EpochDerivativesEquations.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.numerical;

  19. import java.util.IdentityHashMap;
  20. import java.util.Map;

  22. import org.hipparchus.analysis.differentiation.Gradient;
  23. import org.hipparchus.geometry.euclidean.threed.FieldVector3D;
  24. import org.orekit.errors.OrekitException;
  25. import org.orekit.errors.OrekitMessages;
  26. import org.orekit.forces.ForceModel;
  27. import org.orekit.forces.gravity.ThirdBodyAttractionEpoch;
  28. import org.orekit.propagation.FieldSpacecraftState;
  29. import org.orekit.propagation.SpacecraftState;
  30. import org.orekit.propagation.integration.AdditionalEquations;
  31. import org.orekit.utils.ParameterDriver;
  32. import org.orekit.utils.ParameterDriversList;

  34. /** This class is a copy of {@link AbsolutePartialDerivativesEquations}
  35.  *  The computation of the derivatives of the acceleration due to a ThirdBodyAttraction
  36.  *  has been added.
  37.  *
  38.  *  Set of {@link AdditionalEquations additional equations} computing the partial derivatives
  39.  * of the state (orbit) with respect to initial state and force models parameters.
  40.  * <p>
  41.  * This set of equations are automatically added to a {@link NumericalPropagator numerical propagator}
  42.  * in order to compute partial derivatives of the orbit along with the orbit itself. This is
  43.  * useful for example in orbit determination applications.
  44.  * </p>
  45.  * <p>
  46.  * The partial derivatives with respect to initial state can be either dimension 6
  47.  * (orbit only) or 7 (orbit and mass).
  48.  * </p>
  49.  * <p>
  50.  * The partial derivatives with respect to force models parameters has a dimension
  51.  * equal to the number of selected parameters. Parameters selection is implemented at
  52.  * {@link ForceModel force models} level. Users must retrieve a {@link ParameterDriver
  53.  * parameter driver} using {@link ForceModel#getParameterDriver(String)} and then
  54.  * select it by calling {@link ParameterDriver#setSelected(boolean) setSelected(true)}.
  55.  * </p>
  56.  * <p>
  57.  * If several force models provide different {@link ParameterDriver drivers} for the
  58.  * same parameter name, selecting any of these drivers has the side effect of
  59.  * selecting all the drivers for this shared parameter. In this case, the partial
  60.  * derivatives will be the sum of the partial derivatives contributed by the
  61.  * corresponding force models. This case typically arises for central attraction
  62.  * coefficient, which has an influence on {@link org.orekit.forces.gravity.NewtonianAttraction
  63.  * Newtonian attraction}, {@link org.orekit.forces.gravity.HolmesFeatherstoneAttractionModel
  64.  * gravity field}, and {@link org.orekit.forces.gravity.Relativity relativity}.
  65.  * </p>
  66.  * @author V&eacute;ronique Pommier-Maurussane
  67.  * @author Luc Maisonobe
  68.  * @since 10.2
  69.  */
  70. public class EpochDerivativesEquations implements AdditionalEquations {

  72.     /** Propagator computing state evolution. */
  73.     private final NumericalPropagator propagator;

  75.     /** Selected parameters for Jacobian computation. */
  76.     private ParameterDriversList selected;

  78.     /** Parameters map. */
  79.     private Map<ParameterDriver, Integer> map;

  81.     /** Name. */
  82.     private final String name;

  84.     /** Flag for Jacobian matrices initialization. */
  85.     private boolean initialized;

  87.     /** Simple constructor.
  88.      * <p>
  89.      * Upon construction, this set of equations is <em>automatically</em> added to
  90.      * the propagator by calling its {@link
  91.      * NumericalPropagator#addAdditionalEquations(AdditionalEquations)} method. So
  92.      * there is no need to call this method explicitly for these equations.
  93.      * </p>
  94.      * @param name name of the partial derivatives equations
  95.      * @param propagator the propagator that will handle the orbit propagation
  96.      */
  97.     public EpochDerivativesEquations(final String name, final NumericalPropagator propagator) {
  98.         this.name                   = name;
  99.         this.selected               = null;
  100.         this.map                    = null;
  101.         this.propagator             = propagator;
  102.         this.initialized            = false;
  103.         propagator.addAdditionalEquations(this);
  104.     }

