProvider, mass, teme);
  312.         }
  313.     }

  315.     /** Get the Earth gravity coefficient used for TLE propagation.
  316.      * @return the Earth gravity coefficient.
  317.      */
  318.     public static double getMU() {
  319.         return TLEConstants.MU;
  320.     }

  322.     /** Get the extrapolated position and velocity from an initial TLE.
  323.      * @param date the final date
  324.      * @return the final PVCoordinates
  325.      */
  326.     public PVCoordinates getPVCoordinates(final AbsoluteDate date) {

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

  330.         // Compute PV with previous calculated parameters
  331.         return computePVCoordinates();
  332.     }

  334.     /** Computation of the first commons parameters.
  335.      */
  336.     private void initializeCommons() {

  338.         // Sine and cosine of inclination
  339.         final SinCos scI0 = FastMath.sinCos(tle.getI());

  341.         final double a1 = FastMath.pow(TLEConstants.XKE / (tle.getMeanMotion() * 60.0), TLEConstants.TWO_THIRD);
  342.         cosi0 = scI0.cos();
  343.         theta2 = cosi0 * cosi0;
  344.         final double x3thm1 = 3.0 * theta2 - 1.0;
  345.         e0sq = tle.getE() * tle.getE();
  346.         beta02 = 1.0 - e0sq;
  347.         beta0 = FastMath.sqrt(beta02);
  348.         final double tval = TLEConstants.CK2 * 1.5 * x3thm1 / (beta0 * beta02);
  349.         final double delta1 = tval / (a1 * a1);
  350.         final double a0 = a1 * (1.0 - delta1 * (TLEConstants.ONE_THIRD + delta1 * (1.0 + 134.0 / 81.0 * delta1)));
  351.         final double delta0 = tval / (a0 * a0);

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

  357.         // Values of s and qms2t :
  358.         s4 = TLEConstants.S;  // unmodified value for s
  359.         double q0ms24 = TLEConstants.QOMS2T; // unmodified value for q0ms2T

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

  363.         //  For perigee below 156 km, the values of s and qoms2t are changed :
  364.         if (perige < 156.0) {
  365.             if (perige <= 98.0) {
  366.                 s4 = 20.0;
  367.             } else {
  368.                 s4 = perige - 78.0;
  369.             }
  370.             final double temp_val = (120.0 - s4) * TLEConstants.NORMALIZED_EQUATORIAL_RADIUS / TLEConstants.EARTH_RADIUS;
  371.             final double temp_val_squared = temp_val * temp_val;
  372.             q0ms24 = temp_val_squared * temp_val_squared;
  373.             s4 = s4 / TLEConstants.EARTH_RADIUS + TLEConstants.NORMALIZED_EQUATORIAL_RADIUS; // new value for q0ms2T and s
  374.         }

  376.         final double pinv = 1.0 / (a0dp * beta02);
  377.         final double pinvsq = pinv * pinv;
  378.         tsi = 1.0 / (a0dp - s4);
  379.         eta = a0dp * tle.getE() * tsi;
  380.         etasq = eta * eta;
  381.         eeta = tle.getE() * eta;

  383.         final double psisq = FastMath.abs(1.0 - etasq); // abs because pow 3.5 needs positive value
  384.         final double tsi_squared = tsi * tsi;
  385.         coef = q0ms24 * tsi_squared * tsi_squared;
  386.         coef1 = coef / FastMath.pow(psisq, 3.5);

  388.         // C2 and C1 coefficients computation :
  389.         c2 = coef1 * xn0dp * (a0dp * (1.0 + 1.5 * etasq + eeta * (4.0 + etasq)) +
  390.              0.75 * TLEConstants.CK2 * tsi / psisq * x3thm1 * (8.0 + 3.0 * etasq * (8.0 + etasq)));
  391.         c1 = tle.getBStar() * c2;
  392.         sini0 = scI0.sin();

  394.         final double x1mth2 = 1.0 - theta2;

  396.         // C4 coefficient computation :
  397.         c4 = 2.0 * xn0dp * coef1 * a0dp * beta02 * (eta * (2.0 + 0.5 * etasq) +
  398.              tle.getE() * (0.5 + 2.0 * etasq) -
  399.              2 * TLEConstants.CK2 * tsi / (a0dp * psisq) *
  400.              (-3.0 * x3thm1 * (1.0 - 2.0 * eeta + etasq * (1.5 - 0.5 * eeta)) +
  401.               0.75 * x1mth2 * (2.0 * etasq - eeta * (1.0 + etasq)) * FastMath.cos(2.0 * tle.getPerigeeArgument())));

