GroundStation.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.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.FieldTransform;
  37. import org.orekit.frames.Frame;
  38. import org.orekit.frames.FramesFactory;
  39. import org.orekit.frames.TopocentricFrame;
  40. import org.orekit.frames.Transform;
  41. import org.orekit.models.earth.displacement.StationDisplacement;
  42. import org.orekit.time.AbsoluteDate;
  43. import org.orekit.time.FieldAbsoluteDate;
  44. import org.orekit.time.UT1Scale;
  45. import org.orekit.utils.ParameterDriver;

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

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

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

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

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

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

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

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

  118.     /** Base frame associated with the station. */
  119.     private final TopocentricFrame baseFrame;

  121.     /** Fundamental nutation arguments. */
  122.     private final FundamentalNutationArguments arguments;

  124.     /** Displacement models. */
  125.     private final StationDisplacement[] displacements;

  127.     /** Driver for clock offset. */
  128.     private final ParameterDriver clockOffsetDriver;

  130.     /** Driver for clock drift. */
  131.     private final ParameterDriver clockDriftDriver;

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

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

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

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

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

  186.         this.baseFrame = baseFrame;

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

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

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

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

  208.         this.clockOffsetDriver = new ParameterDriver(baseFrame.getName() + OFFSET_SUFFIX + "-clock",
  209.                                                      0.0, CLOCK_OFFSET_SCALE,
  210.                                                      Double.NEGATIVE_INFINITY, Double.POSITIVE_INFINITY);

  212.         this.clockDriftDriver = new ParameterDriver(baseFrame.getName() + DRIFT_SUFFIX,
  213.                                                     0.0, CLOCK_OFFSET_SCALE,
  214.                                                     Double.NEGATIVE_INFINITY, Double.POSITIVE_INFINITY);

  216.         this.eastOffsetDriver = new ParameterDriver(baseFrame.getName() + OFFSET_SUFFIX + "-East",
  217.                                                     0.0, POSITION_OFFSET_SCALE,
  218.                                                     Double.NEGATIVE_INFINITY, Double.POSITIVE_INFINITY);

  220.         this.northOffsetDriver = new ParameterDriver(baseFrame.getName() + OFFSET_SUFFIX + "-North",
  221.                                                      0.0, POSITION_OFFSET_SCALE,
  222.                                                      Double.NEGATIVE_INFINITY, Double.POSITIVE_INFINITY);

  224.         this.zenithOffsetDriver = new ParameterDriver(baseFrame.getName() + OFFSET_SUFFIX + "-Zenith",
  225.                                                       0.0, POSITION_OFFSET_SCALE,
  226.                                                       Double.NEGATIVE_INFINITY, Double.POSITIVE_INFINITY);

  228.     }

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  421.         return baseShape.transform(origin, baseShape.getBodyFrame(), null);

  423.     }

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

  441.         // take clock offset into account
  442.         final double offset = clockOffsetDriver.getValue();
  443.         final AbsoluteDate offsetCompensatedDate = new AbsoluteDate(clockDate, -offset);

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

  448.         // take station offsets into account
  449.         final double    x          = eastOffsetDriver.getValue();
  450.         final double    y          = northOffsetDriver.getValue();
  451.         final double    z          = zenithOffsetDriver.getValue();
  452.         final BodyShape baseShape  = baseFrame.getParentShape();
  453.         final Transform baseToBody = baseFrame.getTransformTo(baseShape.getBodyFrame(), offsetCompensatedDate);
  454.         Vector3D        origin     = baseToBody.transformPosition(new Vector3D(x, y, z));
  455.         origin = origin.add(computeDisplacement(offsetCompensatedDate, origin));

  457.         final GeodeticPoint originGP = baseShape.transform(origin, baseShape.getBodyFrame(), offsetCompensatedDate);
  458.         final Transform offsetToIntermediate =
  459.                         new Transform(offsetCompensatedDate,
  460.                                       new Transform(offsetCompensatedDate,
  461.                                                     new Rotation(Vector3D.PLUS_I, Vector3D.PLUS_K,
  462.                                                                  originGP.getEast(), originGP.getZenith()),
  463.                                                     Vector3D.ZERO),
  464.                                       new Transform(offsetCompensatedDate, origin));

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

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

  471.     }

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

  498.         return getOffsetToInertial(inertial, offsetCompensatedDate, freeParameters, indices);
  499.     }

  501.     /** Get the transform between offset frame and inertial frame with derivatives.
  502.      * <p>
  503.      * As the East and North vectors are not well defined at pole, the derivatives
  504.      * of these two vectors diverge to infinity as we get closer to the pole.
  505.      * So this method should not be used for stations less than 0.0001 degree from
  506.      * either poles.
  507.      * </p>
  508.      * @param inertial inertial frame to transform to
  509.      * @param offsetCompensatedDate date of the transform, clock offset and its derivatives already compensated
  510.      * @param freeParameters total number of free parameters in the gradient
  511.      * @param indices indices of the estimated parameters in derivatives computations
  512.      * @return transform between offset frame and inertial frame, at specified date
  513.      * @since 10.2
  514.      */
  515.     public FieldTransform<Gradient> getOffsetToInertial(final Frame inertial,
  516.                                                         final FieldAbsoluteDate<Gradient> offsetCompensatedDate,
  517.                                                         final int freeParameters,
  518.                                                         final Map<String, Integer> indices) {

  520.         final Field<Gradient>         field = offsetCompensatedDate.getField();
  521.         final FieldVector3D<Gradient> zero  = FieldVector3D.getZero(field);
  522.         final FieldVector3D<Gradient> plusI = FieldVector3D.getPlusI(field);
  523.         final FieldVector3D<Gradient> plusK = FieldVector3D.getPlusK(field);

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

  529.         // take station offsets into account
  530.         final Gradient  x          = eastOffsetDriver.getValue(freeParameters, indices);
  531.         final Gradient  y          = northOffsetDriver.getValue(freeParameters, indices);
  532.         final Gradient  z          = zenithOffsetDriver.getValue(freeParameters, indices);
  533.         final BodyShape            baseShape  = baseFrame.getParentShape();
  534.         final Transform            baseToBody = baseFrame.getTransformTo(baseShape.getBodyFrame(), (AbsoluteDate) null);

  536.         FieldVector3D<Gradient> origin = baseToBody.transformPosition(new FieldVector3D<>(x, y, z));
  537.         origin = origin.add(computeDisplacement(offsetCompensatedDate.toAbsoluteDate(), origin.toVector3D()));
  538.         final FieldGeodeticPoint<Gradient> originGP = baseShape.transform(origin, baseShape.getBodyFrame(), offsetCompensatedDate);
  539.         final FieldTransform<Gradient> offsetToIntermediate =
  540.                         new FieldTransform<>(offsetCompensatedDate,
  541.                                              new FieldTransform<>(offsetCompensatedDate,
  542.                                                                   new FieldRotation<>(plusI, plusK,
  543.                                                                                       originGP.getEast(), originGP.getZenith()),
  544.                                                                   zero),
  545.                                              new FieldTransform<>(offsetCompensatedDate, origin));

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

  550.         return new FieldTransform<>(offsetCompensatedDate,
  551.                                     offsetToIntermediate,
  552.                                     new FieldTransform<>(offsetCompensatedDate, intermediateToBody, bodyToInert));

  554.     }

  556. }
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