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    * 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
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    *   http://www.apache.org/licenses/LICENSE-2.0
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   * Unless required by applicable law or agreed to in writing, software
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  package org.orekit.propagation.analytical.gnss;
  
  import java.util.ArrayList;
  import java.util.Collections;
  import java.util.List;
  
  import org.hipparchus.analysis.differentiation.Gradient;
  import org.hipparchus.analysis.differentiation.GradientField;
  import org.hipparchus.analysis.differentiation.UnivariateDerivative2;
  import org.hipparchus.geometry.euclidean.threed.FieldVector3D;
  import org.hipparchus.geometry.euclidean.threed.Vector3D;
  import org.hipparchus.linear.MatrixUtils;
  import org.hipparchus.linear.QRDecomposition;
  import org.hipparchus.linear.RealMatrix;
  import org.hipparchus.linear.RealVector;
  import org.hipparchus.util.FastMath;
  import org.hipparchus.util.FieldSinCos;
  import org.hipparchus.util.SinCos;
  import org.orekit.attitudes.Attitude;
  import org.orekit.attitudes.AttitudeProvider;
  import org.orekit.attitudes.FrameAlignedProvider;
  import org.orekit.frames.Frame;
  import org.orekit.orbits.FieldKeplerianAnomalyUtility;
  import org.orekit.orbits.FieldKeplerianOrbit;
  import org.orekit.orbits.FieldKeplerianParameters;
  import org.orekit.orbits.KeplerianAnomalyUtility;
  import org.orekit.orbits.KeplerianOrbit;
  import org.orekit.orbits.Orbit;
  import org.orekit.orbits.PositionAngleType;
  import org.orekit.propagation.AbstractMatricesHarvester;
  import org.orekit.propagation.Propagator;
  import org.orekit.propagation.SpacecraftState;
  import org.orekit.propagation.analytical.AbstractAnalyticalPropagator;
  import org.orekit.propagation.analytical.gnss.data.FieldGnssOrbitalElements;
  import org.orekit.propagation.analytical.gnss.data.GNSSOrbitalElements;
  import org.orekit.propagation.analytical.gnss.data.GNSSOrbitalElementsFactory;
  import org.orekit.propagation.analytical.gnss.data.NonKeplerianDriversFactory;
  import org.orekit.time.AbsoluteDate;
  import org.orekit.time.FieldAbsoluteDate;
  import org.orekit.time.GNSSDate;
  import org.orekit.utils.DoubleArrayDictionary;
  import org.orekit.utils.FieldPVCoordinates;
  import org.orekit.utils.PVCoordinates;
  import org.orekit.utils.ParameterDriver;
  import org.orekit.utils.ParameterDriversProvider;
  import org.orekit.utils.TimeSpanMap.Span;
  
  /** Common handling of {@link AbstractAnalyticalPropagator} methods for GNSS propagators.
   * <p>
   * This class allows to provide easily a subset of {@link AbstractAnalyticalPropagator} methods
   * for specific GNSS propagators.
   * </p>
   * @param <O> type of the orbital elements
   * @author Pascal Parraud
   */
  public class GNSSPropagator<O extends GNSSOrbitalElements<O>>
      extends AbstractAnalyticalPropagator implements ParameterDriversProvider {
  
      /** Maximum number of iterations for internal loops.
       * @since 13.0
       */
      private static final int MAX_ITER = 100;
  
      /** Tolerance on position for rebuilding orbital elements from initial state.
       * @since 13.0
       */
      private static final double TOL_P = 1.0e-6;
  
      /** Tolerance on velocity for rebuilding orbital elements from initial state.
       * @since 13.0
       */
      private static final double TOL_V = 1.0e-9;
  
      /** Number of free parameters for orbital elements.
       * @since 13.0
       */
      private static final int FREE_PARAMETERS = 6;
  
      /** Convergence parameter.
       * @since 13.0
       */
      private static final double EPS = 1.0e-12;
  
     /** The GNSS propagation model used. */
     private O orbitalElements;
 