  106.     /** {@inheritDoc} */
  107.     public String getName() {
  108.         return name;
  109.     }

  111.     /** Freeze the selected parameters from the force models.
  112.      */
  113.     private void freezeParametersSelection() {
  114.         if (selected == null) {

  116.             // first pass: gather all parameters, binding similar names together
  117.             selected = new ParameterDriversList();
  118.             for (final ForceModel provider : propagator.getAllForceModels()) {
  119.                 for (final ParameterDriver driver : provider.getParametersDrivers()) {
  120.                     selected.add(driver);
  121.                 }
  122.             }

  124.             // second pass: now that shared parameter names are bound together,
  125.             // their selections status have been synchronized, we can filter them
  126.             selected.filter(true);

  128.             // third pass: sort parameters lexicographically
  129.             selected.sort();

  131.             // fourth pass: set up a map between parameters drivers and matrices columns
  132.             map = new IdentityHashMap<>();
  133.             int parameterIndex = 0;
  134.             for (final ParameterDriver selectedDriver : selected.getDrivers()) {
  135.                 for (final ForceModel provider : propagator.getAllForceModels()) {
  136.                     for (final ParameterDriver driver : provider.getParametersDrivers()) {
  137.                         if (driver.getName().equals(selectedDriver.getName())) {
  138.                             map.put(driver, parameterIndex);
  139.                         }
  140.                     }
  141.                 }
  142.                 ++parameterIndex;
  143.             }

  145.         }
  146.     }

  148.     /** Get the selected parameters, in Jacobian matrix column order.
  149.      * <p>
  150.      * The force models parameters for which partial derivatives are desired,
  151.      * <em>must</em> have been {@link ParameterDriver#setSelected(boolean) selected}
  152.      * before this method is called, so the proper list is returned.
  153.      * </p>
  154.      * @return selected parameters, in Jacobian matrix column order which
  155.      * is lexicographic order
  156.      */
  157.     public ParameterDriversList getSelectedParameters() {
  158.         freezeParametersSelection();
  159.         return selected;
  160.     }

  162.     /** Set the initial value of the Jacobian with respect to state and parameter.
  163.      * <p>
  164.      * This method is equivalent to call {@link #setInitialJacobians(SpacecraftState,
  165.      * double[][], double[][])} with dYdY0 set to the identity matrix and dYdP set
  166.      * to a zero matrix.
  167.      * </p>
  168.      * <p>
  169.      * The force models parameters for which partial derivatives are desired,
  170.      * <em>must</em> have been {@link ParameterDriver#setSelected(boolean) selected}
  171.      * before this method is called, so proper matrices dimensions are used.
  172.      * </p>
  173.      * @param s0 initial state
  174.      * @return state with initial Jacobians added
  175.      * @see #getSelectedParameters()
  176.      * @since 9.0
  177.      */
  178.     public SpacecraftState setInitialJacobians(final SpacecraftState s0) {
  179.         freezeParametersSelection();
  180.         final int epochStateDimension = 6;
  181.         final double[][] dYdY0 = new double[epochStateDimension][epochStateDimension];
  182.         final double[][] dYdP  = new double[epochStateDimension][selected.getNbParams() + 6];
  183.         for (int i = 0; i < epochStateDimension; ++i) {
  184.             dYdY0[i][i] = 1.0;
  185.         }
  186.         return setInitialJacobians(s0, dYdY0, dYdP);
  187.     }

