GroundStation.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.estimation.measurements;

  19. import java.util.Map;

  21. import org.hipparchus.Field;
  22. import org.hipparchus.analysis.differentiation.Gradient;
  23. import org.hipparchus.geometry.euclidean.threed.FieldRotation;
  24. import org.hipparchus.geometry.euclidean.threed.FieldVector3D;
  25. import org.hipparchus.geometry.euclidean.threed.Rotation;
  26. import org.hipparchus.geometry.euclidean.threed.Vector3D;
  27. import org.hipparchus.util.FastMath;
  28. import org.orekit.bodies.BodyShape;
  29. import org.orekit.bodies.FieldGeodeticPoint;
  30. import org.orekit.bodies.GeodeticPoint;
  31. import org.orekit.data.BodiesElements;
  32. import org.orekit.data.FundamentalNutationArguments;
  33. import org.orekit.errors.OrekitException;
  34. import org.orekit.errors.OrekitMessages;
  35. import org.orekit.frames.EOPHistory;
  36. import org.orekit.frames.FieldStaticTransform;
  37. import org.orekit.frames.FieldTransform;
  38. import org.orekit.frames.Frame;
  39. import org.orekit.frames.FramesFactory;
  40. import org.orekit.frames.StaticTransform;
  41. import org.orekit.frames.TopocentricFrame;
  42. import org.orekit.frames.Transform;
  43. import org.orekit.models.earth.displacement.StationDisplacement;
  44. import org.orekit.time.AbsoluteDate;
  45. import org.orekit.time.FieldAbsoluteDate;
  46. import org.orekit.time.UT1Scale;
  47. import org.orekit.utils.ParameterDriver;

  49. /** Class modeling a ground station that can perform some measurements.
  50.  * <p>
  51.  * This class adds a position offset parameter to a base {@link TopocentricFrame
  52.  * topocentric frame}.
  53.  * </p>
  54.  * <p>
  55.  * Since 9.0, this class also adds parameters for an additional polar motion
  56.  * and an additional prime meridian orientation. Since these parameters will
  57.  * have the same name for all ground stations, they will be managed consistently
  58.  * and allow to estimate Earth orientation precisely (this is needed for precise
  59.  * orbit determination). The polar motion and prime meridian orientation will
  60.  * be applied <em>after</em> regular Earth orientation parameters, so the value
  61.  * of the estimated parameters will be correction to EOP, they will not be the
  62.  * complete EOP values by themselves. Basically, this means that for Earth, the
  63.  * following transforms are applied in order, between inertial frame and ground
  64.  * station frame (for non-Earth based ground stations, different precession nutation
  65.  * models and associated planet oritentation parameters would be applied, if available):
  66.  * </p>
  67.  * <p>
  68.  * Since 9.3, this class also adds a station clock offset parameter, which manages
  69.  * the value that must be subtracted from the observed measurement date to get the real
  70.  * physical date at which the measurement was performed (i.e. the offset is negative
  71.  * if the ground station clock is slow and positive if it is fast).
  72.  * </p>
  73.  * <ol>
  74.  *   <li>precession/nutation, as theoretical model plus celestial pole EOP parameters</li>
  75.  *   <li>body rotation, as theoretical model plus prime meridian EOP parameters</li>
  76.  *   <li>polar motion, which is only from EOP parameters (no theoretical models)</li>
  77.  *   <li>additional body rotation, controlled by {@link #getPrimeMeridianOffsetDriver()} and {@link #getPrimeMeridianDriftDriver()}</li>
  78.  *   <li>additional polar motion, controlled by {@link #getPolarOffsetXDriver()}, {@link #getPolarDriftXDriver()},
  79.  *   {@link #getPolarOffsetYDriver()} and {@link #getPolarDriftYDriver()}</li>
  80.  *   <li>station clock offset, controlled by {@link #getClockOffsetDriver()}</li>
  81.  *   <li>station position offset, controlled by {@link #getEastOffsetDriver()},
  82.  *   {@link #getNorthOffsetDriver()} and {@link #getZenithOffsetDriver()}</li>
  83.  * </ol>
  84.  * @author Luc Maisonobe
  85.  * @since 8.0
  86.  */
  87. public class GroundStation {

