EpochDerivativesEquations.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.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.AdditionalDerivativesProvider;
  31. import org.orekit.propagation.integration.AdditionalEquations;
  32. import org.orekit.propagation.integration.CombinedDerivatives;
  33. import org.orekit.time.AbsoluteDate;
  34. import org.orekit.utils.ParameterDriver;
  35. import org.orekit.utils.ParameterDriversList;

  37. /** This class is a copy of {@link AbsolutePartialDerivativesEquations}
  38.  *  The computation of the derivatives of the acceleration due to a ThirdBodyAttraction
  39.  *  has been added.
  40.  *
  41.  * {@link AdditionalDerivativesProvider Provider} computing the partial derivatives
  42.  * of the state (orbit) with respect to initial state and force models parameters.
  43.  * <p>
  44.  * This set of equations are automatically added to a {@link NumericalPropagator numerical propagator}
  45.  * in order to compute partial derivatives of the orbit along with the orbit itself. This is
  46.  * useful for example in orbit determination applications.
  47.  * </p>
  48.  * <p>
  49.  * The partial derivatives with respect to initial state can be either dimension 6
  50.  * (orbit only) or 7 (orbit and mass).
  51.  * </p>
  52.  * <p>
  53.  * The partial derivatives with respect to force models parameters has a dimension
  54.  * equal to the number of selected parameters. Parameters selection is implemented at
  55.  * {@link ForceModel force models} level. Users must retrieve a {@link ParameterDriver
  56.  * parameter driver} using {@link ForceModel#getParameterDriver(String)} and then
  57.  * select it by calling {@link ParameterDriver#setSelected(boolean) setSelected(true)}.
  58.  * </p>
  59.  * <p>
  60.  * If several force models provide different {@link ParameterDriver drivers} for the
  61.  * same parameter name, selecting any of these drivers has the side effect of
  62.  * selecting all the drivers for this shared parameter. In this case, the partial
  63.  * derivatives will be the sum of the partial derivatives contributed by the
  64.  * corresponding force models. This case typically arises for central attraction
  65.  * coefficient, which has an influence on {@link org.orekit.forces.gravity.NewtonianAttraction
  66.  * Newtonian attraction}, {@link org.orekit.forces.gravity.HolmesFeatherstoneAttractionModel
  67.  * gravity field}, and {@link org.orekit.forces.gravity.Relativity relativity}.
  68.  * </p>
  69.  * @author V&eacute;ronique Pommier-Maurussane
  70.  * @author Luc Maisonobe
  71.  * @since 10.2
  72.  */
  73. @SuppressWarnings("deprecation")
  74. public class EpochDerivativesEquations
  75.     implements AdditionalDerivativesProvider,
  76.     org.orekit.propagation.integration.AdditionalEquations  {

  78.     /** Propagator computing state evolution. */
  79.     private final NumericalPropagator propagator;

  81.     /** Selected parameters for Jacobian computation. */
  82.     private ParameterDriversList selected;

  84.     /** Parameters map. */
  85.     private Map<ParameterDriver, Integer> map;

  87.     /** Name. */
  88.     private final String name;

  90.     /** Flag for Jacobian matrices initialization. */
  91.     private boolean initialized;

  93.     /** Simple constructor.
  94.      * <p>
  95.      * Upon construction, this set of equations is <em>automatically</em> added to
  96.      * the propagator by calling its {@link
  97.      * NumericalPropagator#addAdditionalEquations(AdditionalEquations)} method. So
  98.      * there is no need to call this method explicitly for these equations.
  99.      * </p>
  100.      * @param name name of the partial derivatives equations
  101.      * @param propagator the propagator that will handle the orbit propagation
  102.      */
  103.     public EpochDerivativesEquations(final String name, final NumericalPropagator propagator) {
  104.         this.name                   = name;
  105.         this.selected               = null;
  106.         this.map                    = null;
  107.         this.propagator             = propagator;
  108.         this.initialized            = false;
  109.         propagator.addAdditionalDerivativesProvider(this);
  110.     }