     /** Factory for non-Keplerian elements drivers.
      * @since 14.0
      */
     private final NonKeplerianDriversFactory driversFactory;
 
     /** The ECI frame used for GNSS propagation. */
     private final Frame eci;
 
     /** The ECEF frame used for GNSS propagation. */
     private final Frame ecef;
 
     /** Build a new instance.
      * <p>
      * Beware that since GNSS orbital elements refer to an Earth frame frozen at a specific date
      * to become an inertial frame, the factory date <em>must</em> have been initialized properly
      * (by calling {@link GNSSOrbitalElementsFactory#setTimeOfEphemeris(GNSSDate)}). Setting the date
      * allows the frozen frame to be set properly, otherwise a null pointer exception will be thrown
      * when the propagator builder attempts to use the frame.
      * </p>
      * <p>
      * The attitude provider is set by default to be aligned with the provided inertial frame.
      * This can be changed (typically to {@link org.orekit.gnss.attitude.GenericGNSS}) after
      * construction by calling {@link #setAttitudeProvider(org.orekit.attitudes.AttitudeProvider)
      * setAttitudeProvider}
      * </p>
      * <p>
      * The mass is set to the {@link org.orekit.propagation.Propagator#DEFAULT_MASS DEFAULT_MASS}.
      * </p>
      * @param factory factory for the elements and frames
      * @since 14.0
      */
 
     public GNSSPropagator(final GNSSOrbitalElementsFactory<O> factory) {
         this(factory.createFromDrivers(), factory.getInertial(), factory.getBodyFixed(),
              FrameAlignedProvider.of(factory.getInertial()),
              Propagator.DEFAULT_MASS);
     }
 
     /** Build a new instance.
      * @param orbitalElements GNSS orbital elements
      * @param eci Earth Centered Inertial frame
      * @param ecef Earth Centered Earth Fixed frame
      * @param provider attitude provider
      * @param mass satellite mass (kg)
      */
     public GNSSPropagator(final O orbitalElements, final Frame eci, final Frame ecef,
                           final AttitudeProvider provider, final double mass) {
         super(provider);
         // Stores the GNSS orbital elements
         this.orbitalElements = orbitalElements;
         this.driversFactory  = new NonKeplerianDriversFactory();
         driversFactory.reset(orbitalElements);
         // Sets the Earth Centered Inertial frame
         this.eci  = eci;
         // Sets the Earth Centered Earth Fixed frame
         this.ecef = ecef;
 
         // Sets initial state
         final Orbit orbit = propagateOrbit(orbitalElements.getDate());
         final Attitude attitude = provider.getAttitude(orbit, orbit.getDate(), orbit.getFrame());
 
         // calling the method from constructor because the one overridden below recomputes the orbital elements
         super.resetInitialState(new SpacecraftState(orbit, attitude).withMass(mass));
 
     }
 
     /**
      * Build a new instance from an initial state.
      * <p>
      * The Keplerian elements already present in the {@code nonKeplerianElements} argument
      * will be ignored as it is the {@code initialState} argument that will be used to
      * build the complete orbital elements of the propagator
      * </p>
      * @param initialState         initial state
      * @param nonKeplerianElements non-Keplerian orbital elements (the Keplerian orbital elements will be ignored)
      * @param ecef                 Earth Centered Earth Fixed frame
      * @param provider             attitude provider
      * @param mass                 spacecraft mass
      * @since 13.0
      */
     public GNSSPropagator(final SpacecraftState initialState, final O nonKeplerianElements,
                           final Frame ecef, final AttitudeProvider provider, final double mass) {
         this(buildOrbitalElements(initialState, nonKeplerianElements, new NonKeplerianDriversFactory(),
                                   ecef, provider, mass),
              initialState.getFrame(), ecef, provider, initialState.getMass());
     }
 
     /** {@inheritDoc} */
     @Override
     public List<ParameterDriver> getParametersDrivers() {
         return driversFactory.getParametersDrivers();
     }
 