  89.     /** Suffix for ground station position and clock offset parameters names. */
  90.     public static final String OFFSET_SUFFIX = "-offset";

  92.     /** Suffix for ground clock drift parameters name. */
  93.     public static final String DRIFT_SUFFIX = "-drift-clock";

  95.     /** Suffix for ground station intermediate frame name. */
  96.     public static final String INTERMEDIATE_SUFFIX = "-intermediate";

  98.     /** Clock offset scaling factor.
  99.      * <p>
  100.      * We use a power of 2 to avoid numeric noise introduction
  101.      * in the multiplications/divisions sequences.
  102.      * </p>
  103.      */
  104.     private static final double CLOCK_OFFSET_SCALE = FastMath.scalb(1.0, -10);

  106.     /** Position offsets scaling factor.
  107.      * <p>
  108.      * We use a power of 2 (in fact really 1.0 here) to avoid numeric noise introduction
  109.      * in the multiplications/divisions sequences.
  110.      * </p>
  111.      */
  112.     private static final double POSITION_OFFSET_SCALE = FastMath.scalb(1.0, 0);

  114.     /** Provider for Earth frame whose EOP parameters can be estimated. */
  115.     private final EstimatedEarthFrameProvider estimatedEarthFrameProvider;

  117.     /** Earth frame whose EOP parameters can be estimated. */
  118.     private final Frame estimatedEarthFrame;

  120.     /** Base frame associated with the station. */
  121.     private final TopocentricFrame baseFrame;

  123.     /** Fundamental nutation arguments. */
  124.     private final FundamentalNutationArguments arguments;

  126.     /** Displacement models. */
  127.     private final StationDisplacement[] displacements;

  129.     /** Driver for clock offset. */
  130.     private final ParameterDriver clockOffsetDriver;

  132.     /** Driver for clock drift. */
  133.     private final ParameterDriver clockDriftDriver;

  135.     /** Driver for position offset along the East axis. */
  136.     private final ParameterDriver eastOffsetDriver;

  138.     /** Driver for position offset along the North axis. */
  139.     private final ParameterDriver northOffsetDriver;

  141.     /** Driver for position offset along the zenith axis. */
  142.     private final ParameterDriver zenithOffsetDriver;

  144.     /** Build a ground station ignoring {@link StationDisplacement station displacements}.
  145.      * <p>
  146.      * The initial values for the pole and prime meridian parametric linear models
  147.      * ({@link #getPrimeMeridianOffsetDriver()}, {@link #getPrimeMeridianDriftDriver()},
  148.      * {@link #getPolarOffsetXDriver()}, {@link #getPolarDriftXDriver()},
  149.      * {@link #getPolarOffsetXDriver()}, {@link #getPolarDriftXDriver()}) are set to 0.
  150.      * The initial values for the station offset model ({@link #getClockOffsetDriver()},
  151.      * {@link #getEastOffsetDriver()}, {@link #getNorthOffsetDriver()},
  152.      * {@link #getZenithOffsetDriver()}) are set to 0.
  153.      * This implies that as long as these values are not changed, the offset frame is
  154.      * the same as the {@link #getBaseFrame() base frame}. As soon as some of these models
  155.      * are changed, the offset frame moves away from the {@link #getBaseFrame() base frame}.
  156.      * </p>
  157.      * @param baseFrame base frame associated with the station, without *any* parametric
  158.      * model (no station offset, no polar motion, no meridian shift)
  159.      * @see #GroundStation(TopocentricFrame, EOPHistory, StationDisplacement...)
  160.      */
  161.     public GroundStation(final TopocentricFrame baseFrame) {
  162.         this(baseFrame, FramesFactory.findEOP(baseFrame), new StationDisplacement[0]);
  163.     }

