GroundStation.java

/* Copyright 2002-2020 CS GROUP
 * Licensed to CS GROUP (CS) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * CS licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *
 *   http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
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package org.orekit.estimation.measurements;

import java.util.Map;

import org.hipparchus.Field;
import org.hipparchus.analysis.differentiation.DSFactory;
import org.hipparchus.analysis.differentiation.DerivativeStructure;
import org.hipparchus.analysis.differentiation.Gradient;
import org.hipparchus.geometry.euclidean.threed.FieldRotation;
import org.hipparchus.geometry.euclidean.threed.FieldVector3D;
import org.hipparchus.geometry.euclidean.threed.Rotation;
import org.hipparchus.geometry.euclidean.threed.Vector3D;
import org.hipparchus.util.FastMath;
import org.orekit.bodies.BodyShape;
import org.orekit.bodies.FieldGeodeticPoint;
import org.orekit.bodies.GeodeticPoint;
import org.orekit.data.BodiesElements;
import org.orekit.data.FundamentalNutationArguments;
import org.orekit.errors.OrekitException;
import org.orekit.errors.OrekitMessages;
import org.orekit.frames.EOPHistory;
import org.orekit.frames.FieldTransform;
import org.orekit.frames.Frame;
import org.orekit.frames.FramesFactory;
import org.orekit.frames.TopocentricFrame;
import org.orekit.frames.Transform;
import org.orekit.models.earth.displacement.StationDisplacement;
import org.orekit.time.AbsoluteDate;
import org.orekit.time.FieldAbsoluteDate;
import org.orekit.time.UT1Scale;
import org.orekit.utils.ParameterDriver;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

        this.baseFrame = baseFrame;

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

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

        if (displacements.length == 0) {
            arguments = null;
        } else {
            arguments = eopHistory.getConventions().getNutationArguments(
                    estimatedEarthFrameProvider.getEstimatedUT1(),
                    eopHistory.getTimeScales());
        }

        this.displacements = displacements.clone();

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

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

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

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

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

    }

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

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

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

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

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

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

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

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

    /** Get a driver allowing to add a polar offset along X.
     * <p>
     * The parameter is an angle in radians
     * </p>
     * @return driver for polar offset along X
     */
    public ParameterDriver getPolarOffsetXDriver() {
        return estimatedEarthFrameProvider.getPolarOffsetXDriver();
    }

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

    /** Get a driver allowing to add a polar offset along Y.
     * <p>
     * The parameter is an angle in radians
     * </p>
     * @return driver for polar offset along Y
     */
    public ParameterDriver getPolarOffsetYDriver() {
        return estimatedEarthFrameProvider.getPolarOffsetYDriver();
    }

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

    /** Get the base frame associated with the station.
     * <p>
     * The base frame corresponds to a null position offset, null
     * polar motion, null meridian shift
     * </p>
     * @return base frame associated with the station
     */
    public TopocentricFrame getBaseFrame() {
        return baseFrame;
    }

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

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

    /** Get the station displacement.
     * @param date current date
     * @param position raw position of the station in Earth frame
     * before displacement is applied
     * @return station displacement
     * @since 9.1
     */
    private Vector3D computeDisplacement(final AbsoluteDate date, final Vector3D position) {
        Vector3D displacement = Vector3D.ZERO;
        if (arguments != null) {
            final BodiesElements elements = arguments.evaluateAll(date);
            for (final StationDisplacement sd : displacements) {
                // we consider all displacements apply to the same initial position,
                // i.e. they apply simultaneously, not according to some order
                displacement = displacement.add(sd.displacement(elements, estimatedEarthFrame, position));
            }
        }
        return displacement;
    }

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

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

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

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

    }

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

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

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

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

        final GeodeticPoint originGP = baseShape.transform(origin, baseShape.getBodyFrame(), offsetCompensatedDate);
        final Transform offsetToIntermediate =
                        new Transform(offsetCompensatedDate,
                                      new Transform(offsetCompensatedDate,
                                                    new Rotation(Vector3D.PLUS_I, Vector3D.PLUS_K,
                                                                 originGP.getEast(), originGP.getZenith()),
                                                    Vector3D.ZERO),
                                      new Transform(offsetCompensatedDate, origin));

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

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

    }

    /** Get the transform between offset frame and inertial frame with derivatives.
     * <p>
     * As the East and North vectors are not well defined at pole, the derivatives
     * of these two vectors diverge to infinity as we get closer to the pole.
     * So this method should not be used for stations less than 0.0001 degree from
     * either poles.
     * </p>
     * @param inertial inertial frame to transform to
     * @param clockDate date of the transform as read by the ground station clock (i.e. clock offset <em>not</em> compensated)
     * @param factory factory for the derivatives
     * @param indices indices of the estimated parameters in derivatives computations
     * @return transform between offset frame and inertial frame, at <em>real</em> measurement
     * date (i.e. with clock, Earth and station offsets applied)
     * @see #getOffsetToInertial(Frame, FieldAbsoluteDate, DSFactory, Map)
     * @since 9.3
     * @deprecated as of 10.2, replaced by {@link #getOffsetToInertial(Frame, AbsoluteDate, int, Map)}
     */
    @Deprecated
    public FieldTransform<DerivativeStructure> getOffsetToInertial(final Frame inertial,
                                                                   final AbsoluteDate clockDate,
                                                                   final DSFactory factory,
                                                                   final Map<String, Integer> indices) {
        // take clock offset into account
        final DerivativeStructure offset = clockOffsetDriver.getValue(factory, indices);
        final FieldAbsoluteDate<DerivativeStructure> offsetCompensatedDate =
                        new FieldAbsoluteDate<DerivativeStructure>(clockDate, offset.negate());

        return getOffsetToInertial(inertial, offsetCompensatedDate, factory, indices);
    }

