KlobucharIonoModel.java
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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.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 {
/** 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) {
// Elevation in radians
final Vector3D position = state.getPosition(baseFrame);
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.add(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.add(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) {
// Elevation and azimuth in radians
final FieldVector3D<T> position = state.getPosition(baseFrame);
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();
}
}