IodLaplace.java

  1. /* Copyright 2002-2022 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.estimation.iod;

  19. import org.hipparchus.analysis.solvers.LaguerreSolver;
  20. import org.hipparchus.complex.Complex;
  21. import org.hipparchus.geometry.euclidean.threed.Vector3D;
  22. import org.hipparchus.linear.Array2DRowRealMatrix;
  23. import org.hipparchus.linear.LUDecomposition;
  24. import org.hipparchus.util.FastMath;
  25. import org.orekit.estimation.measurements.AngularRaDec;
  26. import org.orekit.frames.Frame;
  27. import org.orekit.orbits.CartesianOrbit;
  28. import org.orekit.time.AbsoluteDate;
  29. import org.orekit.utils.PVCoordinates;

  31. /**
  32.  * Laplace angles-only initial orbit determination, assuming Keplerian motion.
  33.  * An orbit is determined from three angular observations from the same site.
  34.  *
  35.  *
  36.  * Reference:
  37.  *    Bate, R., Mueller, D. D., & White, J. E. (1971). Fundamentals of astrodynamics.
  38.  *    New York: Dover Publications.
  39.  *
  40.  * @author Shiva Iyer
  41.  * @since 10.1
  42.  */
  43. public class IodLaplace {

  45.     /** Gravitational constant. */
  46.     private final double mu;

  48.     /** Constructor.
  49.      *
  50.      * @param mu  gravitational constant
  51.      */
  52.     public IodLaplace(final double mu) {
  53.         this.mu = mu;
  54.     }

  56.     /** Estimate the orbit from three angular observations at the same location.
  57.      *
  58.      * @param frame inertial frame for observer coordinates and orbit estimate
  59.      * @param obsPva Observer coordinates at time of raDec2
  60.      * @param raDec1 first angular observation
  61.      * @param raDec2 second angular observation
  62.      * @param raDec3 third angular observation
  63.      * @return estimate of the orbit at the central date obsDate2 or null if
  64.      *         no estimate is possible with the given data
  65.      * @since 11.0
  66.      */
  67.     public CartesianOrbit estimate(final Frame frame, final PVCoordinates obsPva,
  68.                                    final AngularRaDec raDec1, final AngularRaDec raDec2,
  69.                                    final AngularRaDec raDec3) {
  70.         return estimate(frame, obsPva,
  71.                         raDec1.getDate(), lineOfSight(raDec1),
  72.                         raDec2.getDate(), lineOfSight(raDec2),
  73.                         raDec3.getDate(), lineOfSight(raDec3));
  74.     }

  76.     /** Estimate orbit from three line of sight angles from the same location.
  77.      *
  78.      * @param frame inertial frame for observer coordinates and orbit estimate
  79.      * @param obsPva Observer coordinates at time obsDate2
  80.      * @param obsDate1 date of observation 1
  81.      * @param los1 line of sight unit vector 1
  82.      * @param obsDate2 date of observation 2
  83.      * @param los2 line of sight unit vector 2
  84.      * @param obsDate3 date of observation 3
  85.      * @param los3 line of sight unit vector 3
  86.      * @return estimate of the orbit at the central date obsDate2 or null if
  87.      *         no estimate is possible with the given data
  88.      */
  89.     public CartesianOrbit estimate(final Frame frame, final PVCoordinates obsPva,
  90.                                    final AbsoluteDate obsDate1, final Vector3D los1,
  91.                                    final AbsoluteDate obsDate2, final Vector3D los2,
  92.                                    final AbsoluteDate obsDate3, final Vector3D los3) {
  93.         // The first observation is taken as t1 = 0
  94.         final double t2 = obsDate2.durationFrom(obsDate1);
  95.         final double t3 = obsDate3.durationFrom(obsDate1);

  97.         // Calculate the first and second derivatives of the Line Of Sight vector at t2
  98.         final Vector3D Ldot = los1.scalarMultiply((t2 - t3) / (t2 * t3)).
  99.                         add(los2.scalarMultiply((2.0 * t2 - t3) / (t2 * (t2 - t3)))).
  100.                         add(los3.scalarMultiply(t2 / (t3 * (t3 - t2))));
  101.         final Vector3D Ldotdot = los1.scalarMultiply(2.0 / (t2 * t3)).
  102.                         add(los2.scalarMultiply(2.0 / (t2 * (t2 - t3)))).
  103.                         add(los3.scalarMultiply(2.0 / (t3 * (t3 - t2))));

  105.         // The determinant will vanish if the observer lies in the plane of the orbit at t2
  106.         final double D = 2.0 * getDeterminant(los2, Ldot, Ldotdot);
  107.         if (FastMath.abs(D) < 1.0E-14) {
  108.             return null;
  109.         }