     /** Get the factory for non-Keplerian elements drivers.
      * @return factory for non-Keplerian elements drivers
      */
     public NonKeplerianDriversFactory getDriversFactory() {
         return driversFactory;
     }
 
     /**
      * Gets the Earth Centered Inertial frame used to propagate the orbit.
      *
      * @return the ECI frame
      */
     public Frame getECI() {
         return eci;
     }
 
     /**
      * Gets the Earth Centered Earth Fixed frame used to propagate GNSS orbits according to the
      * Interface Control Document.
      *
      * @return the ECEF frame
      */
     public Frame getECEF() {
         return ecef;
     }
 
     /**
      * Gets the Earth gravity coefficient used for GNSS propagation.
      *
      * @return the Earth gravity coefficient.
      */
     public double getMU() {
         return orbitalElements.getOrbit().getMu();
     }
 
     /** Get the underlying GNSS propagation orbital elements.
      * @return the underlying GNSS orbital elements
      * @since 13.0
      */
     public O getOrbitalElements() {
         return orbitalElements;
     }
 
     /** {@inheritDoc}
      * @since 13.0
      */
     @Override
     protected AbstractMatricesHarvester createHarvester(final String stmName, final RealMatrix initialStm,
                                                         final DoubleArrayDictionary initialJacobianColumns) {
 
         // Create the harvester
         final GnssHarvester<O> harvester = new GnssHarvester<>(this, stmName, initialStm, initialJacobianColumns);
 
         // Update the list of additional state provider
         addAdditionalDataProvider(harvester);
 
         // Return the configured harvester
         return harvester;
 
     }
 
     /** {@inheritDoc}
      * @since 13.0
      */
     @Override
     protected List<String> getJacobiansColumnsNames() {
         final List<String> columnsNames = new ArrayList<>();
         for (final ParameterDriver driver : getParametersDrivers()) {
             if (driver.isSelected() && !columnsNames.contains(driver.getNamesSpanMap().getFirstSpan().getData())) {
                 // As driver with same name should have same NamesSpanMap we only check if the first span is present,
                 // if not we add all span names to columnsNames
                 for (Span<String> span = driver.getNamesSpanMap().getFirstSpan(); span != null; span = span.next()) {
                     columnsNames.add(span.getData());
                 }
             }
         }
         Collections.sort(columnsNames);
         return columnsNames;
     }
 
     /** {@inheritDoc} */
     @Override
     public Orbit propagateOrbit(final AbsoluteDate date) {
         // Get the PVCoordinates in ECEF frame
         final PVCoordinates pvaInECEF = propagateInEcef(date);
         // Transform the PVCoordinates to ECI frame
         final PVCoordinates pvaInECI = ecef.getTransformTo(eci, date).transformPVCoordinates(pvaInECEF);
         // Return the Keplerian orbit
         return new KeplerianOrbit(pvaInECI, eci, date, getMU());
     }
 
     /**
      * Gets the PVCoordinates of the GNSS SV in {@link #getECEF() ECEF frame}.
      *
      * <p>The algorithm uses automatic differentiation to compute velocity and
      * acceleration.</p>
      *
      * @param date the computation date
      * @return the GNSS SV PVCoordinates in {@link #getECEF() ECEF frame}
      */
     public PVCoordinates propagateInEcef(final AbsoluteDate date) {
 
         final KeplerianOrbit orbit = orbitalElements.getOrbit();
 
