Chan1997.java
- /* Copyright 2002-2024 CS GROUP
- * Licensed to CS GROUP (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.ssa.collision.shorttermencounter.probability.twod;
- import org.hipparchus.CalculusFieldElement;
- import org.hipparchus.Field;
- import org.hipparchus.util.FastMath;
- import org.hipparchus.util.MathArrays;
- import org.orekit.ssa.metrics.FieldProbabilityOfCollision;
- import org.orekit.ssa.metrics.ProbabilityOfCollision;
- /**
- * Compute the probability of collision using the method described in : <br> "Chan, K. “Collision Probability Analyses for
- * Earth Orbiting Satellites.” In Space Cooperation into the 21st Century: 7th AAS/JRS/CSA Symposium, International Space
- * Conference of Pacific-Basin Societies (ISCOPS; formerly PISSTA) (July 15-18, 1997, Nagasaki, Japan), edited by Peter M.
- * Bainum, et al., 1033-1048. Advances in the Astronautical Sciences Series 96. San Diego, California: Univelt, 1997. (Zeroth
- * order analytical expression).
- * <p>
- * This method is also described in depth in : "CHAN, F. Kenneth, et al. Spacecraft collision probability. El Segundo, CA :
- * Aerospace Press, 2008."
- * <p>
- * It assumes :
- * <ul>
- * <li>Short encounter leading to a linear relative motion.</li>
- * <li>Spherical collision object.</li>
- * <li>Uncorrelated positional covariance.</li>
- * <li>Gaussian distribution of the position uncertainties.</li>
- * <li>Deterministic velocity i.e. no velocity uncertainties.</li>
- * <li>Approximate ellipse by a disk</li>
- * </ul>
- *
- * @author Vincent Cucchietti
- * @since 12.0
- */
- public class Chan1997 extends AbstractShortTermEncounter2DPOCMethod {
- /** Empty constructor. */
- public Chan1997() {
- super(ShortTermEncounter2DPOCMethodType.CHAN_1997.name());
- }
- /** {@inheritDoc} */
- public ProbabilityOfCollision compute(final double xm, final double ym,
- final double sigmaX, final double sigmaY,
- final double radius) {
- // Intermediary terms u and v
- final double u = radius * radius / (sigmaX * sigmaY);
- final double v = (xm * xm / (sigmaX * sigmaX)) + (ym * ym / (sigmaY * sigmaY));
- // Number of terms M recommended by Chan
- final int M;
- if (u <= 0.01 || v <= 1) {
- M = 3;
- } else if (u > 0.01 && u <= 1 || v > 1 && v <= 9) {
- M = 10;
- } else if (u > 1 && u <= 25 || v > 9 && v <= 25) {
- M = 20;
- } else {
- M = 60;
- }
- double t = 1.0;
- double s = 1.0;
- double sum = 1.0;
- // first iteration
- double value = FastMath.exp(-v * 0.5) * t - FastMath.exp(-(u + v) * 0.5) * t * sum;
- // iterative expression
- for (int i = 1; i < M; i++) {
- t = (v * 0.5) / i * t;
- s = (u * 0.5) / i * s;
- sum = sum + s;
- value = MathArrays.linearCombination(1, value, FastMath.exp(-v * 0.5), t) -
- FastMath.exp(-(u + v) * 0.5) * t * sum;
- }
- return new ProbabilityOfCollision(value, getName(), isAMaximumProbabilityOfCollisionMethod());
- }
- /** {@inheritDoc} */
- public <T extends CalculusFieldElement<T>> FieldProbabilityOfCollision<T> compute(final T xm, final T ym,
- final T sigmaX, final T sigmaY,
- final T radius) {
- // Intermediary terms u and v
- final T u = radius.pow(2).divide(sigmaX.multiply(sigmaY));
- final T v = xm.divide(sigmaX).pow(2).add(ym.divide(sigmaY).pow(2));
- // Number of terms M recommended by Chan
- final int M;
- if (u.getReal() <= 0.01 || v.getReal() <= 1) {
- M = 3;
- } else if (u.getReal() > 0.01 && u.getReal() <= 1 || v.getReal() > 1 && v.getReal() <= 9) {
- M = 10;
- } else if (u.getReal() > 1 && u.getReal() <= 25 || v.getReal() > 9 && v.getReal() <= 25) {
- M = 20;
- } else {
- M = 60;
- }
- final Field<T> field = radius.getField();
- T t = field.getOne();
- T s = field.getOne();
- T sum = field.getOne();
- // first iteration
- T value = v.multiply(-0.5).exp().multiply(t)
- .subtract(u.add(v).multiply(-0.5).exp().multiply(t).multiply(sum));
- // iterative expression
- for (int i = 1; i < M; i++) {
- t = v.multiply(0.5).divide(i).multiply(t);
- s = u.multiply(0.5).divide(i).multiply(s);
- sum = sum.add(s);
- value = value.add(v.multiply(-0.5).exp().multiply(t)
- .subtract(u.add(v).multiply(-0.5).exp().multiply(t).multiply(sum)));
- }
- return new FieldProbabilityOfCollision<>(value, getName(), isAMaximumProbabilityOfCollisionMethod());
- }
- /** {@inheritDoc} */
- @Override
- public ShortTermEncounter2DPOCMethodType getType() {
- return ShortTermEncounter2DPOCMethodType.CHAN_1997;
- }
- }