SaastamoinenModel.java
/* Copyright 2011-2012 Space Applications Services
* Licensed to CS Communication & Systèmes (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.
*/
package org.orekit.models.earth.troposphere;
import java.util.Collections;
import java.util.List;
import org.hipparchus.Field;
import org.hipparchus.RealFieldElement;
import org.hipparchus.analysis.interpolation.BilinearInterpolatingFunction;
import org.hipparchus.analysis.interpolation.LinearInterpolator;
import org.hipparchus.analysis.polynomials.PolynomialFunction;
import org.hipparchus.analysis.polynomials.PolynomialSplineFunction;
import org.hipparchus.util.FastMath;
import org.hipparchus.util.MathArrays;
import org.orekit.data.DataProvidersManager;
import org.orekit.errors.OrekitException;
import org.orekit.errors.OrekitMessages;
import org.orekit.time.AbsoluteDate;
import org.orekit.time.FieldAbsoluteDate;
import org.orekit.utils.InterpolationTableLoader;
import org.orekit.utils.ParameterDriver;
/** The modified Saastamoinen model. Estimates the path delay imposed to
* electro-magnetic signals by the troposphere according to the formula:
* <pre>
* δ = 2.277e-3 / cos z * (P + (1255 / T + 0.05) * e - B * tan²
* z) + δR
* </pre>
* with the following input data provided to the model:
* <ul>
* <li>z: zenith angle</li>
* <li>P: atmospheric pressure</li>
* <li>T: temperature</li>
* <li>e: partial pressure of water vapour</li>
* <li>B, δR: correction terms</li>
* </ul>
* <p>
* The model supports custom δR correction terms to be read from a
* configuration file (saastamoinen-correction.txt) via the
* {@link DataProvidersManager}.
* </p>
* @author Thomas Neidhart
* @see "Guochang Xu, GPS - Theory, Algorithms and Applications, Springer, 2007"
*/
public class SaastamoinenModel implements DiscreteTroposphericModel {
/** Default file name for δR correction term table. */
public static final String DELTA_R_FILE_NAME = "^saastamoinen-correction\\.txt$";
/** X values for the B function. */
private static final double[] X_VALUES_FOR_B = {
0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 4.0, 5.0
};
/** E values for the B function. */
private static final double[] Y_VALUES_FOR_B = {
1.156, 1.079, 1.006, 0.938, 0.874, 0.813, 0.757, 0.654, 0.563
};
/** Coefficients for the partial pressure of water vapor polynomial. */
private static final double[] E_COEFFICIENTS = {
-37.2465, 0.213166, -0.000256908
};
/** Interpolation function for the B correction term. */
private final PolynomialSplineFunction bFunction;
/** Polynomial function for the e term. */
private final PolynomialFunction eFunction;
/** Interpolation function for the delta R correction term. */
private final BilinearInterpolatingFunction deltaRFunction;
/** The temperature at the station [K]. */
private double t0;
/** The atmospheric pressure [mbar]. */
private double p0;
/** The humidity [percent]. */
private double r0;
/** Create a new Saastamoinen model for the troposphere using the given
* environmental conditions.
* @param t0 the temperature at the station [K]
* @param p0 the atmospheric pressure at the station [mbar]
* @param r0 the humidity at the station [fraction] (50% -> 0.5)
* @param deltaRFileName regular expression for filename containing δR
* correction term table (typically {@link #DELTA_R_FILE_NAME}), if null
* default values from the reference book are used
* @since 7.1
*/
public SaastamoinenModel(final double t0, final double p0, final double r0,
final String deltaRFileName) {
this(t0, p0, r0,
deltaRFileName == null ? defaultDeltaR() : loadDeltaR(deltaRFileName));
}
/** Create a new Saastamoinen model.
* @param t0 the temperature at the station [K]
* @param p0 the atmospheric pressure at the station [mbar]
* @param r0 the humidity at the station [fraction] (50% -> 0.5)
* @param deltaR δR correction term function
* @since 7.1
*/
private SaastamoinenModel(final double t0, final double p0, final double r0,
final BilinearInterpolatingFunction deltaR) {
this.t0 = t0;
this.p0 = p0;
this.r0 = r0;
this.bFunction = new LinearInterpolator().interpolate(X_VALUES_FOR_B, Y_VALUES_FOR_B);
this.eFunction = new PolynomialFunction(E_COEFFICIENTS);
this.deltaRFunction = deltaR;
}
/** Create a new Saastamoinen model using a standard atmosphere model.