  112.     /** {@inheritDoc} */
  113.     public String getName() {
  114.         return name;
  115.     }

  117.     /** {@inheritDoc} */
  118.     @Override
  119.     public int getDimension() {
  120.         freezeParametersSelection();
  121.         return 6 * (6 + selected.getNbParams() + 1);
  122.     }

  124.     /** Freeze the selected parameters from the force models.
  125.      */
  126.     private void freezeParametersSelection() {
  127.         if (selected == null) {

  129.             // first pass: gather all parameters, binding similar names together
  130.             selected = new ParameterDriversList();
  131.             for (final ForceModel provider : propagator.getAllForceModels()) {
  132.                 for (final ParameterDriver driver : provider.getParametersDrivers()) {
  133.                     selected.add(driver);
  134.                 }
  135.             }

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

  141.             // third pass: sort parameters lexicographically
  142.             selected.sort();

  144.             // fourth pass: set up a map between parameters drivers and matrices columns
  145.             map = new IdentityHashMap<>();
  146.             int parameterIndex = 0;
  147.             for (final ParameterDriver selectedDriver : selected.getDrivers()) {
  148.                 for (final ForceModel provider : propagator.getAllForceModels()) {
  149.                     for (final ParameterDriver driver : provider.getParametersDrivers()) {
  150.                         if (driver.getName().equals(selectedDriver.getName())) {
  151.                             map.put(driver, parameterIndex);
  152.                         }
  153.                     }
  154.                 }
  155.                 ++parameterIndex;
  156.             }

  158.         }
  159.     }

  161.     /** Get the selected parameters, in Jacobian matrix column order.
  162.      * <p>
  163.      * The force models parameters for which partial derivatives are desired,
  164.      * <em>must</em> have been {@link ParameterDriver#setSelected(boolean) selected}
  165.      * before this method is called, so the proper list is returned.
  166.      * </p>
  167.      * @return selected parameters, in Jacobian matrix column order which
  168.      * is lexicographic order
  169.      */
  170.     public ParameterDriversList getSelectedParameters() {
  171.         freezeParametersSelection();
  172.         return selected;
  173.     }

  175.     /** Set the initial value of the Jacobian with respect to state and parameter.
  176.      * <p>
  177.      * This method is equivalent to call {@link #setInitialJacobians(SpacecraftState,
  178.      * double[][], double[][])} with dYdY0 set to the identity matrix and dYdP set
  179.      * to a zero matrix.
  180.      * </p>
  181.      * <p>
  182.      * The force models parameters for which partial derivatives are desired,
  183.      * <em>must</em> have been {@link ParameterDriver#setSelected(boolean) selected}
  184.      * before this method is called, so proper matrices dimensions are used.
  185.      * </p>
  186.      * @param s0 initial state
  187.      * @return state with initial Jacobians added
  188.      * @see #getSelectedParameters()
  189.      * @since 9.0
  190.      */
  191.     public SpacecraftState setInitialJacobians(final SpacecraftState s0) {
  192.         freezeParametersSelection();
  193.         final int epochStateDimension = 6;
  194.         final double[][] dYdY0 = new double[epochStateDimension][epochStateDimension];
  195.         final double[][] dYdP  = new double[epochStateDimension][selected.getNbParams() + 6];
  196.         for (int i = 0; i < epochStateDimension; ++i) {
  197.             dYdY0[i][i] = 1.0;
  198.         }
  199.         return setInitialJacobians(s0, dYdY0, dYdP);
  200.     }

