SecularAndHarmonic.java
/* Copyright 2002-2013 CS Systèmes d'Information
* Licensed to CS Systèmes d'Information (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.utils;
import org.apache.commons.math3.analysis.ParametricUnivariateFunction;
import org.apache.commons.math3.fitting.CurveFitter;
import org.apache.commons.math3.fitting.PolynomialFitter;
import org.apache.commons.math3.optim.nonlinear.vector.jacobian.LevenbergMarquardtOptimizer;
import org.apache.commons.math3.util.FastMath;
import org.orekit.time.AbsoluteDate;
/** Class for fitting evolution of osculating orbital parameters.
* <p>
* This class allows conversion from osculating parameters to mean parameters.
* </p>
*
* @author Luc Maisonobe
*/
public class SecularAndHarmonic {
/** Degree of polynomial secular part. */
private final int secularDegree;
/** Pulsations of harmonic part. */
private final double[] pulsations;
/** Curve fitting engine. */
private CurveFitter<LocalParametricFunction> fitter;
/** Reference date for the model. */
private AbsoluteDate reference;
/** Fitted parameters. */
private double[] fitted;
/** Simple constructor.
* @param secularDegree degree of polynomial secular part
* @param pulsations pulsations of harmonic part
*/
public SecularAndHarmonic(final int secularDegree, final double ... pulsations) {
this.secularDegree = secularDegree;
this.pulsations = pulsations.clone();
}
/** Reset fitting.
* @param date reference date
* @param initialGuess initial guess for the parameters
* @see #getReferenceDate()
*/
public void resetFitting(final AbsoluteDate date, final double ... initialGuess) {
fitter = new CurveFitter<LocalParametricFunction>(new LevenbergMarquardtOptimizer());
reference = date;
fitted = initialGuess.clone();
}
/** Add a fitting point.
* @param date date of the point
* @param osculatingValue osculating value
*/
public void addPoint(final AbsoluteDate date, final double osculatingValue) {
fitter.addObservedPoint(date.durationFrom(reference), osculatingValue);
}
/** Get the reference date.
* @return reference date
* @see #resetFitting(AbsoluteDate, double...)
*/
public AbsoluteDate getReferenceDate() {
return reference;
}
/** Get an upper bound of the fitted harmonic amplitude.
* @return upper bound of the fitted harmonic amplitude
*/
public double getHarmonicAmplitude() {
double amplitude = 0;
for (int i = 0; i < pulsations.length; ++i) {
amplitude += FastMath.hypot(fitted[secularDegree + 2 * i + 1],
fitted[secularDegree + 2 * i + 2]);
}
return amplitude;
}
/** Fit parameters.
* @see #getFittedParameters()
*/
public void fit() {
fitted = fitter.fit(new LocalParametricFunction(), fitted);
}
/** Local parametric function used for fitting. */
private class LocalParametricFunction implements ParametricUnivariateFunction {
/** {@inheritDoc} */
public double value(final double x, final double... parameters) {
return truncatedValue(secularDegree, pulsations.length, x, parameters);
}
/** {@inheritDoc} */
public double[] gradient(final double x, final double... parameters) {
final double[] gradient = new double[secularDegree + 1 + 2 * pulsations.length];
// secular part
double xN = 1.0;
for (int i = 0; i <= secularDegree; ++i) {
gradient[i] = xN;
xN *= x;
}
// harmonic part
for (int i = 0; i < pulsations.length; ++i) {
gradient[secularDegree + 2 * i + 1] = FastMath.cos(pulsations[i] * x);
gradient[secularDegree + 2 * i + 2] = FastMath.sin(pulsations[i] * x);
}
return gradient;
}
}
/** Get a copy of the last fitted parameters.
* @return copy of the last fitted parameters.
* @see #fit()
*/
public double[] getFittedParameters() {
return fitted.clone();
}
/** Get fitted osculating value.
* @param date current date
* @return osculating value at current date
*/
public double osculatingValue(final AbsoluteDate date) {
return truncatedValue(secularDegree, pulsations.length,
date.durationFrom(reference), fitted);
}
/** Get fitted osculating derivative.
* @param date current date
* @return osculating derivative at current date
*/
public double osculatingDerivative(final AbsoluteDate date) {
return truncatedDerivative(secularDegree, pulsations.length,
date.durationFrom(reference), fitted);
}
/** Get fitted osculating second derivative.
* @param date current date
* @return osculating second derivative at current date
*/
public double osculatingSecondDerivative(final AbsoluteDate date) {
return truncatedSecondDerivative(secularDegree, pulsations.length,
date.durationFrom(reference), fitted);
}
/** Get mean value, truncated to first components.
* @param date current date
* @param degree degree of polynomial secular part to consider
* @param harmonics number of harmonics terms to consider
* @return mean value at current date
*/
public double meanValue(final AbsoluteDate date, final int degree, final int harmonics) {
return truncatedValue(degree, harmonics, date.durationFrom(reference), fitted);
}
/** Get mean derivative, truncated to first components.
