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    * contributor license agreements.  See the NOTICE file distributed with
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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.models.earth.ionosphere;
  
  import java.util.Collections;
  import java.util.List;
  
  import org.hipparchus.Field;
  import org.hipparchus.CalculusFieldElement;
  import org.hipparchus.geometry.euclidean.threed.FieldVector3D;
  import org.hipparchus.geometry.euclidean.threed.Vector3D;
  import org.hipparchus.util.FastMath;
  import org.hipparchus.util.FieldSinCos;
  import org.hipparchus.util.MathUtils;
  import org.hipparchus.util.SinCos;
  import org.orekit.annotation.DefaultDataContext;
  import org.orekit.bodies.FieldGeodeticPoint;
  import org.orekit.bodies.GeodeticPoint;
  import org.orekit.data.DataContext;
  import org.orekit.frames.FieldStaticTransform;
  import org.orekit.frames.StaticTransform;
  import org.orekit.frames.TopocentricFrame;
  import org.orekit.propagation.FieldSpacecraftState;
  import org.orekit.propagation.SpacecraftState;
  import org.orekit.time.AbsoluteDate;
  import org.orekit.time.DateTimeComponents;
  import org.orekit.time.FieldAbsoluteDate;
  import org.orekit.time.TimeScale;
  import org.orekit.utils.Constants;
  import org.orekit.utils.ParameterDriver;
  
  /**
   * Klobuchar ionospheric delay model.
   * Klobuchar ionospheric delay model is designed as a GNSS correction model.
   * The parameters for the model are provided by the GPS satellites in their broadcast
   * messsage.
   * This model is based on the assumption the electron content is concentrated
   * in 350 km layer.
   *
   * The delay refers to L1 (1575.42 MHz).
   * If the delay is sought for L2 (1227.60 MHz), multiply the result by 1.65 (Klobuchar, 1996).
   * More generally, since ionospheric delay is inversely proportional to the square of the signal
   * frequency f, to adapt this model to other GNSS frequencies f, multiply by (L1 / f)^2.
   *
   * References:
   *     ICD-GPS-200, Rev. C, (1997), pp. 125-128
   *     Klobuchar, J.A., Ionospheric time-delay algorithm for single-frequency GPS users,
   *         IEEE Transactions on Aerospace and Electronic Systems, Vol. 23, No. 3, May 1987
   *     Klobuchar, J.A., "Ionospheric Effects on GPS", Global Positioning System: Theory and
   *         Applications, 1996, pp.513-514, Parkinson, Spilker.
   *
   * @author Joris Olympio
   * @since 7.1
   *
   */
  public class KlobucharIonoModel implements IonosphericModel, IonosphericDelayModel {
  
      /** The 4 coefficients of a cubic equation representing the amplitude of the vertical delay. Units are sec/semi-circle^(i-1) for the i-th coefficient, i=1, 2, 3, 4. */
      private final double[] alpha;
  
      /** The 4 coefficients of a cubic equation representing the period of the model. Units are sec/semi-circle^(i-1) for the i-th coefficient, i=1, 2, 3, 4. */
      private final double[] beta;
  
      /** GPS time scale. */
      private final TimeScale gps;
  
      /** Create a new Klobuchar ionospheric delay model, when a single frequency system is used.
       * This model accounts for at least 50 percent of RMS error due to ionospheric propagation effect (ICD-GPS-200)
       *
       * <p>This constructor uses the {@link DataContext#getDefault() default data context}.
       *
       * @param alpha coefficients of a cubic equation representing the amplitude of the vertical delay.
       * @param beta coefficients of a cubic equation representing the period of the model.
       * @see #KlobucharIonoModel(double[], double[], TimeScale)
       */
      @DefaultDataContext
      public KlobucharIonoModel(final double[] alpha, final double[] beta) {
          this(alpha, beta, DataContext.getDefault().getTimeScales().getGPS());
      }
  