  189.     /** Set the initial value of the Jacobian with respect to state and parameter.
  190.      * <p>
  191.      * The returned state must be added to the propagator (it is not done
  192.      * automatically, as the user may need to add more states to it).
  193.      * </p>
  194.      * <p>
  195.      * The force models parameters for which partial derivatives are desired,
  196.      * <em>must</em> have been {@link ParameterDriver#setSelected(boolean) selected}
  197.      * before this method is called, and the {@code dY1dP} matrix dimension <em>must</em>
  198.      * be consistent with the selection.
  199.      * </p>
  200.      * @param s1 current state
  201.      * @param dY1dY0 Jacobian of current state at time t₁ with respect
  202.      * to state at some previous time t₀ (must be 6x6)
  203.      * @param dY1dP Jacobian of current state at time t₁ with respect
  204.      * to parameters (may be null if no parameters are selected)
  205.      * @return state with initial Jacobians added
  206.      * @see #getSelectedParameters()
  207.      */
  208.     public SpacecraftState setInitialJacobians(final SpacecraftState s1,
  209.                                                final double[][] dY1dY0, final double[][] dY1dP) {

  211.         freezeParametersSelection();

  213.         // Check dimensions
  214.         final int stateDimEpoch = dY1dY0.length;
  215.         if (stateDimEpoch != 6 || stateDimEpoch != dY1dY0[0].length) {
  216.             throw new OrekitException(OrekitMessages.STATE_JACOBIAN_NOT_6X6,
  217.                                       stateDimEpoch, dY1dY0[0].length);
  218.         }
  219.         if (dY1dP != null && stateDimEpoch != dY1dP.length) {
  220.             throw new OrekitException(OrekitMessages.STATE_AND_PARAMETERS_JACOBIANS_ROWS_MISMATCH,
  221.                                       stateDimEpoch, dY1dP.length);
  222.         }

  224.         // store the matrices as a single dimension array
  225.         initialized = true;
  226.         final AbsoluteJacobiansMapper absoluteMapper = getMapper();
  227.         final double[] p = new double[absoluteMapper.getAdditionalStateDimension() + 6];
  228.         absoluteMapper.setInitialJacobians(s1, dY1dY0, dY1dP, p);

  230.         // set value in propagator
  231.         return s1.addAdditionalState(name, p);

  233.     }

  235.     /** Get a mapper between two-dimensional Jacobians and one-dimensional additional state.
  236.      * @return a mapper between two-dimensional Jacobians and one-dimensional additional state,
  237.      * with the same name as the instance
  238.      * @see #setInitialJacobians(SpacecraftState)
  239.      * @see #setInitialJacobians(SpacecraftState, double[][], double[][])
  240.      */
  241.     public AbsoluteJacobiansMapper getMapper() {
  242.         if (!initialized) {
  243.             throw new OrekitException(OrekitMessages.STATE_JACOBIAN_NOT_INITIALIZED);
  244.         }
  245.         return new AbsoluteJacobiansMapper(name, selected);
  246.     }

  248.     /** {@inheritDoc} */
  249.     public double[] computeDerivatives(final SpacecraftState s, final double[] pDot) {

  251.         // initialize acceleration Jacobians to zero
  252.         final int paramDimEpoch = selected.getNbParams() + 1; // added epoch
  253.         final int dimEpoch      = 3;
  254.         final double[][] dAccdParam = new double[dimEpoch][paramDimEpoch];
  255.         final double[][] dAccdPos   = new double[dimEpoch][dimEpoch];
  256.         final double[][] dAccdVel   = new double[dimEpoch][dimEpoch];

  258.         final NumericalGradientConverter fullConverter    = new NumericalGradientConverter(s, 6, propagator.getAttitudeProvider());
  259.         final NumericalGradientConverter posOnlyConverter = new NumericalGradientConverter(s, 3, propagator.getAttitudeProvider());

  261.         // compute acceleration Jacobians, finishing with the largest force: Newtonian attraction
  262.         for (final ForceModel forceModel : propagator.getAllForceModels()) {
  263.             final NumericalGradientConverter converter = forceModel.dependsOnPositionOnly() ? posOnlyConverter : fullConverter;
  264.             final FieldSpacecraftState<Gradient> dsState = converter.getState(forceModel);
  265.             final Gradient[] parameters = converter.getParameters(dsState, forceModel);

  267.             final FieldVector3D<Gradient> acceleration = forceModel.acceleration(dsState, parameters);
  268.             final double[] derivativesX = acceleration.getX().getGradient();
  269.             final double[] derivativesY = acceleration.getY().getGradient();
  270.             final double[] derivativesZ = acceleration.getZ().getGradient();