* @param date current date
* @param degree degree of polynomial secular part to consider
* @param harmonics number of harmonics terms to consider
* @return mean derivative at current date
*/
public double meanDerivative(final AbsoluteDate date, final int degree, final int harmonics) {
return truncatedDerivative(degree, harmonics, date.durationFrom(reference), fitted);
}
/** Approximate an already fitted model to polynomial only terms.
* <p>
* This method is mainly used in order to combine the large amplitude long
* periods with the secular part as a new approximate polynomial model over
* some time range. This should be used rather than simply extracting the
* polynomial coefficients from {@link #getFittedParameters()} when some
* periodic terms amplitudes are large (for example Sun resonance effects
* on local solar time in sun synchronous orbits). In theses cases, the pure
* polynomial secular part in the coefficients may be far from the mean model.
* </p>
* @param combinedDegree desired degree for the combined polynomial
* @param combinedReference desired reference date for the combined polynomial
* @param meanDegree degree of polynomial secular part to consider
* @param meanHarmonics number of harmonics terms to consider
* @param start start date of the approximation time range
* @param end end date of the approximation time range
* @param step sampling step
* @return coefficients of the approximate polynomial (in increasing degree order),
* using the user provided reference date
*/
public double[] approximateAsPolynomialOnly(final int combinedDegree, final AbsoluteDate combinedReference,
final int meanDegree, final int meanHarmonics,
final AbsoluteDate start, final AbsoluteDate end,
final double step) {
final PolynomialFitter pf = new PolynomialFitter(new LevenbergMarquardtOptimizer());
for (AbsoluteDate date = start; date.compareTo(end) < 0; date = date.shiftedBy(step)) {
pf.addObservedPoint(date.durationFrom(combinedReference),
meanValue(date, meanDegree, meanHarmonics));
}
return pf.fit(new double[combinedDegree + 1]);
}
/** Get mean second derivative, truncated to first components.
* @param date current date
* @param degree degree of polynomial secular part
* @param harmonics number of harmonics terms to consider
* @return mean second derivative at current date
*/
public double meanSecondDerivative(final AbsoluteDate date, final int degree, final int harmonics) {
return truncatedSecondDerivative(degree, harmonics, date.durationFrom(reference), fitted);
}
/** Get value truncated to first components.
* @param degree degree of polynomial secular part
* @param harmonics number of harmonics terms to consider
* @param time time parameter
* @param parameters models parameters (must include all parameters,
* including the ones ignored due to model truncation)
* @return truncated value
*/
private double truncatedValue(final int degree, final int harmonics,
final double time, final double ... parameters) {
double value = 0;
// secular part
double tN = 1.0;
for (int i = 0; i <= degree; ++i) {
value += parameters[i] * tN;
tN *= time;
}
// harmonic part
for (int i = 0; i < harmonics; ++i) {
value += parameters[secularDegree + 2 * i + 1] * FastMath.cos(pulsations[i] * time) +
parameters[secularDegree + 2 * i + 2] * FastMath.sin(pulsations[i] * time);
}
return value;
}
/** Get derivative truncated to first components.
* @param degree degree of polynomial secular part
* @param harmonics number of harmonics terms to consider
* @param time time parameter
* @param parameters models parameters (must include all parameters,
* including the ones ignored due to model truncation)
* @return truncated derivative
*/
private double truncatedDerivative(final int degree, final int harmonics,
final double time, final double ... parameters) {
double derivative = 0;
// secular part
double tN = 1.0;
for (int i = 1; i <= degree; ++i) {
derivative += i * parameters[i] * tN;
tN *= time;
}
// harmonic part
for (int i = 0; i < harmonics; ++i) {
derivative += pulsations[i] * (-parameters[secularDegree + 2 * i + 1] * FastMath.sin(pulsations[i] * time) +
parameters[secularDegree + 2 * i + 2] * FastMath.cos(pulsations[i] * time));
}
return derivative;
}
/** Get second derivative truncated to first components.
* @param degree degree of polynomial secular part
* @param harmonics number of harmonics terms to consider
* @param time time parameter
* @param parameters models parameters (must include all parameters,
* including the ones ignored due to model truncation)
* @return truncated second derivative
*/
private double truncatedSecondDerivative(final int degree, final int harmonics,
final double time, final double ... parameters) {
double d2 = 0;
// secular part
double tN = 1.0;
for (int i = 2; i <= degree; ++i) {
d2 += (i - 1) * i * parameters[i] * tN;
tN *= time;
}
// harmonic part
for (int i = 0; i < harmonics; ++i) {
d2 += -pulsations[i] * pulsations[i] *
(parameters[secularDegree + 2 * i + 1] * FastMath.cos(pulsations[i] * time) +
parameters[secularDegree + 2 * i + 2] * FastMath.sin(pulsations[i] * time));
}
return d2;
}
}