Chan1997.java
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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;
}
}