         // Duration from GNSS ephemeris Reference date
         final UnivariateDerivative2 tk = new UnivariateDerivative2(getTk(date), 1.0, 0.0);
         // Semi-major axis
         final UnivariateDerivative2 ak = tk.multiply(orbitalElements.getADot()).add(orbit.getA());
         // Mean motion
         final UnivariateDerivative2 nA = tk.multiply(orbitalElements.getDeltaN0Dot() * 0.5).
                                          add(orbitalElements.getDeltaN0()).
                                          add(orbit.getKeplerianMeanMotion());
         // Mean anomaly
         final UnivariateDerivative2 mk = tk.multiply(nA).add(orbit.getMeanAnomaly());
         // Eccentric Anomaly
         final UnivariateDerivative2 e  = tk.newInstance(orbit.getE());
         final UnivariateDerivative2 ek = FieldKeplerianAnomalyUtility.ellipticMeanToEccentric(e, mk);
         // True Anomaly
         final UnivariateDerivative2 vk =  FieldKeplerianAnomalyUtility.ellipticEccentricToTrue(e, ek);
         // Argument of Latitude
         final UnivariateDerivative2 phik    = vk.add(orbit.getPeriapsisArgument());
         final FieldSinCos<UnivariateDerivative2> cs2phi = FastMath.sinCos(phik.multiply(2));
         // Argument of Latitude Correction
         final UnivariateDerivative2 dphik = cs2phi.cos().multiply(orbitalElements.getCuc()).add(cs2phi.sin().multiply(orbitalElements.getCus()));
         // Radius Correction
         final UnivariateDerivative2 drk = cs2phi.cos().multiply(orbitalElements.getCrc()).add(cs2phi.sin().multiply(orbitalElements.getCrs()));
         // Inclination Correction
         final UnivariateDerivative2 dik = cs2phi.cos().multiply(orbitalElements.getCic()).add(cs2phi.sin().multiply(orbitalElements.getCis()));
         // Corrected Argument of Latitude
         final FieldSinCos<UnivariateDerivative2> csuk = FastMath.sinCos(phik.add(dphik));
         // Corrected Radius
         final UnivariateDerivative2 rk = ek.cos().multiply(e.negate()).add(1).multiply(ak).add(drk);
         // Corrected Inclination
         final UnivariateDerivative2 ik  = tk.multiply(orbitalElements.getIDot()).add(orbit.getI()).add(dik);
         final FieldSinCos<UnivariateDerivative2> csik = FastMath.sinCos(ik);
         // Positions in orbital plane
         final UnivariateDerivative2 xk = csuk.cos().multiply(rk);
         final UnivariateDerivative2 yk = csuk.sin().multiply(rk);
         // Corrected longitude of ascending node
         final double thetaDot = orbitalElements.getAngularVelocity();
         final double toe = orbitalElements.getTimeOfEphemeris().getSecondsInWeek();
         final FieldSinCos<UnivariateDerivative2> csomk =
             FastMath.sinCos(tk.multiply(orbitalElements.getOmegaDot() - thetaDot).
                             add(orbit.getRightAscensionOfAscendingNode() - thetaDot * toe));
         // returns the Earth-fixed coordinates
         final FieldVector3D<UnivariateDerivative2> positionWithDerivatives =
                         new FieldVector3D<>(xk.multiply(csomk.cos()).subtract(yk.multiply(csomk.sin()).multiply(csik.cos())),
                                             xk.multiply(csomk.sin()).add(yk.multiply(csomk.cos()).multiply(csik.cos())),
                                             yk.multiply(csik.sin()));
         return new PVCoordinates(positionWithDerivatives);
     }
 
     /**
      * Gets the duration from GNSS Reference epoch.
      * <p>This takes the GNSS week roll-over into account.</p>
      * @param date the considered date
      * @return the duration from GNSS orbit Reference epoch (s)
      */
     private double getTk(final AbsoluteDate date) {
         final double cycleDuration = orbitalElements.getCycleDuration();
         // Time from ephemeris reference epoch
         double tk = date.durationFrom(orbitalElements.getDate());
         // Adjusts the time to take roll over week into account
         while (tk > 0.5 * cycleDuration) {
             tk -= cycleDuration;
         }
         while (tk < -0.5 * cycleDuration) {
             tk += cycleDuration;
         }
         // Returns the time from ephemeris reference epoch
         return tk;
     }
 
     /** {@inheritDoc} */
     @Override
     public Frame getFrame() {
         return eci;
     }
 
     /** {@inheritDoc} */
     @Override
     protected double getMass(final AbsoluteDate date) {
         return getInitialState().getMass();
     }
 