  202.     /** Set the initial value of the Jacobian with respect to state and parameter.
  203.      * <p>
  204.      * The returned state must be added to the propagator (it is not done
  205.      * automatically, as the user may need to add more states to it).
  206.      * </p>
  207.      * <p>
  208.      * The force models parameters for which partial derivatives are desired,
  209.      * <em>must</em> have been {@link ParameterDriver#setSelected(boolean) selected}
  210.      * before this method is called, and the {@code dY1dP} matrix dimension <em>must</em>
  211.      * be consistent with the selection.
  212.      * </p>
  213.      * @param s1 current state
  214.      * @param dY1dY0 Jacobian of current state at time t₁ with respect
  215.      * to state at some previous time t₀ (must be 6x6)
  216.      * @param dY1dP Jacobian of current state at time t₁ with respect
  217.      * to parameters (may be null if no parameters are selected)
  218.      * @return state with initial Jacobians added
  219.      * @see #getSelectedParameters()
  220.      */
  221.     public SpacecraftState setInitialJacobians(final SpacecraftState s1,
  222.                                                final double[][] dY1dY0, final double[][] dY1dP) {

  224.         freezeParametersSelection();

  226.         // Check dimensions
  227.         final int stateDimEpoch = dY1dY0.length;
  228.         if (stateDimEpoch != 6 || stateDimEpoch != dY1dY0[0].length) {
  229.             throw new OrekitException(OrekitMessages.STATE_JACOBIAN_NOT_6X6,
  230.                                       stateDimEpoch, dY1dY0[0].length);
  231.         }
  232.         if (dY1dP != null && stateDimEpoch != dY1dP.length) {
  233.             throw new OrekitException(OrekitMessages.STATE_AND_PARAMETERS_JACOBIANS_ROWS_MISMATCH,
  234.                                       stateDimEpoch, dY1dP.length);
  235.         }

  237.         // store the matrices as a single dimension array
  238.         initialized = true;
  239.         final AbsoluteJacobiansMapper absoluteMapper = getMapper();
  240.         final double[] p = new double[absoluteMapper.getAdditionalStateDimension() + 6];
  241.         absoluteMapper.setInitialJacobians(s1, dY1dY0, dY1dP, p);

  243.         // set value in propagator
  244.         return s1.addAdditionalState(name, p);

  246.     }

  248.     /** Get a mapper between two-dimensional Jacobians and one-dimensional additional state.
  249.      * @return a mapper between two-dimensional Jacobians and one-dimensional additional state,
  250.      * with the same name as the instance
  251.      * @see #setInitialJacobians(SpacecraftState)
  252.      * @see #setInitialJacobians(SpacecraftState, double[][], double[][])
  253.      */
  254.     public AbsoluteJacobiansMapper getMapper() {
  255.         if (!initialized) {
  256.             throw new OrekitException(OrekitMessages.STATE_JACOBIAN_NOT_INITIALIZED);
  257.         }
  258.         return new AbsoluteJacobiansMapper(name, selected);
  259.     }

  261.     /** {@inheritDoc} */
  262.     public void init(final SpacecraftState initialState, final AbsoluteDate target) {
  263.         // FIXME: remove in 12.0 when AdditionalEquations is removed
  264.         AdditionalDerivativesProvider.super.init(initialState, target);
  265.     }

  267.     /** {@inheritDoc} */
  268.     public double[] computeDerivatives(final SpacecraftState s, final double[] pDot) {
  269.         // FIXME: remove in 12.0 when AdditionalEquations is removed
  270.         System.arraycopy(derivatives(s), 0, pDot, 0, pDot.length);
  271.         return null;
  272.     }

  274.     /** {@inheritDoc} */
  275.     @Override
  276.     @Deprecated
  277.     public double[] derivatives(final SpacecraftState state) {
  278.         return combinedDerivatives(state).getAdditionalDerivatives();
  279.     }

  281.     /** {@inheritDoc} */
  282.     public CombinedDerivatives combinedDerivatives(final SpacecraftState s) {