*
* <ul>
* <li>temperature: 18 degree Celsius
* <li>pressure: 1013.25 mbar
* <li>humidity: 50%
* </ul>
*
* @return a Saastamoinen model with standard environmental values
*/
public static SaastamoinenModel getStandardModel() {
return new SaastamoinenModel(273.16 + 18, 1013.25, 0.5, (String) null);
}
/** {@inheritDoc}
* <p>
* The Saastamoinen model is not defined for altitudes below 0.0. for continuity
* reasons, we use the value for h = 0 when altitude is negative.
* </p>
*/
public double pathDelay(final double elevation, final double height,
final double[] parameters, final AbsoluteDate date) {
// there are no data in the model for negative altitudes
// we use the data for the lowest available altitude: 0.0
final double fixedHeight = FastMath.max(0.0, height);
// the corrected temperature using a temperature gradient of -6.5 K/km
final double T = t0 - 6.5e-3 * fixedHeight;
// the corrected pressure
final double P = p0 * FastMath.pow(1.0 - 2.26e-5 * fixedHeight, 5.225);
// the corrected humidity
final double R = r0 * FastMath.exp(-6.396e-4 * fixedHeight);
// interpolate the b correction term
final double B = bFunction.value(fixedHeight / 1e3);
// calculate e
final double e = R * FastMath.exp(eFunction.value(T));
// calculate the zenith angle from the elevation
final double z = FastMath.abs(0.5 * FastMath.PI - elevation);
// get correction factor
final double deltaR = getDeltaR(fixedHeight, z);
// calculate the path delay in m
final double tan = FastMath.tan(z);
final double delta = 2.277e-3 / FastMath.cos(z) *
(P + (1255d / T + 5e-2) * e - B * tan * tan) + deltaR;
return delta;
}
/** {@inheritDoc}
* <p>
* The Saastamoinen model is not defined for altitudes below 0.0. for continuity
* reasons, we use the value for h = 0 when altitude is negative.
* </p>
*/
public <T extends RealFieldElement<T>> T pathDelay(final T elevation, final T height,
final T[] parameters, final FieldAbsoluteDate<T> date) {
final Field<T> field = height.getField();
final T zero = field.getZero();
// there are no data in the model for negative altitudes
// we use the data for the lowest available altitude: 0.0
final T fixedHeight = FastMath.max(zero, height);
// the corrected temperature using a temperature gradient of -6.5 K/km
final T T = fixedHeight.multiply(6.5e-3).negate().add(t0);
// the corrected pressure
final T P = fixedHeight.multiply(2.26e-5).negate().add(1.0).pow(5.225).multiply(p0);
// the corrected humidity
final T R = FastMath.exp(fixedHeight.multiply(-6.396e-4)).multiply(r0);
// interpolate the b correction term
final T B = bFunction.value(fixedHeight.divide(1e3));
// calculate e
final T e = R.multiply(FastMath.exp(eFunction.value(T)));
// calculate the zenith angle from the elevation
final T z = FastMath.abs(elevation.negate().add(0.5 * FastMath.PI));
// get correction factor
final T deltaR = getDeltaR(fixedHeight, z, field);
// calculate the path delay in m
final T tan = FastMath.tan(z);
final T delta = FastMath.cos(z).divide(2.277e-3).reciprocal().
multiply(P.add(T.divide(1255d).reciprocal().add(5e-2).multiply(e)).subtract(B.multiply(tan).multiply(tan))).add(deltaR);
return delta;
}
/** Calculates the delta R correction term using linear interpolation.
* @param height the height of the station in m
* @param zenith the zenith angle of the satellite
* @return the delta R correction term in m
*/
private double getDeltaR(final double height, final double zenith) {
// limit the height to a range of [0, 5000] m
final double h = FastMath.min(FastMath.max(0, height), 5000);
// limit the zenith angle to 90 degree
// Note: the function is symmetric for negative zenith angles
final double z = FastMath.min(Math.abs(zenith), 0.5 * FastMath.PI);
return deltaRFunction.value(h, z);
}
/** Calculates the delta R correction term using linear interpolation.
* @param <T> type of the elements
* @param height the height of the station in m
* @param zenith the zenith angle of the satellite
* @param field field used by default
* @return the delta R correction term in m
*/
private <T extends RealFieldElement<T>> T getDeltaR(final T height, final T zenith,
final Field<T> field) {
final T zero = field.getZero();
// limit the height to a range of [0, 5000] m
final T h = FastMath.min(FastMath.max(zero, height), zero.add(5000));
// limit the zenith angle to 90 degree
// Note: the function is symmetric for negative zenith angles
final T z = FastMath.min(zenith.abs(), zero.add(0.5 * FastMath.PI));
return deltaRFunction.value(h, z);
}
/** Load δR function.