     /** {@inheritDoc} */
     @Override
     public void resetInitialState(final SpacecraftState state) {
         orbitalElements = buildOrbitalElements(state, orbitalElements, driversFactory,
                                                ecef, getAttitudeProvider(), state.getMass());
         final Orbit orbit = propagateOrbit(orbitalElements.getDate());
         final Attitude attitude = getAttitudeProvider().getAttitude(orbit, orbit.getDate(), orbit.getFrame());
         super.resetInitialState(new SpacecraftState(orbit, attitude).withMass(state.getMass()));
     }
 
     /** {@inheritDoc} */
     @Override
     protected void resetIntermediateState(final SpacecraftState state, final boolean forward) {
         resetInitialState(state);
     }
 
     /**
      * Build orbital elements from initial state.
      * <p>
      * This method is roughly the inverse of {@link #propagateInEcef(AbsoluteDate)}, except it starts from a state in
      * inertial frame
      * </p>
      *
      * @param <O> type of the orbital elements (non-field version)
      * @param initialState         initial state
      * @param nonKeplerianElements non-Keplerian orbital elements (the Keplerian orbital elements will be overridden)
      * @param driversFactory       factory for non-Keplerian drivers
      * @param ecef                 Earth Centered Earth Fixed frame
      * @param provider             attitude provider
      * @param mass                 satellite mass (kg)
      * @return orbital elements that generate the {@code initialState} when used with a propagator
      * @since 13.0
      */
     public static <O extends GNSSOrbitalElements<O>>
         O buildOrbitalElements(final SpacecraftState initialState,
                                final O nonKeplerianElements,
                                final NonKeplerianDriversFactory driversFactory,
                                final Frame ecef, final AttitudeProvider provider,
                                final double mass) {
 
         // get approximate initial orbit
         final Frame frozenEcef = ecef.getFrozenFrame(initialState.getFrame(), initialState.getDate(),
                                                      GNSSOrbitalElementsFactory.FROZEN + ecef.getName());
         final KeplerianOrbit orbit = approximateInitialOrbit(initialState, nonKeplerianElements, frozenEcef);
         driversFactory.reset(nonKeplerianElements);
 
         // refine orbit using simple differential correction to reach target PV
         final PVCoordinates targetPV = initialState.getPVCoordinates(frozenEcef);
         FieldGnssOrbitalElements<Gradient, O> gElements = toGradient(nonKeplerianElements, orbit, driversFactory);
         for (int i = 0; i < MAX_ITER; ++i) {
 
             // get position-velocity derivatives with respect to initial orbit
             final FieldGnssPropagator<Gradient, O> gPropagator =
                 new FieldGnssPropagator<>(gElements, frozenEcef, ecef, provider,
                                           gElements.getTgd().newInstance(mass));
             final FieldPVCoordinates<Gradient> gPV = gPropagator.getInitialState().getPVCoordinates();
 
             // compute Jacobian matrix
             final RealMatrix jacobian = MatrixUtils.createRealMatrix(FREE_PARAMETERS, FREE_PARAMETERS);
             jacobian.setRow(0, gPV.getPosition().getX().getGradient());
             jacobian.setRow(1, gPV.getPosition().getY().getGradient());
             jacobian.setRow(2, gPV.getPosition().getZ().getGradient());
             jacobian.setRow(3, gPV.getVelocity().getX().getGradient());
             jacobian.setRow(4, gPV.getVelocity().getY().getGradient());
             jacobian.setRow(5, gPV.getVelocity().getZ().getGradient());
 
             // compute residuals
             final RealVector residuals = MatrixUtils.createRealVector(FREE_PARAMETERS);
             residuals.setEntry(0, targetPV.getPosition().getX() - gPV.getPosition().getX().getValue());
             residuals.setEntry(1, targetPV.getPosition().getY() - gPV.getPosition().getY().getValue());
             residuals.setEntry(2, targetPV.getPosition().getZ() - gPV.getPosition().getZ().getValue());
             residuals.setEntry(3, targetPV.getVelocity().getX() - gPV.getVelocity().getX().getValue());
             residuals.setEntry(4, targetPV.getVelocity().getY() - gPV.getVelocity().getY().getValue());
             residuals.setEntry(5, targetPV.getVelocity().getZ() - gPV.getVelocity().getZ().getValue());
 