  272.             // update Jacobians with respect to state
  273.             addToRow(derivativesX, 0, converter.getFreeStateParameters(), dAccdPos, dAccdVel);
  274.             addToRow(derivativesY, 1, converter.getFreeStateParameters(), dAccdPos, dAccdVel);
  275.             addToRow(derivativesZ, 2, converter.getFreeStateParameters(), dAccdPos, dAccdVel);

  277.             int index = converter.getFreeStateParameters();
  278.             for (ParameterDriver driver : forceModel.getParametersDrivers()) {
  279.                 if (driver.isSelected()) {
  280.                     final int parameterIndex = map.get(driver);
  281.                     dAccdParam[0][parameterIndex] += derivativesX[index];
  282.                     dAccdParam[1][parameterIndex] += derivativesY[index];
  283.                     dAccdParam[2][parameterIndex] += derivativesZ[index];
  284.                     ++index;
  285.                 }
  286.             }

  288.             // Add the derivatives of the acceleration w.r.t. the Epoch
  289.             if (forceModel instanceof ThirdBodyAttractionEpoch) {
  290.                 final double[] parametersValues = new double[] {parameters[0].getValue()};
  291.                 final double[] derivatives = ((ThirdBodyAttractionEpoch) forceModel).getDerivativesToEpoch(s, parametersValues);
  292.                 dAccdParam[0][paramDimEpoch - 1] += derivatives[0];
  293.                 dAccdParam[1][paramDimEpoch - 1] += derivatives[1];
  294.                 dAccdParam[2][paramDimEpoch - 1] += derivatives[2];
  295.             }

  297.         }

  299.         // the variational equations of the complete state Jacobian matrix have the following form:

  301.         // [        |        ]   [                 |                  ]   [     |     ]
  302.         // [  Adot  |  Bdot  ]   [  dVel/dPos = 0  |  dVel/dVel = Id  ]   [  A  |  B  ]
  303.         // [        |        ]   [                 |                  ]   [     |     ]
  304.         // ---------+---------   ------------------+------------------- * ------+------
  305.         // [        |        ]   [                 |                  ]   [     |     ]
  306.         // [  Cdot  |  Ddot  ] = [    dAcc/dPos    |     dAcc/dVel    ]   [  C  |  D  ]
  307.         // [        |        ]   [                 |                  ]   [     |     ]

  309.         // The A, B, C and D sub-matrices and their derivatives (Adot ...) are 3x3 matrices

  311.         // The expanded multiplication above can be rewritten to take into account
  312.         // the fixed values found in the sub-matrices in the left factor. This leads to:

  314.         //     [ Adot ] = [ C ]
  315.         //     [ Bdot ] = [ D ]
  316.         //     [ Cdot ] = [ dAcc/dPos ] * [ A ] + [ dAcc/dVel ] * [ C ]
  317.         //     [ Ddot ] = [ dAcc/dPos ] * [ B ] + [ dAcc/dVel ] * [ D ]

  319.         // The following loops compute these expressions taking care of the mapping of the
  320.         // (A, B, C, D) matrices into the single dimension array p and of the mapping of the
  321.         // (Adot, Bdot, Cdot, Ddot) matrices into the single dimension array pDot.

  323.         // copy C and E into Adot and Bdot
  324.         final int stateDim = 6;
  325.         final double[] p = s.getAdditionalState(getName());
  326.         System.arraycopy(p, dimEpoch * stateDim, pDot, 0, dimEpoch * stateDim);

  328.         // compute Cdot and Ddot
  329.         for (int i = 0; i < dimEpoch; ++i) {
  330.             final double[] dAdPi = dAccdPos[i];
  331.             final double[] dAdVi = dAccdVel[i];
  332.             for (int j = 0; j < stateDim; ++j) {
  333.                 pDot[(dimEpoch + i) * stateDim + j] =
  334.                     dAdPi[0] * p[j]                + dAdPi[1] * p[j +     stateDim] + dAdPi[2] * p[j + 2 * stateDim] +
  335.                     dAdVi[0] * p[j + 3 * stateDim] + dAdVi[1] * p[j + 4 * stateDim] + dAdVi[2] * p[j + 5 * stateDim];
  336.             }
  337.         }