      /**
       * Create a new Klobuchar ionospheric delay model, when a single frequency system is
       * used. This model accounts for at least 50 percent of RMS error due to ionospheric
       * propagation effect (ICD-GPS-200)
       *
      * @param alpha coefficients of a cubic equation representing the amplitude of the
      *              vertical delay.
      * @param beta  coefficients of a cubic equation representing the period of the
      *              model.
      * @param gps   GPS time scale.
      * @since 10.1
      */
     public KlobucharIonoModel(final double[] alpha,
                               final double[] beta,
                               final TimeScale gps) {
         this.alpha = alpha.clone();
         this.beta  = beta.clone();
         this.gps = gps;
     }
 
     /**
      * Calculates the ionospheric path delay for the signal path from a ground
      * station to a satellite.
      * <p>
      * The path delay is computed for any elevation angle.
      * </p>
      * @param date current date
      * @param geo geodetic point of receiver/station
      * @param elevation elevation of the satellite in radians
      * @param azimuth azimuth of the satellite in radians
      * @param frequency frequency of the signal in Hz
      * @param parameters ionospheric model parameters
      * @return the path delay due to the ionosphere in m
      */
     public double pathDelay(final AbsoluteDate date, final GeodeticPoint geo,
                             final double elevation, final double azimuth, final double frequency,
                             final double[] parameters) {
 
         // Sine and cosine of the azimuth
         final SinCos sc = FastMath.sinCos(azimuth);
 
         // degrees to semicircles
         final double rad2semi = 1. / FastMath.PI;
         final double semi2rad = FastMath.PI;
 
         // Earth Centered angle
         final double psi = 0.0137 / (elevation / FastMath.PI + 0.11) - 0.022;
 
         // Subionospheric latitude: the latitude of the IPP (Ionospheric Pierce Point)
         // in [-0.416, 0.416], semicircle
         final double latIono = FastMath.min(
                                       FastMath.max(geo.getLatitude() * rad2semi + psi * sc.cos(), -0.416),
                                       0.416);
 
         // Subionospheric longitude: the longitude of the IPP
         // in semicircle
         final double lonIono = geo.getLongitude() * rad2semi + (psi * sc.sin() / FastMath.cos(latIono * semi2rad));
 
         // Geomagnetic latitude, semicircle
         final double latGeom = latIono + 0.064 * FastMath.cos((lonIono - 1.617) * semi2rad);
 
         // day of week and tow (sec)
         // Note: Sunday=0, Monday=1, Tuesday=2, Wednesday=3, Thursday=4, Friday=5, Saturday=6
         final DateTimeComponents dtc = date.getComponents(gps);
         final int dofweek = dtc.getDate().getDayOfWeek();
         final double secday = dtc.getTime().getSecondsInLocalDay();
         final double tow = dofweek * 86400. + secday;
 
         final double t = 43200. * lonIono + tow;
         final double tsec = t - FastMath.floor(t / 86400.) * 86400; // Seconds of day
 
         // Slant factor, semicircle
         final double slantFactor = 1.0 + 16.0 * FastMath.pow(0.53 - elevation / FastMath.PI, 3);
 
         // Period of model, seconds
         final double period = FastMath.max(72000., beta[0] + (beta[1]  + (beta[2] + beta[3] * latGeom) * latGeom) * latGeom);
 
         // Phase of the model, radians
         // (Max at 14.00 = 50400 sec local time)
         final double x = 2.0 * FastMath.PI * (tsec - 50400.0) / period;
 
         // Amplitude of the model, seconds
         final double amplitude = FastMath.max(0, alpha[0] + (alpha[1]  + (alpha[2] + alpha[3] * latGeom) * latGeom) * latGeom);
 
         // Ionospheric correction (L1)
         double ionoTimeDelayL1 = slantFactor * (5. * 1e-9);
         if (FastMath.abs(x) < 1.570) {
             ionoTimeDelayL1 += slantFactor * (amplitude * (1.0 - FastMath.pow(x, 2) / 2.0 + FastMath.pow(x, 4) / 24.0));
         }
 