             // check convergence
             final double deltaP = FastMath.sqrt(residuals.getEntry(0) * residuals.getEntry(0) +
                                                 residuals.getEntry(1) * residuals.getEntry(1) +
                                                 residuals.getEntry(2) * residuals.getEntry(2));
             final double deltaV = FastMath.sqrt(residuals.getEntry(3) * residuals.getEntry(3) +
                                                 residuals.getEntry(4) * residuals.getEntry(4) +
                                                 residuals.getEntry(5) * residuals.getEntry(5));
             if (deltaP < TOL_P && deltaV < TOL_V) {
                 break;
             }
 
             // linear correction to get closer to target PV
             final RealVector correction = new QRDecomposition(jacobian, EPS).getSolver().solve(residuals);
 
             // prevent correction to produce invalid values
             final FieldKeplerianOrbit<Gradient> previous = gElements.getOrbit();
             Gradient updatedA;
             Gradient updatedE;
             double factor = 2;
             do {
                 // loop until eccentricity is valid
                 factor *= 0.5;
                 updatedA = previous.getA().add(correction.getEntry(0) * factor);
                 updatedE = previous.getE().add(correction.getEntry(1) * factor);
             } while (updatedA.getValue() < 0 || updatedE.getValue() < 0 || updatedE.getValue() >= 1);
 
             // update initial orbit
             final FieldKeplerianOrbit<Gradient> updated =
                 new FieldKeplerianOrbit<>(new FieldKeplerianParameters<>(updatedA,
                                                                          updatedE,
                                                                          previous.getI().add(correction.getEntry(2) * factor),
                                                                          previous.getPeriapsisArgument().add(correction.getEntry(3) * factor),
                                                                          previous.getRightAscensionOfAscendingNode().add(correction.getEntry(4) * factor),
                                                                          previous.getMeanAnomaly().add(correction.getEntry(5) * factor),
                                                                          PositionAngleType.MEAN),
                                           previous.getFrame(), previous.getDate(), previous.getMu());
             gElements = toGradient(nonKeplerianElements, updated.toOrbit(), driversFactory);
 
         }
 
         return gElements.toNonField();
 
     }
 
     /** Compute approximate initial orbit.
      * @param initialState         initial state
      * @param nonKeplerianElements non-Keplerian orbital elements (the Keplerian orbital elements will be ignored)
      * @param frozenEcef           inertial frame aligned with Earth Centered Earth Fixed frame at orbit date
      * @return approximate initial orbit that generate a state close to {@code initialState}
      * @since 13.0
      */
     private static KeplerianOrbit approximateInitialOrbit(final SpacecraftState initialState,
                                                           final GNSSOrbitalElements<?> nonKeplerianElements,
                                                           final Frame frozenEcef) {
 
         // rotate the state to a frame that is inertial but aligned with Earth frame,
         // as analytical model is expressed in Earth frame
         final PVCoordinates pv = initialState.getPVCoordinates(frozenEcef);
         final Vector3D      p  = pv.getPosition();
         final Vector3D      v  = pv.getVelocity();
 
         // compute Keplerian orbital parameters
         final double   rk  = p.getNorm();
 
         // compute orbital plane orientation
         final Vector3D normal = pv.getMomentum().normalize();
         final double   cosIk  = normal.getZ();
         final double   ik     = Vector3D.angle(normal, Vector3D.PLUS_K);
 
         // compute position in orbital plane
         final double   q   = FastMath.hypot(normal.getX(), normal.getY());
         final double   cos = -normal.getY() / q;
         final double   sin =  normal.getX() / q;
         final double   xk  =  p.getX() * cos + p.getY() * sin;
         final double   yk  = (p.getY() * cos - p.getX() * sin) / cosIk;
 
         // corrected latitude argument
         final double   uk  = FastMath.atan2(yk, xk);
 