  284.         // initialize acceleration Jacobians to zero
  285.         final int paramDimEpoch = selected.getNbParams() + 1; // added epoch
  286.         final int dimEpoch      = 3;
  287.         final double[][] dAccdParam = new double[dimEpoch][paramDimEpoch];
  288.         final double[][] dAccdPos   = new double[dimEpoch][dimEpoch];
  289.         final double[][] dAccdVel   = new double[dimEpoch][dimEpoch];

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

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

  300.             final FieldVector3D<Gradient> acceleration = forceModel.acceleration(dsState, parameters);
  301.             final double[] derivativesX = acceleration.getX().getGradient();
  302.             final double[] derivativesY = acceleration.getY().getGradient();
  303.             final double[] derivativesZ = acceleration.getZ().getGradient();

  305.             // update Jacobians with respect to state
  306.             addToRow(derivativesX, 0, converter.getFreeStateParameters(), dAccdPos, dAccdVel);
  307.             addToRow(derivativesY, 1, converter.getFreeStateParameters(), dAccdPos, dAccdVel);
  308.             addToRow(derivativesZ, 2, converter.getFreeStateParameters(), dAccdPos, dAccdVel);

  310.             int index = converter.getFreeStateParameters();
  311.             for (ParameterDriver driver : forceModel.getParametersDrivers()) {
  312.                 if (driver.isSelected()) {
  313.                     final int parameterIndex = map.get(driver);
  314.                     dAccdParam[0][parameterIndex] += derivativesX[index];
  315.                     dAccdParam[1][parameterIndex] += derivativesY[index];
  316.                     dAccdParam[2][parameterIndex] += derivativesZ[index];
  317.                     ++index;
  318.                 }
  319.             }

  321.             // Add the derivatives of the acceleration w.r.t. the Epoch
  322.             if (forceModel instanceof ThirdBodyAttractionEpoch) {
  323.                 final double[] parametersValues = new double[] {parameters[0].getValue()};
  324.                 final double[] derivatives = ((ThirdBodyAttractionEpoch) forceModel).getDerivativesToEpoch(s, parametersValues);
  325.                 dAccdParam[0][paramDimEpoch - 1] += derivatives[0];
  326.                 dAccdParam[1][paramDimEpoch - 1] += derivatives[1];
  327.                 dAccdParam[2][paramDimEpoch - 1] += derivatives[2];
  328.             }

  330.         }

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

  334.         // [        |        ]   [                 |                  ]   [     |     ]
  335.         // [  Adot  |  Bdot  ]   [  dVel/dPos = 0  |  dVel/dVel = Id  ]   [  A  |  B  ]
  336.         // [        |        ]   [                 |                  ]   [     |     ]
  337.         // ---------+---------   ------------------+------------------- * ------+------
  338.         // [        |        ]   [                 |                  ]   [     |     ]
  339.         // [  Cdot  |  Ddot  ] = [    dAcc/dPos    |     dAcc/dVel    ]   [  C  |  D  ]
  340.         // [        |        ]   [                 |                  ]   [     |     ]

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

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

  347.         //     [ Adot ] = [ C ]
  348.         //     [ Bdot ] = [ D ]
  349.         //     [ Cdot ] = [ dAcc/dPos ] * [ A ] + [ dAcc/dVel ] * [ C ]
  350.         //     [ Ddot ] = [ dAcc/dPos ] * [ B ] + [ dAcc/dVel ] * [ D ]

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

  356.         // copy C and E into Adot and Bdot
  357.         final int stateDim = 6;
  358.         final double[] p = s.getAdditionalState(getName());
  359.         final double[] pDot = new double[p.length];
  360.         System.arraycopy(p, dimEpoch * stateDim, pDot, 0, dimEpoch * stateDim);