  165.     /** Simple constructor.
  166.      * <p>
  167.      * The initial values for the pole and prime meridian parametric linear models
  168.      * ({@link #getPrimeMeridianOffsetDriver()}, {@link #getPrimeMeridianDriftDriver()},
  169.      * {@link #getPolarOffsetXDriver()}, {@link #getPolarDriftXDriver()},
  170.      * {@link #getPolarOffsetXDriver()}, {@link #getPolarDriftXDriver()}) are set to 0.
  171.      * The initial values for the station offset model ({@link #getClockOffsetDriver()},
  172.      * {@link #getEastOffsetDriver()}, {@link #getNorthOffsetDriver()},
  173.      * {@link #getZenithOffsetDriver()}, {@link #getClockOffsetDriver()}) are set to 0.
  174.      * This implies that as long as these values are not changed, the offset frame is
  175.      * the same as the {@link #getBaseFrame() base frame}. As soon as some of these models
  176.      * are changed, the offset frame moves away from the {@link #getBaseFrame() base frame}.
  177.      * </p>
  178.      * @param baseFrame base frame associated with the station, without *any* parametric
  179.      * model (no station offset, no polar motion, no meridian shift)
  180.      * @param eopHistory EOP history associated with Earth frames
  181.      * @param displacements ground station displacement model (tides, ocean loading,
  182.      * atmospheric loading, thermal effects...)
  183.      * @since 9.1
  184.      */
  185.     public GroundStation(final TopocentricFrame baseFrame, final EOPHistory eopHistory,
  186.                          final StationDisplacement... displacements) {

  188.         this.baseFrame = baseFrame;

  190.         if (eopHistory == null) {
  191.             throw new OrekitException(OrekitMessages.NO_EARTH_ORIENTATION_PARAMETERS);
  192.         }

  194.         final UT1Scale baseUT1 = eopHistory.getTimeScales()
  195.                 .getUT1(eopHistory.getConventions(), eopHistory.isSimpleEop());
  196.         this.estimatedEarthFrameProvider = new EstimatedEarthFrameProvider(baseUT1);
  197.         this.estimatedEarthFrame = new Frame(baseFrame.getParent(), estimatedEarthFrameProvider,
  198.                                              baseFrame.getParent() + "-estimated");

  200.         if (displacements.length == 0) {
  201.             arguments = null;
  202.         } else {
  203.             arguments = eopHistory.getConventions().getNutationArguments(
  204.                     estimatedEarthFrameProvider.getEstimatedUT1(),
  205.                     eopHistory.getTimeScales());
  206.         }

  208.         this.displacements = displacements.clone();

  210.         this.clockOffsetDriver = new ParameterDriver(baseFrame.getName() + OFFSET_SUFFIX + "-clock",
  211.                                                      0.0, CLOCK_OFFSET_SCALE,
  212.                                                      Double.NEGATIVE_INFINITY, Double.POSITIVE_INFINITY);

  214.         this.clockDriftDriver = new ParameterDriver(baseFrame.getName() + DRIFT_SUFFIX,
  215.                                                     0.0, CLOCK_OFFSET_SCALE,
  216.                                                     Double.NEGATIVE_INFINITY, Double.POSITIVE_INFINITY);

  218.         this.eastOffsetDriver = new ParameterDriver(baseFrame.getName() + OFFSET_SUFFIX + "-East",
  219.                                                     0.0, POSITION_OFFSET_SCALE,
  220.                                                     Double.NEGATIVE_INFINITY, Double.POSITIVE_INFINITY);

  222.         this.northOffsetDriver = new ParameterDriver(baseFrame.getName() + OFFSET_SUFFIX + "-North",
  223.                                                      0.0, POSITION_OFFSET_SCALE,
  224.                                                      Double.NEGATIVE_INFINITY, Double.POSITIVE_INFINITY);

  226.         this.zenithOffsetDriver = new ParameterDriver(baseFrame.getName() + OFFSET_SUFFIX + "-Zenith",
  227.                                                       0.0, POSITION_OFFSET_SCALE,
  228.                                                       Double.NEGATIVE_INFINITY, Double.POSITIVE_INFINITY);

  230.     }

  232.     /** Get the displacement models.
  233.      * @return displacement models (empty if no model has been set up)
  234.      * @since 9.1
  235.      */
  236.     public StationDisplacement[] getDisplacements() {
  237.         return displacements.clone();
  238.     }

