BatchLSEstimator.java
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*
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* Unless required by applicable law or agreed to in writing, software
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package org.orekit.estimation.leastsquares;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.List;
import java.util.Map;
import org.hipparchus.exception.LocalizedCoreFormats;
import org.hipparchus.exception.MathIllegalArgumentException;
import org.hipparchus.exception.MathRuntimeException;
import org.hipparchus.linear.RealMatrix;
import org.hipparchus.linear.RealVector;
import org.hipparchus.optim.ConvergenceChecker;
import org.hipparchus.optim.nonlinear.vector.leastsquares.EvaluationRmsChecker;
import org.hipparchus.optim.nonlinear.vector.leastsquares.LeastSquaresBuilder;
import org.hipparchus.optim.nonlinear.vector.leastsquares.LeastSquaresOptimizer;
import org.hipparchus.optim.nonlinear.vector.leastsquares.LeastSquaresOptimizer.Optimum;
import org.hipparchus.optim.nonlinear.vector.leastsquares.LeastSquaresProblem;
import org.hipparchus.optim.nonlinear.vector.leastsquares.ParameterValidator;
import org.hipparchus.util.Incrementor;
import org.orekit.errors.OrekitException;
import org.orekit.estimation.measurements.EstimatedMeasurement;
import org.orekit.estimation.measurements.EstimationsProvider;
import org.orekit.estimation.measurements.ObservedMeasurement;
import org.orekit.orbits.Orbit;
import org.orekit.propagation.Propagator;
import org.orekit.propagation.conversion.AbstractPropagatorBuilder;
import org.orekit.propagation.conversion.OrbitDeterminationPropagatorBuilder;
import org.orekit.propagation.conversion.PropagatorBuilder;
import org.orekit.propagation.numerical.NumericalPropagator;
import org.orekit.propagation.semianalytical.dsst.DSSTPropagator;
import org.orekit.utils.ParameterDriver;
import org.orekit.utils.ParameterDriversList;
import org.orekit.utils.ParameterDriversList.DelegatingDriver;
/** Least squares estimator for orbit determination.
* <p>
* Since 10.0, the least squares estimator can be used with both
* {@link NumericalPropagator numerical} and {@link DSSTPropagator DSST}
* orbit propagators.
* </p>
* @author Luc Maisonobe
* @since 8.0
*/
public class BatchLSEstimator {
/** Builders for propagator. */
private final OrbitDeterminationPropagatorBuilder[] builders;
/** Measurements. */
private final List<ObservedMeasurement<?>> measurements;
/** Solver for least squares problem. */
private final LeastSquaresOptimizer optimizer;
/** Convergence checker. */
private ConvergenceChecker<LeastSquaresProblem.Evaluation> convergenceChecker;
/** Builder for the least squares problem. */
private final LeastSquaresBuilder lsBuilder;
/** Observer for iterations. */
private BatchLSObserver observer;
/** Last estimations. */
private Map<ObservedMeasurement<?>, EstimatedMeasurement<?>> estimations;
/** Last orbits. */
private Orbit[] orbits;
/** Optimum found. */
private Optimum optimum;
/** Counter for the evaluations. */
private Incrementor evaluationsCounter;
/** Counter for the iterations. */
private Incrementor iterationsCounter;
/** Simple constructor.
* <p>
* If multiple {@link PropagatorBuilder propagator builders} are set up,
* the orbits of several spacecrafts will be used simultaneously.
* This is useful if the propagators share some model or measurements
* parameters (typically pole motion, prime meridian correction or
* ground stations positions).
* </p>
* <p>
* Setting up multiple {@link PropagatorBuilder propagator builders} is
* also useful when inter-satellite measurements are used, even if only one
* of the orbit is estimated and the other ones are fixed. This is typically
* used when very high accuracy GNSS measurements are needed and the
* navigation bulletins are not considered accurate enough and the navigation
* constellation must be propagated numerically.
* </p>
* @param optimizer solver for least squares problem
* @param propagatorBuilder builders to use for propagation
*/
public BatchLSEstimator(final LeastSquaresOptimizer optimizer,
final OrbitDeterminationPropagatorBuilder... propagatorBuilder) {
this.builders = propagatorBuilder;
this.measurements = new ArrayList<ObservedMeasurement<?>>();
this.optimizer = optimizer;
this.lsBuilder = new LeastSquaresBuilder();
this.observer = null;
this.estimations = null;
this.orbits = new Orbit[builders.length];
setParametersConvergenceThreshold(Double.NaN);
// our model computes value and Jacobian in one call,
// so we don't use the lazy evaluation feature
lsBuilder.lazyEvaluation(false);
// we manage weight by ourselves, as we change them during
// iterations (setting to 0 the identified outliers measurements)
// so the least squares problem should not see our weights
lsBuilder.weight(null);
}
/** Set an observer for iterations.