    /** Get the transform between offset frame and inertial frame with derivatives.
     * <p>
     * As the East and North vectors are not well defined at pole, the derivatives
     * of these two vectors diverge to infinity as we get closer to the pole.
     * So this method should not be used for stations less than 0.0001 degree from
     * either poles.
     * </p>
     * @param inertial inertial frame to transform to
     * @param offsetCompensatedDate date of the transform, clock offset and its derivatives already compensated
     * @param factory factory for the derivatives
     * @param indices indices of the estimated parameters in derivatives computations
     * @return transform between offset frame and inertial frame, at specified date
     * @see #getOffsetToInertial(Frame, AbsoluteDate, DSFactory, Map)
     * @since 9.0
     * @deprecated as of 10.2, replaced by {@link #getOffsetToInertial(Frame, FieldAbsoluteDate, int, Map)}
     */
    @Deprecated
    public FieldTransform<DerivativeStructure> getOffsetToInertial(final Frame inertial,
                                                                   final FieldAbsoluteDate<DerivativeStructure> offsetCompensatedDate,
                                                                   final DSFactory factory,
                                                                   final Map<String, Integer> indices) {

        final Field<DerivativeStructure>         field = factory.getDerivativeField();
        final FieldVector3D<DerivativeStructure> zero  = FieldVector3D.getZero(field);
        final FieldVector3D<DerivativeStructure> plusI = FieldVector3D.getPlusI(field);
        final FieldVector3D<DerivativeStructure> plusK = FieldVector3D.getPlusK(field);

        // take Earth offsets into account
        final FieldTransform<DerivativeStructure> intermediateToBody =
                        estimatedEarthFrameProvider.getTransform(offsetCompensatedDate, factory, indices).getInverse();

        // take station offsets into account
        final DerivativeStructure  x          = eastOffsetDriver.getValue(factory, indices);
        final DerivativeStructure  y          = northOffsetDriver.getValue(factory, indices);
        final DerivativeStructure  z          = zenithOffsetDriver.getValue(factory, indices);
        final BodyShape            baseShape  = baseFrame.getParentShape();
        final Transform            baseToBody = baseFrame.getTransformTo(baseShape.getBodyFrame(), (AbsoluteDate) null);

        FieldVector3D<DerivativeStructure>            origin   = baseToBody.transformPosition(new FieldVector3D<>(x, y, z));
        origin = origin.add(computeDisplacement(offsetCompensatedDate.toAbsoluteDate(), origin.toVector3D()));
        final FieldGeodeticPoint<DerivativeStructure> originGP = baseShape.transform(origin, baseShape.getBodyFrame(), offsetCompensatedDate);
        final FieldTransform<DerivativeStructure> offsetToIntermediate =
                        new FieldTransform<>(offsetCompensatedDate,
                                             new FieldTransform<>(offsetCompensatedDate,
                                                                  new FieldRotation<>(plusI, plusK,
                                                                                      originGP.getEast(), originGP.getZenith()),
                                                                  zero),
                                             new FieldTransform<>(offsetCompensatedDate, origin));

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

        return new FieldTransform<>(offsetCompensatedDate,
                                    offsetToIntermediate,
                                    new FieldTransform<>(offsetCompensatedDate, intermediateToBody, bodyToInert));

    }

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

        return getOffsetToInertial(inertial, offsetCompensatedDate, freeParameters, indices);
    }

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

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

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

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

        FieldVector3D<Gradient> origin = baseToBody.transformPosition(new FieldVector3D<>(x, y, z));
        origin = origin.add(computeDisplacement(offsetCompensatedDate.toAbsoluteDate(), origin.toVector3D()));
        final FieldGeodeticPoint<Gradient> originGP = baseShape.transform(origin, baseShape.getBodyFrame(), offsetCompensatedDate);
        final FieldTransform<Gradient> offsetToIntermediate =
                        new FieldTransform<>(offsetCompensatedDate,
                                             new FieldTransform<>(offsetCompensatedDate,
                                                                  new FieldRotation<>(plusI, plusK,
                                                                                      originGP.getEast(), originGP.getZenith()),
                                                                  zero),
                                             new FieldTransform<>(offsetCompensatedDate, origin));

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

        return new FieldTransform<>(offsetCompensatedDate,
                                    offsetToIntermediate,
                                    new FieldTransform<>(offsetCompensatedDate, intermediateToBody, bodyToInert));

    }

}