  240.     /** Get a driver allowing to change station clock (which is related to measurement date).
  241.      * @return driver for station clock offset
  242.      * @since 9.3
  243.      */
  244.     public ParameterDriver getClockOffsetDriver() {
  245.         return clockOffsetDriver;
  246.     }

  248.     /** Get a driver allowing to change station clock drift (which is related to measurement date).
  249.      * @return driver for station clock drift
  250.      * @since 10.3
  251.      */
  252.     public ParameterDriver getClockDriftDriver() {
  253.         return clockDriftDriver;
  254.     }

  256.     /** Get a driver allowing to change station position along East axis.
  257.      * @return driver for station position offset along East axis
  258.      */
  259.     public ParameterDriver getEastOffsetDriver() {
  260.         return eastOffsetDriver;
  261.     }

  263.     /** Get a driver allowing to change station position along North axis.
  264.      * @return driver for station position offset along North axis
  265.      */
  266.     public ParameterDriver getNorthOffsetDriver() {
  267.         return northOffsetDriver;
  268.     }

  270.     /** Get a driver allowing to change station position along Zenith axis.
  271.      * @return driver for station position offset along Zenith axis
  272.      */
  273.     public ParameterDriver getZenithOffsetDriver() {
  274.         return zenithOffsetDriver;
  275.     }

  277.     /** Get a driver allowing to add a prime meridian rotation.
  278.      * <p>
  279.      * The parameter is an angle in radians. In order to convert this
  280.      * value to a DUT1 in seconds, the value must be divided by
  281.      * {@code ave = 7.292115146706979e-5} (which is the nominal Angular Velocity
  282.      * of Earth from the TIRF model).
  283.      * </p>
  284.      * @return driver for prime meridian rotation
  285.      */
  286.     public ParameterDriver getPrimeMeridianOffsetDriver() {
  287.         return estimatedEarthFrameProvider.getPrimeMeridianOffsetDriver();
  288.     }

  290.     /** Get a driver allowing to add a prime meridian rotation rate.
  291.      * <p>
  292.      * The parameter is an angle rate in radians per second. In order to convert this
  293.      * value to a LOD in seconds, the value must be multiplied by -86400 and divided by
  294.      * {@code ave = 7.292115146706979e-5} (which is the nominal Angular Velocity
  295.      * of Earth from the TIRF model).
  296.      * </p>
  297.      * @return driver for prime meridian rotation rate
  298.      */
  299.     public ParameterDriver getPrimeMeridianDriftDriver() {
  300.         return estimatedEarthFrameProvider.getPrimeMeridianDriftDriver();
  301.     }

  303.     /** Get a driver allowing to add a polar offset along X.
  304.      * <p>
  305.      * The parameter is an angle in radians
  306.      * </p>
  307.      * @return driver for polar offset along X
  308.      */
  309.     public ParameterDriver getPolarOffsetXDriver() {
  310.         return estimatedEarthFrameProvider.getPolarOffsetXDriver();
  311.     }

  313.     /** Get a driver allowing to add a polar drift along X.
  314.      * <p>
  315.      * The parameter is an angle rate in radians per second
  316.      * </p>
  317.      * @return driver for polar drift along X
  318.      */
  319.     public ParameterDriver getPolarDriftXDriver() {
  320.         return estimatedEarthFrameProvider.getPolarDriftXDriver();
  321.     }

  323.     /** Get a driver allowing to add a polar offset along Y.
  324.      * <p>
  325.      * The parameter is an angle in radians
  326.      * </p>
  327.      * @return driver for polar offset along Y
  328.      */
  329.     public ParameterDriver getPolarOffsetYDriver() {
  330.         return estimatedEarthFrameProvider.getPolarOffsetYDriver();
  331.     }

  333.     /** Get a driver allowing to add a polar drift along Y.
  334.      * <p>
  335.      * The parameter is an angle rate in radians per second
  336.      * </p>
  337.      * @return driver for polar drift along Y
  338.      */
  339.     public ParameterDriver getPolarDriftYDriver() {
  340.         return estimatedEarthFrameProvider.getPolarDriftYDriver();
  341.     }