  339.         for (int k = 0; k < paramDimEpoch; ++k) {
  340.             // the variational equations of the parameters Jacobian matrix are computed
  341.             // one column at a time, they have the following form:
  342.             // [      ]   [                 |                  ]   [   ]   [                  ]
  343.             // [ Edot ]   [  dVel/dPos = 0  |  dVel/dVel = Id  ]   [ E ]   [  dVel/dParam = 0 ]
  344.             // [      ]   [                 |                  ]   [   ]   [                  ]
  345.             // --------   ------------------+------------------- * ----- + --------------------
  346.             // [      ]   [                 |                  ]   [   ]   [                  ]
  347.             // [ Fdot ] = [    dAcc/dPos    |     dAcc/dVel    ]   [ F ]   [    dAcc/dParam   ]
  348.             // [      ]   [                 |                  ]   [   ]   [                  ]

  350.             // The E and F sub-columns and their derivatives (Edot, Fdot) are 3 elements columns.

  352.             // The expanded multiplication and addition above can be rewritten to take into
  353.             // account the fixed values found in the sub-matrices in the left factor. This leads to:

  355.             //     [ Edot ] = [ F ]
  356.             //     [ Fdot ] = [ dAcc/dPos ] * [ E ] + [ dAcc/dVel ] * [ F ] + [ dAcc/dParam ]

  358.             // The following loops compute these expressions taking care of the mapping of the
  359.             // (E, F) columns into the single dimension array p and of the mapping of the
  360.             // (Edot, Fdot) columns into the single dimension array pDot.

  362.             // copy F into Edot
  363.             final int columnTop = stateDim * stateDim + k;
  364.             pDot[columnTop]                     = p[columnTop + 3 * paramDimEpoch];
  365.             pDot[columnTop +     paramDimEpoch] = p[columnTop + 4 * paramDimEpoch];
  366.             pDot[columnTop + 2 * paramDimEpoch] = p[columnTop + 5 * paramDimEpoch];

  368.             // compute Fdot
  369.             for (int i = 0; i < dimEpoch; ++i) {
  370.                 final double[] dAdP = dAccdPos[i];
  371.                 final double[] dAdV = dAccdVel[i];
  372.                 pDot[columnTop + (dimEpoch + i) * paramDimEpoch] =
  373.                     dAccdParam[i][k] +
  374.                     dAdP[0] * p[columnTop]                     + dAdP[1] * p[columnTop +     paramDimEpoch] + dAdP[2] * p[columnTop + 2 * paramDimEpoch] +
  375.                     dAdV[0] * p[columnTop + 3 * paramDimEpoch] + dAdV[1] * p[columnTop + 4 * paramDimEpoch] + dAdV[2] * p[columnTop + 5 * paramDimEpoch];
  376.             }

  378.         }

  380.         // these equations have no effect on the main state itself
  381.         return null;

  383.     }

  385.     /** Fill Jacobians rows.
  386.      * @param derivatives derivatives of a component of acceleration (along either x, y or z)
  387.      * @param index component index (0 for x, 1 for y, 2 for z)
  388.      * @param freeStateParameters number of free parameters, either 3 (position),
  389.      * 6 (position-velocity) or 7 (position-velocity-mass)
  390.      * @param dAccdPos Jacobian of acceleration with respect to spacecraft position
  391.      * @param dAccdVel Jacobian of acceleration with respect to spacecraft velocity
  392.      */
  393.     private void addToRow(final double[] derivatives, final int index, final int freeStateParameters,
  394.                           final double[][] dAccdPos, final double[][] dAccdVel) {

  396.         for (int i = 0; i < 3; ++i) {
  397.             dAccdPos[index][i] += derivatives[i];
  398.         }
  399.         if (freeStateParameters > 3) {
  400.             for (int i = 0; i < 3; ++i) {
  401.                 dAccdVel[index][i] += derivatives[i + 3];
  402.             }
  403.         }

  405.     }

  407. }
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