         // recover latitude argument before correction, using a fixed-point method
         double phi = uk;
         for (int i = 0; i < MAX_ITER; ++i) {
             final double previous = phi;
             final SinCos cs2Phi = FastMath.sinCos(2 * phi);
             phi = uk - (cs2Phi.cos() * nonKeplerianElements.getCuc() + cs2Phi.sin() * nonKeplerianElements.getCus());
             if (FastMath.abs(phi - previous) <= EPS) {
                 break;
             }
         }
         final SinCos cs2phi = FastMath.sinCos(2 * phi);
 
         // recover plane orientation before correction
         // here, we know that tk = 0 since our orbital elements will be at initial state date
         final double i0  = ik - (cs2phi.cos() * nonKeplerianElements.getCic() + cs2phi.sin() * nonKeplerianElements.getCis());
         final double om0 = FastMath.atan2(sin, cos) +
                            nonKeplerianElements.getAngularVelocity() *
                            nonKeplerianElements.getTimeOfEphemeris().getSecondsInWeek();
 
         // recover eccentricity and anomaly
         final double mu = initialState.getOrbit().getMu();
         final double rV2OMu           = rk * v.getNorm2Sq() / mu;
         final double sma              = rk / (2 - rV2OMu);
         final double eCosE            = rV2OMu - 1;
         final double eSinE            = Vector3D.dotProduct(p, v) / FastMath.sqrt(mu * sma);
         final double e                = FastMath.hypot(eCosE, eSinE);
         final double eccentricAnomaly = FastMath.atan2(eSinE, eCosE);
         final double aop              = phi - eccentricAnomaly;
         final double meanAnomaly      = KeplerianAnomalyUtility.ellipticEccentricToMean(e, eccentricAnomaly);
 
         return new KeplerianOrbit(sma, e, i0, aop, om0, meanAnomaly, PositionAngleType.MEAN, frozenEcef,
                                   initialState.getDate(), mu);
 
     }
 
     /** Convert orbital elements to gradient.
      * @param <O> type of the orbital elements (non-field version)
      * @param elements       primitive double elements
      * @param orbit          Keplerian orbit
      * @param driversFactory factory for non-Kepleria drivers
      * @return converted elements, set up as gradient relative to Keplerian orbit
      * @since 14.0
      */
     private static <O extends GNSSOrbitalElements<O>>
         FieldGnssOrbitalElements<Gradient, O> toGradient(final O elements,
                                                          final KeplerianOrbit orbit,
                                                          final NonKeplerianDriversFactory driversFactory) {
 
         // build orbit with gradient
         final Gradient aG    = Gradient.variable(FREE_PARAMETERS, 0, orbit.getA());
         final Gradient eG    = Gradient.variable(FREE_PARAMETERS, 1, orbit.getE());
         final Gradient iG    = Gradient.variable(FREE_PARAMETERS, 2, orbit.getI());
         final Gradient paG   = Gradient.variable(FREE_PARAMETERS, 3, orbit.getPeriapsisArgument());
         final Gradient raanG = Gradient.variable(FREE_PARAMETERS, 4, orbit.getRightAscensionOfAscendingNode());
         final Gradient mG    = Gradient.variable(FREE_PARAMETERS, 5, orbit.getMeanAnomaly());
         final FieldKeplerianOrbit<Gradient> orbitG =
             new FieldKeplerianOrbit<>(new FieldKeplerianParameters<>(aG, eG, iG, paG, raanG, mG,
                                                                      PositionAngleType.MEAN),
                                       orbit.getFrame(),
                                       new FieldAbsoluteDate<>(GradientField.getField(FREE_PARAMETERS),
                                                               orbit.getDate()),
                                       Gradient.constant(FREE_PARAMETERS, orbit.getMu()));
 
         // convert to GNSS orbital elements
         return elements.toField(orbitG,
                                 driversFactory.toGradients(FREE_PARAMETERS),
                                 d -> Gradient.constant(FREE_PARAMETERS, d));
 
     }
 
 }