  343.     /** Get the base frame associated with the station.
  344.      * <p>
  345.      * The base frame corresponds to a null position offset, null
  346.      * polar motion, null meridian shift
  347.      * </p>
  348.      * @return base frame associated with the station
  349.      */
  350.     public TopocentricFrame getBaseFrame() {
  351.         return baseFrame;
  352.     }

  354.     /** Get the estimated Earth frame, including the estimated linear models for pole and prime meridian.
  355.      * <p>
  356.      * This frame is bound to the {@link #getPrimeMeridianOffsetDriver() driver for prime meridian offset},
  357.      * {@link #getPrimeMeridianDriftDriver() driver prime meridian drift},
  358.      * {@link #getPolarOffsetXDriver() driver for polar offset along X},
  359.      * {@link #getPolarDriftXDriver() driver for polar drift along X},
  360.      * {@link #getPolarOffsetYDriver() driver for polar offset along Y},
  361.      * {@link #getPolarDriftYDriver() driver for polar drift along Y}, so its orientation changes when
  362.      * the {@link ParameterDriver#setValue(double) setValue} methods of the drivers are called.
  363.      * </p>
  364.      * @return estimated Earth frame
  365.      * @since 9.1
  366.      */
  367.     public Frame getEstimatedEarthFrame() {
  368.         return estimatedEarthFrame;
  369.     }

  371.     /** Get the estimated UT1 scale, including the estimated linear models for prime meridian.
  372.      * <p>
  373.      * This time scale is bound to the {@link #getPrimeMeridianOffsetDriver() driver for prime meridian offset},
  374.      * and {@link #getPrimeMeridianDriftDriver() driver prime meridian drift}, so its offset from UTC changes when
  375.      * the {@link ParameterDriver#setValue(double) setValue} methods of the drivers are called.
  376.      * </p>
  377.      * @return estimated Earth frame
  378.      * @since 9.1
  379.      */
  380.     public UT1Scale getEstimatedUT1() {
  381.         return estimatedEarthFrameProvider.getEstimatedUT1();
  382.     }

  384.     /** Get the station displacement.
  385.      * @param date current date
  386.      * @param position raw position of the station in Earth frame
  387.      * before displacement is applied
  388.      * @return station displacement
  389.      * @since 9.1
  390.      */
  391.     private Vector3D computeDisplacement(final AbsoluteDate date, final Vector3D position) {
  392.         Vector3D displacement = Vector3D.ZERO;
  393.         if (arguments != null) {
  394.             final BodiesElements elements = arguments.evaluateAll(date);
  395.             for (final StationDisplacement sd : displacements) {
  396.                 // we consider all displacements apply to the same initial position,
  397.                 // i.e. they apply simultaneously, not according to some order
  398.                 displacement = displacement.add(sd.displacement(elements, estimatedEarthFrame, position));
  399.             }
  400.         }
  401.         return displacement;
  402.     }

  404.     /** Get the geodetic point at the center of the offset frame.
  405.      * @param date current date (may be null if displacements are ignored)
  406.      * @return geodetic point at the center of the offset frame
  407.      * @since 9.1
  408.      */
  409.     public GeodeticPoint getOffsetGeodeticPoint(final AbsoluteDate date) {

  411.         // take station offset into account
  412.         final double    x          = eastOffsetDriver.getValue();
  413.         final double    y          = northOffsetDriver.getValue();
  414.         final double    z          = zenithOffsetDriver.getValue();
  415.         final BodyShape baseShape  = baseFrame.getParentShape();
  416.         final StaticTransform baseToBody = baseFrame.getStaticTransformTo(baseShape.getBodyFrame(), date);
  417.         Vector3D        origin     = baseToBody.transformPosition(new Vector3D(x, y, z));

  419.         if (date != null) {
  420.             origin = origin.add(computeDisplacement(date, origin));
  421.         }

  423.         return baseShape.transform(origin, baseShape.getBodyFrame(), date);