  403.         final double theta4 = theta2 * theta2;
  404.         final double temp1 = 3 * TLEConstants.CK2 * pinvsq * xn0dp;
  405.         final double temp2 = temp1 * TLEConstants.CK2 * pinvsq;
  406.         final double temp3 = 1.25 * TLEConstants.CK4 * pinvsq * pinvsq * xn0dp;

  408.         // atmospheric and gravitation coefs :(Mdf and OMEGAdf)
  409.         xmdot = xn0dp +
  410.                 0.5 * temp1 * beta0 * x3thm1 +
  411.                 0.0625 * temp2 * beta0 * (13.0 - 78.0 * theta2 + 137.0 * theta4);

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

  415.         omgdot = -0.5 * temp1 * x1m5th +
  416.                  0.0625 * temp2 * (7.0 - 114.0 * theta2 + 395.0 * theta4) +
  417.                  temp3 * (3.0 - 36.0 * theta2 + 49.0 * theta4);

  419.         final double xhdot1 = -temp1 * cosi0;

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

  425.     }

  427.     /** Retrieves the position and velocity.
  428.      * @return the computed PVCoordinates.
  429.      */
  430.     private PVCoordinates computePVCoordinates() {

  432.         // Sine and cosine of final perigee argument
  433.         final SinCos scOmega = FastMath.sinCos(omega);

  435.         // Long period periodics
  436.         final double axn = e * scOmega.cos();
  437.         double temp = 1.0 / (a * (1.0 - e * e));
  438.         final double xlcof = 0.125 * TLEConstants.A3OVK2 * sini0 * (3.0 + 5.0 * cosi0) / (1.0 + cosi0);
  439.         final double aycof = 0.25 * TLEConstants.A3OVK2 * sini0;
  440.         final double xll = temp * xlcof * axn;
  441.         final double aynl = temp * aycof;
  442.         final double xlt = xl + xll;
  443.         final double ayn = e * scOmega.sin() + aynl;
  444.         final double elsq = axn * axn + ayn * ayn;
  445.         final double capu = MathUtils.normalizeAngle(xlt - xnode, FastMath.PI);
  446.         double epw = capu;
  447.         double ecosE = 0;
  448.         double esinE = 0;
  449.         double sinEPW = 0;
  450.         double cosEPW = 0;

  452.         // Dundee changes:  items dependent on cosio get recomputed:
  453.         final double cosi0Sq = cosi0 * cosi0;
  454.         final double x3thm1 = 3.0 * cosi0Sq - 1.0;
  455.         final double x1mth2 = 1.0 - cosi0Sq;
  456.         final double x7thm1 = 7.0 * cosi0Sq - 1.0;

  458.         if (e > (1 - 1e-6)) {
  459.             throw new OrekitException(OrekitMessages.TOO_LARGE_ECCENTRICITY_FOR_PROPAGATION_MODEL, e);
  460.         }

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

  466.             boolean doSecondOrderNewtonRaphson = true;

  468.             final SinCos scEPW = FastMath.sinCos(epw);
  469.             sinEPW = scEPW.sin();
  470.             cosEPW = scEPW.cos();
  471.             ecosE = axn * cosEPW + ayn * sinEPW;
  472.             esinE = axn * sinEPW - ayn * cosEPW;
  473.             final double f = capu - epw + esinE;
  474.             if (FastMath.abs(f) < newtonRaphsonEpsilon) {
  475.                 break;
  476.             }
  477.             final double fdot = 1.0 - ecosE;
  478.             double delta_epw = f / fdot;
  479.             if (j == 0) {
  480.                 final double maxNewtonRaphson = 1.25 * FastMath.abs(e);
  481.                 doSecondOrderNewtonRaphson = false;
  482.                 if (delta_epw > maxNewtonRaphson) {
  483.                     delta_epw = maxNewtonRaphson;
  484.                 } else if (delta_epw < -maxNewtonRaphson) {
  485.                     delta_epw = -maxNewtonRaphson;
  486.                 } else {
  487.                     doSecondOrderNewtonRaphson = true;
  488.                 }
  489.             }
  490.             if (doSecondOrderNewtonRaphson) {
  491.                 delta_epw = f / (fdot + 0.5 * esinE * delta_epw);
  492.             }
  493.             epw += delta_epw;
  494.         }