  111.         final double Dsq = D * D;
  112.         final double R = obsPva.getPosition().getNorm();
  113.         final double RdotL = obsPva.getPosition().dotProduct(los2);

  115.         final double D1 = getDeterminant(los2, Ldot, obsPva.getAcceleration());
  116.         final double D2 = getDeterminant(los2, Ldot, obsPva.getPosition());

  118.         // Coefficients of the 8th order polynomial we need to solve to determine "r"
  119.         final double[] coeff = new double[] {-4.0 * mu * mu * D2 * D2 / Dsq,
  120.                                              0.0,
  121.                                              0.0,
  122.                                              4.0 * mu * D2 * (RdotL / D - 2.0 * D1 / Dsq),
  123.                                              0.0,
  124.                                              0.0,
  125.                                              4.0 * D1 * RdotL / D - 4.0 * D1 * D1 / Dsq - R * R, 0.0,
  126.                                              1.0};

  128.         // Use the Laguerre polynomial solver and take the initial guess to be
  129.         // 5 times the observer's position magnitude
  130.         final LaguerreSolver solver = new LaguerreSolver(1E-10, 1E-10, 1E-10);
  131.         final Complex[] roots = solver.solveAllComplex(coeff, 5.0 * R);

  133.         // We consider "r" to be the positive real root with the largest magnitude
  134.         double rMag = 0.0;
  135.         for (int i = 0; i < roots.length; i++) {
  136.             if (roots[i].getReal() > rMag &&
  137.                             FastMath.abs(roots[i].getImaginary()) < solver.getAbsoluteAccuracy()) {
  138.                 rMag = roots[i].getReal();
  139.             }
  140.         }
  141.         if (rMag == 0.0) {
  142.             return null;
  143.         }

  145.         // Calculate rho, the slant range from the observer to the satellite at t2.
  146.         // This yields the "r" vector, which is the satellite's position vector at t2.
  147.         final double rCubed = rMag * rMag * rMag;
  148.         final double rho = -2.0 * D1 / D - 2.0 * mu * D2 / (D * rCubed);
  149.         final Vector3D posVec = los2.scalarMultiply(rho).add(obsPva.getPosition());

  151.         // Calculate rho_dot at t2, which will yield the satellite's velocity vector at t2
  152.         final double D3 = getDeterminant(los2, obsPva.getAcceleration(), Ldotdot);
  153.         final double D4 = getDeterminant(los2, obsPva.getPosition(), Ldotdot);
  154.         final double rhoDot = -D3 / D - mu * D4 / (D * rCubed);
  155.         final Vector3D velVec = los2.scalarMultiply(rhoDot).
  156.                         add(Ldot.scalarMultiply(rho)).
  157.                         add(obsPva.getVelocity());

  159.         // Return the estimated orbit
  160.         return new CartesianOrbit(new PVCoordinates(posVec, velVec), frame, obsDate2, mu);
  161.     }

  163.     /**
  164.      * Calculates the line of sight vector.
  165.      * @param alpha right ascension angle, in radians
  166.      * @param delta declination angle, in radians
  167.      * @return the line of sight vector
  168.      * @since 11.0
  169.      */
  170.     public static Vector3D lineOfSight(final double alpha, final double delta) {
  171.         return new Vector3D(FastMath.cos(delta) * FastMath.cos(alpha),
  172.                             FastMath.cos(delta) * FastMath.sin(alpha),
  173.                             FastMath.sin(delta));
  174.     }

  176.     /**
  177.      * Calculate the line of sight vector from an AngularRaDec measurement.
  178.      * @param raDec measurement
  179.      * @return the line of sight vector
  180.      * @since 11.0
  181.      */
  182.     public static Vector3D lineOfSight(final AngularRaDec raDec) {

  184.         // Observed values
  185.         final double[] observed = raDec.getObservedValue();

  187.         // Return
  188.         return lineOfSight(observed[0], observed[1]);

  190.     }

  192.     /** Calculate the determinant of the matrix with given column vectors.
  193.      *
  194.      * @param col0 Matrix column 0
  195.      * @param col1 Matrix column 1
  196.      * @param col2 Matrix column 2
  197.      * @return matrix determinant
  198.      *
  199.      */
  200.     private double getDeterminant(final Vector3D col0, final Vector3D col1, final Vector3D col2) {
  201.         final Array2DRowRealMatrix mat = new Array2DRowRealMatrix(3, 3);
  202.         mat.setColumn(0, col0.toArray());
  203.         mat.setColumn(1, col1.toArray());
  204.         mat.setColumn(2, col2.toArray());
  205.         return new LUDecomposition(mat).getDeterminant();
  206.     }

  208. }
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