  425.     }

  427.     /** Get the transform between offset frame and inertial frame.
  428.      * <p>
  429.      * The offset frame takes the <em>current</em> position offset,
  430.      * polar motion and the meridian shift into account. The frame
  431.      * returned is disconnected from later changes in the parameters.
  432.      * When the {@link ParameterDriver parameters} managing these
  433.      * offsets are changed, the method must be called again to retrieve
  434.      * a new offset frame.
  435.      * </p>
  436.      * @param inertial inertial frame to transform to
  437.      * @param date date of the transform
  438.      * @param clockOffsetAlreadyApplied if true, the specified {@code date} is as read
  439.      * by the ground station clock (i.e. clock offset <em>not</em> compensated), if false,
  440.      * the specified {@code date} was already compensated and is a physical absolute date
  441.      * @return transform between offset frame and inertial frame, at <em>real</em> measurement
  442.      * date (i.e. with clock, Earth and station offsets applied)
  443.      */
  444.     public Transform getOffsetToInertial(final Frame inertial,
  445.                                          final AbsoluteDate date, final boolean clockOffsetAlreadyApplied) {

  447.         // take clock offset into account
  448.         final AbsoluteDate offsetCompensatedDate = clockOffsetAlreadyApplied ?
  449.                                                    date :
  450.                                                    new AbsoluteDate(date, -clockOffsetDriver.getValue());

  452.         // take Earth offsets into account
  453.         final Transform intermediateToBody = estimatedEarthFrameProvider.getTransform(offsetCompensatedDate).getInverse();

  455.         // take station offsets into account
  456.         final double    x          = eastOffsetDriver.getValue();
  457.         final double    y          = northOffsetDriver.getValue();
  458.         final double    z          = zenithOffsetDriver.getValue();
  459.         final BodyShape baseShape  = baseFrame.getParentShape();
  460.         final StaticTransform baseToBody = baseFrame
  461.                 .getStaticTransformTo(baseShape.getBodyFrame(), offsetCompensatedDate);
  462.         Vector3D        origin     = baseToBody.transformPosition(new Vector3D(x, y, z));
  463.         origin = origin.add(computeDisplacement(offsetCompensatedDate, origin));

  465.         final GeodeticPoint originGP = baseShape.transform(origin, baseShape.getBodyFrame(), offsetCompensatedDate);
  466.         final Transform offsetToIntermediate =
  467.                         new Transform(offsetCompensatedDate,
  468.                                       new Transform(offsetCompensatedDate,
  469.                                                     new Rotation(Vector3D.PLUS_I, Vector3D.PLUS_K,
  470.                                                                  originGP.getEast(), originGP.getZenith()),
  471.                                                     Vector3D.ZERO),
  472.                                       new Transform(offsetCompensatedDate, origin));

  474.         // combine all transforms together
  475.         final Transform bodyToInert        = baseFrame.getParent().getTransformTo(inertial, offsetCompensatedDate);

  477.         return new Transform(offsetCompensatedDate, offsetToIntermediate, new Transform(offsetCompensatedDate, intermediateToBody, bodyToInert));

  479.     }

  481.     /** Get the transform between offset frame and inertial frame with derivatives.
  482.      * <p>
  483.      * As the East and North vectors are not well defined at pole, the derivatives
  484.      * of these two vectors diverge to infinity as we get closer to the pole.
  485.      * So this method should not be used for stations less than 0.0001 degree from
  486.      * either poles.
  487.      * </p>
  488.      * @param inertial inertial frame to transform to
  489.      * @param clockDate date of the transform as read by the ground station clock (i.e. clock offset <em>not</em> compensated)
  490.      * @param freeParameters total number of free parameters in the gradient
  491.      * @param indices indices of the estimated parameters in derivatives computations, must be driver
  492.      * span name in map, not driver name or will not give right results (see {@link ParameterDriver#getValue(int, Map)})
  493.      * @return transform between offset frame and inertial frame, at <em>real</em> measurement
  494.      * date (i.e. with clock, Earth and station offsets applied)
  495.      * @see #getOffsetToInertial(Frame, FieldAbsoluteDate, int, Map)
  496.      * @since 10.2
  497.      */
  498.     public FieldTransform<Gradient> getOffsetToInertial(final Frame inertial,
  499.                                                         final AbsoluteDate clockDate,
  500.                                                         final int freeParameters,
  501.                                                         final Map<String, Integer> indices) {
  502.         // take clock offset into account
  503.         final Gradient offset = clockOffsetDriver.getValue(freeParameters, indices, clockDate);
  504.         final FieldAbsoluteDate<Gradient> offsetCompensatedDate =
  505.                         new FieldAbsoluteDate<>(clockDate, offset.negate());