* @param observer observer to be notified at the end of each iteration
*/
public void setObserver(final BatchLSObserver observer) {
this.observer = observer;
}
/** Add a measurement.
* @param measurement measurement to add
*/
public void addMeasurement(final ObservedMeasurement<?> measurement) {
measurements.add(measurement);
}
/** Set the maximum number of iterations.
* <p>
* The iterations correspond to the top level iterations of
* the {@link LeastSquaresOptimizer least squares optimizer}.
* </p>
* @param maxIterations maxIterations maximum number of iterations
* @see #setMaxEvaluations(int)
* @see #getIterationsCount()
*/
public void setMaxIterations(final int maxIterations) {
lsBuilder.maxIterations(maxIterations);
}
/** Set the maximum number of model evaluations.
* <p>
* The evaluations correspond to the orbit propagations and
* measurements estimations performed with a set of estimated
* parameters.
* </p>
* <p>
* For {@link org.hipparchus.optim.nonlinear.vector.leastsquares.GaussNewtonOptimizer
* Gauss-Newton optimizer} there is one evaluation at each iteration,
* so the maximum numbers may be set to the same value. For {@link
* org.hipparchus.optim.nonlinear.vector.leastsquares.LevenbergMarquardtOptimizer
* Levenberg-Marquardt optimizer}, there can be several evaluations at
* some iterations (typically for the first couple of iterations), so the
* maximum number of evaluations may be set to a higher value than the
* maximum number of iterations.
* </p>
* @param maxEvaluations maximum number of model evaluations
* @see #setMaxIterations(int)
* @see #getEvaluationsCount()
*/
public void setMaxEvaluations(final int maxEvaluations) {
lsBuilder.maxEvaluations(maxEvaluations);
}
/** Get the orbital parameters supported by this estimator.
* <p>
* If there are more than one propagator builder, then the names
* of the drivers have an index marker in square brackets appended
* to them in order to distinguish the various orbits. So for example
* with one builder generating Keplerian orbits the names would be
* simply "a", "e", "i"... but if there are several builders the
* names would be "a[0]", "e[0]", "i[0]"..."a[1]", "e[1]", "i[1]"...
* </p>
* @param estimatedOnly if true, only estimated parameters are returned
* @return orbital parameters supported by this estimator
*/
public ParameterDriversList getOrbitalParametersDrivers(final boolean estimatedOnly) {
final ParameterDriversList estimated = new ParameterDriversList();
for (int i = 0; i < builders.length; ++i) {
final String suffix = builders.length > 1 ? "[" + i + "]" : null;
for (final DelegatingDriver delegating : builders[i].getOrbitalParametersDrivers().getDrivers()) {
if (delegating.isSelected() || !estimatedOnly) {
for (final ParameterDriver driver : delegating.getRawDrivers()) {
if (suffix != null && !driver.getName().endsWith(suffix)) {
// we add suffix only conditionally because the method may already have been called
// and suffixes may have already been appended
driver.setName(driver.getName() + suffix);
}
estimated.add(driver);
}
}
}
}
return estimated;
}
/** Get the propagator parameters supported by this estimator.
* @param estimatedOnly if true, only estimated parameters are returned
* @return propagator parameters supported by this estimator
*/
public ParameterDriversList getPropagatorParametersDrivers(final boolean estimatedOnly) {
final ParameterDriversList estimated = new ParameterDriversList();
for (PropagatorBuilder builder : builders) {
for (final DelegatingDriver delegating : builder.getPropagationParametersDrivers().getDrivers()) {
if (delegating.isSelected() || !estimatedOnly) {
for (final ParameterDriver driver : delegating.getRawDrivers()) {
estimated.add(driver);
}
}
}
}
return estimated;
}
/** Get the measurements parameters supported by this estimator (including measurements and modifiers).
* @param estimatedOnly if true, only estimated parameters are returned
* @return measurements parameters supported by this estimator
*/
public ParameterDriversList getMeasurementsParametersDrivers(final boolean estimatedOnly) {
final ParameterDriversList parameters = new ParameterDriversList();
for (final ObservedMeasurement<?> measurement : measurements) {
for (final ParameterDriver driver : measurement.getParametersDrivers()) {
if (!estimatedOnly || driver.isSelected()) {
parameters.add(driver);
}
}
}
parameters.sort();
return parameters;
}
/**
* Set convergence threshold.
* <p>
* The convergence used for estimation is based on the estimated
* parameters {@link ParameterDriver#getNormalizedValue() normalized values}.