  496.         // Short period preliminary quantities
  497.         temp = 1.0 - elsq;
  498.         final double pl = a * temp;
  499.         final double r = a * (1.0 - ecosE);
  500.         double temp2 = a / r;
  501.         final double betal = FastMath.sqrt(temp);
  502.         temp = esinE / (1.0 + betal);
  503.         final double cosu = temp2 * (cosEPW - axn + ayn * temp);
  504.         final double sinu = temp2 * (sinEPW - ayn - axn * temp);
  505.         final double u = FastMath.atan2(sinu, cosu);
  506.         final double sin2u = 2.0 * sinu * cosu;
  507.         final double cos2u = 2.0 * cosu * cosu - 1.0;
  508.         final double temp1 = TLEConstants.CK2 / pl;
  509.         temp2 = temp1 / pl;

  511.         // Update for short periodics
  512.         final double rk = r * (1.0 - 1.5 * temp2 * betal * x3thm1) + 0.5 * temp1 * x1mth2 * cos2u;
  513.         final double uk = u - 0.25 * temp2 * x7thm1 * sin2u;
  514.         final double xnodek = xnode + 1.5 * temp2 * cosi0 * sin2u;
  515.         final double xinck = i + 1.5 * temp2 * cosi0 * sini0 * cos2u;

  517.         // Orientation vectors
  518.         final SinCos scuk   = FastMath.sinCos(uk);
  519.         final SinCos scik   = FastMath.sinCos(xinck);
  520.         final SinCos scnok  = FastMath.sinCos(xnodek);
  521.         final double sinuk  = scuk.sin();
  522.         final double cosuk  = scuk.cos();
  523.         final double sinik  = scik.sin();
  524.         final double cosik  = scik.cos();
  525.         final double sinnok = scnok.sin();
  526.         final double cosnok = scnok.cos();
  527.         final double xmx = -sinnok * cosik;
  528.         final double xmy = cosnok * cosik;
  529.         final double ux  = xmx * sinuk + cosnok * cosuk;
  530.         final double uy  = xmy * sinuk + sinnok * cosuk;
  531.         final double uz  = sinik * sinuk;

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

  537.         final double rdot   = TLEConstants.XKE * FastMath.sqrt(a) * esinE / r;
  538.         final double rfdot  = TLEConstants.XKE * FastMath.sqrt(pl) / r;
  539.         final double xn     = TLEConstants.XKE / (a * FastMath.sqrt(a));
  540.         final double rdotk  = rdot - xn * temp1 * x1mth2 * sin2u;
  541.         final double rfdotk = rfdot + xn * temp1 * (x1mth2 * cos2u + 1.5 * x3thm1);
  542.         final double vx     = xmx * cosuk - cosnok * sinuk;
  543.         final double vy     = xmy * cosuk - sinnok * sinuk;
  544.         final double vz     = sinik * cosuk;

  546.         final double cv = 1000.0 * TLEConstants.EARTH_RADIUS / 60.0;
  547.         final Vector3D vel = new Vector3D(cv * (rdotk * ux + rfdotk * vx),
  548.                                           cv * (rdotk * uy + rfdotk * vy),
  549.                                           cv * (rdotk * uz + rfdotk * vz));

  551.         return new PVCoordinates(pos, vel);

  553.     }

  555.     /** Initialization proper to each propagator (SGP or SDP).
  556.      */
  557.     protected abstract void sxpInitialize();

  559.     /** Propagation proper to each propagator (SGP or SDP).
  560.      * @param t the offset from initial epoch (min)
  561.      */
  562.     protected abstract void sxpPropagate(double t);

  564.     /** {@inheritDoc}
  565.      * <p>
  566.      * For TLE propagator, calling this method is only recommended
  567.      * for covariance propagation when the new <code>state</code>
  568.      * differs from the previous one by only adding the additional
  569.      * state containing the derivatives.
  570.      * </p>
  571.      */
  572.     public void resetInitialState(final SpacecraftState state) {
  573.         super.resetInitialState(state);
  574.         resetTle(state);
  575.         masses = new HashMap<>();
  576.         masses.put(tle, state.getMass());
  577.         tles = new TimeSpanMap<>(tle);
  578.     }