  507.         return getOffsetToInertial(inertial, offsetCompensatedDate, freeParameters, indices);
  508.     }

  510.     /** Get the transform between offset frame and inertial frame with derivatives.
  511.      * <p>
  512.      * As the East and North vectors are not well defined at pole, the derivatives
  513.      * of these two vectors diverge to infinity as we get closer to the pole.
  514.      * So this method should not be used for stations less than 0.0001 degree from
  515.      * either poles.
  516.      * </p>
  517.      * @param inertial inertial frame to transform to
  518.      * @param offsetCompensatedDate date of the transform, clock offset and its derivatives already compensated
  519.      * @param freeParameters total number of free parameters in the gradient
  520.      * @param indices indices of the estimated parameters in derivatives computations, must be driver
  521.      * span name in map, not driver name or will not give right results (see {@link ParameterDriver#getValue(int, Map)})
  522.      * @return transform between offset frame and inertial frame, at specified date
  523.      * @since 10.2
  524.      */
  525.     public FieldTransform<Gradient> getOffsetToInertial(final Frame inertial,
  526.                                                         final FieldAbsoluteDate<Gradient> offsetCompensatedDate,
  527.                                                         final int freeParameters,
  528.                                                         final Map<String, Integer> indices) {

  530.         final Field<Gradient>         field = offsetCompensatedDate.getField();
  531.         final FieldVector3D<Gradient> zero  = FieldVector3D.getZero(field);
  532.         final FieldVector3D<Gradient> plusI = FieldVector3D.getPlusI(field);
  533.         final FieldVector3D<Gradient> plusK = FieldVector3D.getPlusK(field);

  535.         // take Earth offsets into account
  536.         final FieldTransform<Gradient> intermediateToBody =
  537.                         estimatedEarthFrameProvider.getTransform(offsetCompensatedDate, freeParameters, indices).getInverse();

  539.         // take station offsets into account
  540.         final Gradient                       x          = eastOffsetDriver.getValue(freeParameters, indices);
  541.         final Gradient                       y          = northOffsetDriver.getValue(freeParameters, indices);
  542.         final Gradient                       z          = zenithOffsetDriver.getValue(freeParameters, indices);
  543.         final BodyShape                      baseShape  = baseFrame.getParentShape();
  544.         final FieldStaticTransform<Gradient> baseToBody = baseFrame.getStaticTransformTo(baseShape.getBodyFrame(), offsetCompensatedDate);

  546.         FieldVector3D<Gradient> origin = baseToBody.transformPosition(new FieldVector3D<>(x, y, z));
  547.         origin = origin.add(computeDisplacement(offsetCompensatedDate.toAbsoluteDate(), origin.toVector3D()));
  548.         final FieldGeodeticPoint<Gradient> originGP = baseShape.transform(origin, baseShape.getBodyFrame(), offsetCompensatedDate);
  549.         final FieldTransform<Gradient> offsetToIntermediate =
  550.                         new FieldTransform<>(offsetCompensatedDate,
  551.                                              new FieldTransform<>(offsetCompensatedDate,
  552.                                                                   new FieldRotation<>(plusI, plusK,
  553.                                                                                       originGP.getEast(), originGP.getZenith()),
  554.                                                                   zero),
  555.                                              new FieldTransform<>(offsetCompensatedDate, origin));

  557.         // combine all transforms together
  558.         final FieldTransform<Gradient> bodyToInert = baseFrame.getParent().getTransformTo(inertial, offsetCompensatedDate);

  560.         return new FieldTransform<>(offsetCompensatedDate,
  561.                                     offsetToIntermediate,
  562.                                     new FieldTransform<>(offsetCompensatedDate, intermediateToBody, bodyToInert));

  564.     }

  566. }
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