* Convergence is considered to have been reached when the difference
* between previous and current normalized value is less than the
* convergence threshold for all parameters. The same value is used
* for all parameters since they are normalized and hence dimensionless.
* </p>
* <p>
* Normalized values are computed as {@code (current - reference)/scale},
* so convergence is reached when the following condition holds for
* all estimated parameters:
* {@code |current[i] - previous[i]| <= threshold * scale[i]}
* </p>
* <p>
* So the convergence threshold specified here can be considered as
* a multiplication factor applied to scale. Since for all parameters
* the scale is often small (typically about 1 m for orbital positions
* for example), then the threshold should not be too small. A value
* of 10⁻³ is often quite accurate.
* </p>
* <p>
* Calling this method overrides any checker that could have been set
* beforehand by calling {@link #setConvergenceChecker(ConvergenceChecker)}.
* Both methods are mutually exclusive.
* </p>
*
* @param parametersConvergenceThreshold convergence threshold on
* normalized parameters (dimensionless, related to parameters scales)
* @see #setConvergenceChecker(ConvergenceChecker)
* @see EvaluationRmsChecker
*/
public void setParametersConvergenceThreshold(final double parametersConvergenceThreshold) {
setConvergenceChecker((iteration, previous, current) ->
current.getPoint().getLInfDistance(previous.getPoint()) <= parametersConvergenceThreshold);
}
/** Set a custom convergence checker.
* <p>
* Calling this method overrides any checker that could have been set
* beforehand by calling {@link #setParametersConvergenceThreshold(double)}.
* Both methods are mutually exclusive.
* </p>
* @param convergenceChecker convergence checker to set
* @see #setParametersConvergenceThreshold(double)
* @since 10.1
*/
public void setConvergenceChecker(final ConvergenceChecker<LeastSquaresProblem.Evaluation> convergenceChecker) {
this.convergenceChecker = convergenceChecker;
}
/** Estimate the orbital, propagation and measurements parameters.
* <p>
* The initial guess for all parameters must have been set before calling this method
* using {@link #getOrbitalParametersDrivers(boolean)}, {@link #getPropagatorParametersDrivers(boolean)},
* and {@link #getMeasurementsParametersDrivers(boolean)} and then {@link ParameterDriver#setValue(double)
* setting the values} of the parameters.
* </p>
* <p>
* For parameters whose reference date has not been set to a non-null date beforehand (i.e.
* the parameters for which {@link ParameterDriver#getReferenceDate()} returns {@code null},
* a default reference date will be set automatically at the start of the estimation to the
* {@link AbstractPropagatorBuilder#getInitialOrbitDate() initial orbit date} of the first
* propagator builder. For parameters whose reference date has been set to a non-null date,
* this reference date is untouched.
* </p>
* <p>
* After this method returns, the estimated parameters can be retrieved using
* {@link #getOrbitalParametersDrivers(boolean)}, {@link #getPropagatorParametersDrivers(boolean)},
* and {@link #getMeasurementsParametersDrivers(boolean)} and then {@link ParameterDriver#getValue()
* getting the values} of the parameters.
* </p>
* <p>
* As a convenience, the method also returns a fully configured and ready to use
* propagator set up with all the estimated values.
* </p>
* <p>
* For even more in-depth information, the {@link #getOptimum()} method provides detailed
* elements (covariance matrix, estimated parameters standard deviation, weighted Jacobian, RMS,
* χ², residuals and more).