         // Ionospheric delay for the L1 frequency, in meters, with slant correction.
         final double ratio = FastMath.pow(1575.42e6 / frequency, 2);
         return ratio * Constants.SPEED_OF_LIGHT * ionoTimeDelayL1;
     }
 
     /** {@inheritDoc} */
     @Override
     public double pathDelay(final SpacecraftState state, final TopocentricFrame baseFrame,
                             final double frequency, final double[] parameters) {
         return pathDelay(state, baseFrame, state.getDate(), frequency, parameters);
     }
 
     /** {@inheritDoc} */
     @Override
     public double pathDelay(final SpacecraftState state,
                             final TopocentricFrame baseFrame, final AbsoluteDate receptionDate,
                             final double frequency, final double[] parameters) {
 
         // we use transform from base frame to inert frame and invert it
         // because base frame could be peered with inertial frame (hence improving performances with caching)
         // but the reverse is almost never used
         final StaticTransform base2Inert = baseFrame.getStaticTransformTo(state.getFrame(), receptionDate);
         final Vector3D        position   = base2Inert.getInverse().transformPosition(state.getPosition());
 
         // Elevation in radians
         final double   elevation = position.getDelta();
 
         // Only consider measures above the horizon
         if (elevation > 0.0) {
             // Date
             final AbsoluteDate date = state.getDate();
             // Geodetic point
             final GeodeticPoint geo = baseFrame.getPoint();
             // Azimuth angle in radians
             double azimuth = FastMath.atan2(position.getX(), position.getY());
             if (azimuth < 0.) {
                 azimuth += MathUtils.TWO_PI;
             }
             // Delay
             return pathDelay(date, geo, elevation, azimuth, frequency, parameters);
         }
 
         return 0.0;
     }
 
     /**
      * Calculates the ionospheric path delay for the signal path from a ground
      * station to a satellite.
      * <p>
      * The path delay is computed for any elevation angle.
      * </p>
      * @param <T> type of the elements
      * @param date current date
      * @param geo geodetic point of receiver/station
      * @param elevation elevation of the satellite in radians
      * @param azimuth azimuth of the satellite in radians
      * @param frequency frequency of the signal in Hz
      * @param parameters ionospheric model parameters
      * @return the path delay due to the ionosphere in m
      */
     public <T extends CalculusFieldElement<T>> T pathDelay(final FieldAbsoluteDate<T> date, final FieldGeodeticPoint<T> geo,
                                                        final T elevation, final T azimuth, final double frequency,
                                                        final T[] parameters) {
 
         // Sine and cosine of the azimuth
         final FieldSinCos<T> sc = FastMath.sinCos(azimuth);
 
         // Field
         final Field<T> field = date.getField();
         final T zero = field.getZero();
         final T one  = field.getOne();
 
         // degrees to semicircles
         final T pi       = one.getPi();
         final T rad2semi = pi.reciprocal();
 
         // Earth Centered angle
         final T psi = elevation.divide(pi).add(0.11).divide(0.0137).reciprocal().subtract(0.022);
 
         // Subionospheric latitude: the latitude of the IPP (Ionospheric Pierce Point)
         // in [-0.416, 0.416], semicircle
         final T latIono = FastMath.min(
                                       FastMath.max(geo.getLatitude().multiply(rad2semi).add(psi.multiply(sc.cos())), zero.subtract(0.416)),
                                       zero.newInstance(0.416));
 
         // Subionospheric longitude: the longitude of the IPP
         // in semicircle
         final T lonIono = geo.getLongitude().multiply(rad2semi).add(psi.multiply(sc.sin()).divide(FastMath.cos(latIono.multiply(pi))));
 
         // Geomagnetic latitude, semicircle
         final T latGeom = latIono.add(FastMath.cos(lonIono.subtract(1.617).multiply(pi)).multiply(0.064));
 