  580.     /** {@inheritDoc} */
  581.     protected void resetIntermediateState(final SpacecraftState state, final boolean forward) {
  582.         resetTle(state);
  583.         if (forward) {
  584.             tles.addValidAfter(tle, state.getDate(), false);
  585.         } else {
  586.             tles.addValidBefore(tle, state.getDate(), false);
  587.         }
  588.         stateChanged(state);
  589.         masses.put(tle, state.getMass());
  590.     }

  592.     /** Reset internal TLE from a SpacecraftState.
  593.      * @param state spacecraft state on which to base new TLE
  594.      */
  595.     private void resetTle(final SpacecraftState state) {
  596.         final TleGenerationAlgorithm algorithm = getDefaultTleGenerationAlgorithm(utc, teme);
  597.         final TLE newTle = algorithm.generate(state, tle);
  598.         initializeTle(newTle);
  599.     }

  601.     /** Initialize internal TLE.
  602.      * @param newTle tle to replace current one
  603.      */
  604.     private void initializeTle(final TLE newTle) {
  605.         tle = newTle;
  606.         initializeCommons();
  607.         sxpInitialize();
  608.     }

  610.     /** {@inheritDoc} */
  611.     protected double getMass(final AbsoluteDate date) {
  612.         return masses.get(tles.get(date));
  613.     }

  615.     /** {@inheritDoc} */
  616.     protected Orbit propagateOrbit(final AbsoluteDate date) {
  617.         final TLE closestTle = tles.get(date);
  618.         if (!tle.equals(closestTle)) {
  619.             initializeTle(closestTle);
  620.         }
  621.         return new CartesianOrbit(getPVCoordinates(date), teme, date, TLEConstants.MU);
  622.     }

  624.     /** Get the underlying TLE.
  625.      * If there has been calls to #resetInitialState or #resetIntermediateState,
  626.      * it will not be the same as given to the constructor.
  627.      * @return underlying TLE
  628.      */
  629.     public TLE getTLE() {
  630.         return tle;
  631.     }

  633.     /** {@inheritDoc} */
  634.     public Frame getFrame() {
  635.         return teme;
  636.     }

  638.     /** {@inheritDoc} */
  639.     @Override
  640.     protected AbstractMatricesHarvester createHarvester(final String stmName, final RealMatrix initialStm,
  641.                                                         final DoubleArrayDictionary initialJacobianColumns) {
  642.         // Create the harvester
  643.         final TLEHarvester harvester = new TLEHarvester(this, stmName, initialStm, initialJacobianColumns);
  644.         // Update the list of additional state provider
  645.         addAdditionalStateProvider(harvester);
  646.         // Return the configured harvester
  647.         return harvester;
  648.     }

  650.     /**
  651.      * Get the names of the parameters in the matrix returned by {@link MatricesHarvester#getParametersJacobian}.
  652.      * @return names of the parameters (i.e. columns) of the Jacobian matrix
  653.      */
  654.     protected List<String> getJacobiansColumnsNames() {
  655.         final List<String> columnsNames = new ArrayList<>();
  656.         for (final ParameterDriver driver : tle.getParametersDrivers()) {

  658.             if (driver.isSelected() && !columnsNames.contains(driver.getNamesSpanMap().getFirstSpan().getData())) {
  659.                 // As driver with same name should have same NamesSpanMap we only check the if condition on the
  660.                 // first span map and then if the condition is OK all the span names are added to the jacobian column names
  661.                 for (Span<String> span = driver.getNamesSpanMap().getFirstSpan(); span != null; span = span.next()) {
  662.                     columnsNames.add(span.getData());
  663.                 }
  664.             }
  665.         }
  666.         Collections.sort(columnsNames);
  667.         return columnsNames;
  668.     }

  670.     /**
  671.      * Get the default TLE generation algorithm.
  672.      * @param utc UTC time scale
  673.      * @param teme TEME frame
  674.      * @return a TLE generation algorithm
  675.      * @since 12.0
  676.      */
  677.     public static TleGenerationAlgorithm getDefaultTleGenerationAlgorithm(final TimeScale utc, final Frame teme) {
  678.         return new FixedPointTleGenerationAlgorithm(FixedPointTleGenerationAlgorithm.EPSILON_DEFAULT,
  679.                                                     FixedPointTleGenerationAlgorithm.MAX_ITERATIONS_DEFAULT,
  680.                                                     FixedPointTleGenerationAlgorithm.SCALE_DEFAULT, utc, teme);
  681.     }

  683. }
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