  362.         // compute Cdot and Ddot
  363.         for (int i = 0; i < dimEpoch; ++i) {
  364.             final double[] dAdPi = dAccdPos[i];
  365.             final double[] dAdVi = dAccdVel[i];
  366.             for (int j = 0; j < stateDim; ++j) {
  367.                 pDot[(dimEpoch + i) * stateDim + j] =
  368.                     dAdPi[0] * p[j]                + dAdPi[1] * p[j +     stateDim] + dAdPi[2] * p[j + 2 * stateDim] +
  369.                     dAdVi[0] * p[j + 3 * stateDim] + dAdVi[1] * p[j + 4 * stateDim] + dAdVi[2] * p[j + 5 * stateDim];
  370.             }
  371.         }

  373.         for (int k = 0; k < paramDimEpoch; ++k) {
  374.             // the variational equations of the parameters Jacobian matrix are computed
  375.             // one column at a time, they have the following form:
  376.             // [      ]   [                 |                  ]   [   ]   [                  ]
  377.             // [ Edot ]   [  dVel/dPos = 0  |  dVel/dVel = Id  ]   [ E ]   [  dVel/dParam = 0 ]
  378.             // [      ]   [                 |                  ]   [   ]   [                  ]
  379.             // --------   ------------------+------------------- * ----- + --------------------
  380.             // [      ]   [                 |                  ]   [   ]   [                  ]
  381.             // [ Fdot ] = [    dAcc/dPos    |     dAcc/dVel    ]   [ F ]   [    dAcc/dParam   ]
  382.             // [      ]   [                 |                  ]   [   ]   [                  ]

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

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

  389.             //     [ Edot ] = [ F ]
  390.             //     [ Fdot ] = [ dAcc/dPos ] * [ E ] + [ dAcc/dVel ] * [ F ] + [ dAcc/dParam ]

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

  396.             // copy F into Edot
  397.             final int columnTop = stateDim * stateDim + k;
  398.             pDot[columnTop]                     = p[columnTop + 3 * paramDimEpoch];
  399.             pDot[columnTop +     paramDimEpoch] = p[columnTop + 4 * paramDimEpoch];
  400.             pDot[columnTop + 2 * paramDimEpoch] = p[columnTop + 5 * paramDimEpoch];

  402.             // compute Fdot
  403.             for (int i = 0; i < dimEpoch; ++i) {
  404.                 final double[] dAdP = dAccdPos[i];
  405.                 final double[] dAdV = dAccdVel[i];
  406.                 pDot[columnTop + (dimEpoch + i) * paramDimEpoch] =
  407.                     dAccdParam[i][k] +
  408.                     dAdP[0] * p[columnTop]                     + dAdP[1] * p[columnTop +     paramDimEpoch] + dAdP[2] * p[columnTop + 2 * paramDimEpoch] +
  409.                     dAdV[0] * p[columnTop + 3 * paramDimEpoch] + dAdV[1] * p[columnTop + 4 * paramDimEpoch] + dAdV[2] * p[columnTop + 5 * paramDimEpoch];
  410.             }

  412.         }

  414.         return new CombinedDerivatives(pDot, null);

  416.     }

  418.     /** Fill Jacobians rows.
  419.      * @param derivatives derivatives of a component of acceleration (along either x, y or z)
  420.      * @param index component index (0 for x, 1 for y, 2 for z)
  421.      * @param freeStateParameters number of free parameters, either 3 (position),
  422.      * 6 (position-velocity) or 7 (position-velocity-mass)
  423.      * @param dAccdPos Jacobian of acceleration with respect to spacecraft position
  424.      * @param dAccdVel Jacobian of acceleration with respect to spacecraft velocity
  425.      */
  426.     private void addToRow(final double[] derivatives, final int index, final int freeStateParameters,
  427.                           final double[][] dAccdPos, final double[][] dAccdVel) {

  429.         for (int i = 0; i < 3; ++i) {
  430.             dAccdPos[index][i] += derivatives[i];
  431.         }
  432.         if (freeStateParameters > 3) {
  433.             for (int i = 0; i < 3; ++i) {
  434.                 dAccdVel[index][i] += derivatives[i + 3];
  435.             }
  436.         }

  438.     }

  440. }
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