* @param deltaRFileName regular expression for filename containing δR
* correction term table
* @return δR function
*/
private static BilinearInterpolatingFunction loadDeltaR(final String deltaRFileName) {
// read the δR interpolation function from the config file
final InterpolationTableLoader loader = new InterpolationTableLoader();
DataProvidersManager.getInstance().feed(deltaRFileName, loader);
if (!loader.stillAcceptsData()) {
final double[] elevations = loader.getOrdinateGrid();
for (int i = 0; i < elevations.length; ++i) {
elevations[i] = FastMath.toRadians(elevations[i]);
}
return new BilinearInterpolatingFunction(loader.getAbscissaGrid(), elevations,
loader.getValuesSamples());
}
throw new OrekitException(OrekitMessages.UNABLE_TO_FIND_FILE,
deltaRFileName.replaceAll("^\\^", "").replaceAll("\\$$", ""));
}
/** Create the default δR function.
* @return δR function
*/
private static BilinearInterpolatingFunction defaultDeltaR() {
// the correction table in the referenced book only contains values for an angle of 60 - 80
// degree, thus for 0 degree, the correction term is assumed to be 0, for degrees > 80 it
// is assumed to be the same value as for 80.
// the height in m
final double xValForR[] = {
0, 500, 1000, 1500, 2000, 3000, 4000, 5000
};
// the zenith angle
final double yValForR[] = {
FastMath.toRadians( 0.00), FastMath.toRadians(60.00), FastMath.toRadians(66.00), FastMath.toRadians(70.00),
FastMath.toRadians(73.00), FastMath.toRadians(75.00), FastMath.toRadians(76.00), FastMath.toRadians(77.00),
FastMath.toRadians(78.00), FastMath.toRadians(78.50), FastMath.toRadians(79.00), FastMath.toRadians(79.50),
FastMath.toRadians(79.75), FastMath.toRadians(80.00), FastMath.toRadians(90.00)
};
final double[][] fval = new double[][] {
{
0.000, 0.003, 0.006, 0.012, 0.020, 0.031, 0.039, 0.050, 0.065, 0.075, 0.087, 0.102, 0.111, 0.121, 0.121
}, {
0.000, 0.003, 0.006, 0.011, 0.018, 0.028, 0.035, 0.045, 0.059, 0.068, 0.079, 0.093, 0.101, 0.110, 0.110
}, {
0.000, 0.002, 0.005, 0.010, 0.017, 0.025, 0.032, 0.041, 0.054, 0.062, 0.072, 0.085, 0.092, 0.100, 0.100
}, {
0.000, 0.002, 0.005, 0.009, 0.015, 0.023, 0.029, 0.037, 0.049, 0.056, 0.065, 0.077, 0.083, 0.091, 0.091
}, {
0.000, 0.002, 0.004, 0.008, 0.013, 0.021, 0.026, 0.033, 0.044, 0.051, 0.059, 0.070, 0.076, 0.083, 0.083
}, {
0.000, 0.002, 0.003, 0.006, 0.011, 0.017, 0.021, 0.027, 0.036, 0.042, 0.049, 0.058, 0.063, 0.068, 0.068
}, {
0.000, 0.001, 0.003, 0.005, 0.009, 0.014, 0.017, 0.022, 0.030, 0.034, 0.040, 0.047, 0.052, 0.056, 0.056
}, {
0.000, 0.001, 0.002, 0.004, 0.007, 0.011, 0.014, 0.018, 0.024, 0.028, 0.033, 0.039, 0.043, 0.047, 0.047
}
};
// the actual delta R is interpolated using a a bilinear interpolator
return new BilinearInterpolatingFunction(xValForR, yValForR, fval);
}
@Override
public double[] computeZenithDelay(final double height, final double[] parameters,
final AbsoluteDate date) {
return new double[] {
pathDelay(0.5 * FastMath.PI, height, parameters, date),
0.
};
}
@Override
public <T extends RealFieldElement<T>> T[] computeZenithDelay(final T height, final T[] parameters,
final FieldAbsoluteDate<T> date) {
final Field<T> field = height.getField();
final T zero = field.getZero();
final T[] delay = MathArrays.buildArray(field, 2);
delay[0] = pathDelay(zero.add(0.5 * FastMath.PI), height, parameters, date);
delay[1] = zero;
return delay;
}
@Override
public double[] mappingFactors(final double elevation, final double height,
final double[] parameters, final AbsoluteDate date) {
return new double[] {
1.0,
1.0
};
}
@Override
public <T extends RealFieldElement<T>> T[] mappingFactors(final T elevation, final T height,
final T[] parameters, final FieldAbsoluteDate<T> date) {
final Field<T> field = date.getField();
final T one = field.getOne();
final T[] factors = MathArrays.buildArray(field, 2);
factors[0] = one;
factors[1] = one;
return factors;
}
@Override
public List<ParameterDriver> getParametersDrivers() {
return Collections.emptyList();
}
}