         // day of week and tow (sec)
         // Note: Sunday=0, Monday=1, Tuesday=2, Wednesday=3, Thursday=4, Friday=5, Saturday=6
         final DateTimeComponents dtc = date.getComponents(gps);
         final int dofweek = dtc.getDate().getDayOfWeek();
         final double secday = dtc.getTime().getSecondsInLocalDay();
         final double tow = dofweek * 86400. + secday;
 
         final T t = lonIono.multiply(43200.).add(tow);
         final T tsec = t.subtract(FastMath.floor(t.divide(86400.)).multiply(86400.)); // Seconds of day
 
         // Slant factor, semicircle
         final T slantFactor = FastMath.pow(elevation.divide(pi).negate().add(0.53), 3).multiply(16.0).add(one);
 
         // Period of model, seconds
         final T period = FastMath.max(zero.newInstance(72000.), latGeom.multiply(latGeom.multiply(latGeom.multiply(beta[3]).add(beta[2])).add(beta[1])).add(beta[0]));
 
         // Phase of the model, radians
         // (Max at 14.00 = 50400 sec local time)
         final T x = tsec.subtract(50400.0).multiply(pi.multiply(2.0)).divide(period);
 
         // Amplitude of the model, seconds
         final T amplitude = FastMath.max(zero, latGeom.multiply(latGeom.multiply(latGeom.multiply(alpha[3]).add(alpha[2])).add(alpha[1])).add(alpha[0]));
 
         // Ionospheric correction (L1)
         T ionoTimeDelayL1 = slantFactor.multiply(5. * 1e-9);
         if (FastMath.abs(x.getReal()) < 1.570) {
             ionoTimeDelayL1 = ionoTimeDelayL1.add(slantFactor.multiply(amplitude.multiply(one.subtract(FastMath.pow(x, 2).multiply(0.5)).add(FastMath.pow(x, 4).divide(24.0)))));
         }
 
         // Ionospheric delay for the L1 frequency, in meters, with slant correction.
         final double ratio = FastMath.pow(1575.42e6 / frequency, 2);
         return ionoTimeDelayL1.multiply(Constants.SPEED_OF_LIGHT).multiply(ratio);
     }
 
     /** {@inheritDoc} */
     @Override
     public <T extends CalculusFieldElement<T>> T pathDelay(final FieldSpacecraftState<T> state, final TopocentricFrame baseFrame,
                                                        final double frequency, final T[] parameters) {
         return pathDelay(state, baseFrame, state.getDate(), frequency, parameters);
     }
 
     /** {@inheritDoc} */
     @Override
     public <T extends CalculusFieldElement<T>> T pathDelay(final FieldSpacecraftState<T> state,
                                                            final TopocentricFrame baseFrame, final FieldAbsoluteDate<T> receptionDate,
                                                            final double frequency, final T[] parameters) {
 
         // we use transform from base frame to inert frame and invert it
         // because base frame could be peered with inertial frame (hence improving performances with caching)
         // but the reverse is almost never used
         final FieldStaticTransform<T> base2Inert = baseFrame.getStaticTransformTo(state.getFrame(), receptionDate);
         final FieldVector3D<T>        position   = base2Inert.getInverse().transformPosition(state.getPosition());
 
         // Elevation in radians
         final T elevation = position.getDelta();
 
         if (elevation.getReal() > 0.0) {
             // Date
             final FieldAbsoluteDate<T> date = state.getDate();
             // Geodetic point
             final FieldGeodeticPoint<T> geo = baseFrame.getPoint(date.getField());
             // Azimuth angle in radians
             T azimuth = FastMath.atan2(position.getX(), position.getY());
             if (azimuth.getReal() < 0.) {
                 azimuth = azimuth.add(MathUtils.TWO_PI);
             }
             // Delay
             return pathDelay(date, geo, elevation, azimuth, frequency, parameters);
         }
 
         return elevation.getField().getZero();
     }
 
     @Override
     public List<ParameterDriver> getParametersDrivers() {
         return Collections.emptyList();
     }
 }