* </p>
* @return propagators configured with estimated orbits as initial states, and all
* propagators estimated parameters also set
*/
public Propagator[] estimate() {
// set reference date for all parameters that lack one (including the not estimated parameters)
for (final ParameterDriver driver : getOrbitalParametersDrivers(false).getDrivers()) {
if (driver.getReferenceDate() == null) {
driver.setReferenceDate(builders[0].getInitialOrbitDate());
}
}
for (final ParameterDriver driver : getPropagatorParametersDrivers(false).getDrivers()) {
if (driver.getReferenceDate() == null) {
driver.setReferenceDate(builders[0].getInitialOrbitDate());
}
}
for (final ParameterDriver driver : getMeasurementsParametersDrivers(false).getDrivers()) {
if (driver.getReferenceDate() == null) {
driver.setReferenceDate(builders[0].getInitialOrbitDate());
}
}
// get all estimated parameters
final ParameterDriversList estimatedOrbitalParameters = getOrbitalParametersDrivers(true);
final ParameterDriversList estimatedPropagatorParameters = getPropagatorParametersDrivers(true);
final ParameterDriversList estimatedMeasurementsParameters = getMeasurementsParametersDrivers(true);
// create start point
final double[] start = new double[estimatedOrbitalParameters.getNbParams() +
estimatedPropagatorParameters.getNbParams() +
estimatedMeasurementsParameters.getNbParams()];
int iStart = 0;
for (final ParameterDriver driver : estimatedOrbitalParameters.getDrivers()) {
start[iStart++] = driver.getNormalizedValue();
}
for (final ParameterDriver driver : estimatedPropagatorParameters.getDrivers()) {
start[iStart++] = driver.getNormalizedValue();
}
for (final ParameterDriver driver : estimatedMeasurementsParameters.getDrivers()) {
start[iStart++] = driver.getNormalizedValue();
}
lsBuilder.start(start);
// create target (which is an array set to 0, as we compute weighted residuals ourselves)
int p = 0;
for (final ObservedMeasurement<?> measurement : measurements) {
if (measurement.isEnabled()) {
p += measurement.getDimension();
}
}
final double[] target = new double[p];
lsBuilder.target(target);
// set up the model
final ModelObserver modelObserver = new ModelObserver() {
/** {@inheritDoc} */
@Override
public void modelCalled(final Orbit[] newOrbits,
final Map<ObservedMeasurement<?>, EstimatedMeasurement<?>> newEstimations) {
BatchLSEstimator.this.orbits = newOrbits;
BatchLSEstimator.this.estimations = newEstimations;
}
};
final AbstractBatchLSModel model = builders[0].buildLSModel(builders, measurements, estimatedMeasurementsParameters, modelObserver);
lsBuilder.model(model);
// add a validator for orbital parameters
lsBuilder.parameterValidator(new Validator(estimatedOrbitalParameters,
estimatedPropagatorParameters,
estimatedMeasurementsParameters));
lsBuilder.checker(convergenceChecker);
// set up the problem to solve
final LeastSquaresProblem problem = new TappedLSProblem(lsBuilder.build(),
model,
estimatedOrbitalParameters,
estimatedPropagatorParameters,
estimatedMeasurementsParameters);
try {
// solve the problem
optimum = optimizer.optimize(problem);
// create a new configured propagator with all estimated parameters
return model.createPropagators(optimum.getPoint());
} catch (MathRuntimeException mrte) {
throw new OrekitException(mrte);
}
}
/** Get the last estimations performed.
* @return last estimations performed
*/
public Map<ObservedMeasurement<?>, EstimatedMeasurement<?>> getLastEstimations() {
return Collections.unmodifiableMap(estimations);
}
/** Get the optimum found.
* <p>
* The {@link Optimum} object contains detailed elements (covariance matrix, estimated
* parameters standard deviation, weighted Jacobian, RMS, χ², residuals and more).
* </p>
* <p>
* Beware that the returned object is the raw view from the underlying mathematical
* library. At this raw level, parameters have {@link ParameterDriver#getNormalizedValue()
* normalized values} whereas the space flight parameters have {@link ParameterDriver#getValue()
* physical values} with their units. So there are {@link ParameterDriver#getScale() scaling
* factors} to apply when using these elements.
* </p>
* @return optimum found after last call to {@link #estimate()}
*/
public Optimum getOptimum() {
return optimum;
}
/** Get the covariances matrix in space flight dynamics physical units.
* <p>
* This method retrieve the {@link
* org.hipparchus.optim.nonlinear.vector.leastsquares.LeastSquaresProblem.Evaluation#getCovariances(double)
* covariances} from the [@link {@link #getOptimum() optimum} and applies the scaling factors
* to it in order to convert it from raw normalized values back to physical values.
* </p>
* @param threshold threshold to identify matrix singularity
* @return covariances matrix in space flight dynamics physical units
* @since 9.1
*/
public RealMatrix getPhysicalCovariances(final double threshold) {
final RealMatrix covariances;
try {
// get the normalized matrix
covariances = optimum.getCovariances(threshold).copy();
} catch (MathIllegalArgumentException miae) {
// the problem is singular
throw new OrekitException(miae);
}
// retrieve the scaling factors
final double[] scale = new double[covariances.getRowDimension()];
int index = 0;
for (final ParameterDriver driver : getOrbitalParametersDrivers(true).getDrivers()) {
scale[index++] = driver.getScale();
}
for (final ParameterDriver driver : getPropagatorParametersDrivers(true).getDrivers()) {
scale[index++] = driver.getScale();
}
for (final ParameterDriver driver : getMeasurementsParametersDrivers(true).getDrivers()) {
scale[index++] = driver.getScale();
}
// unnormalize the matrix, to retrieve physical covariances
for (int i = 0; i < covariances.getRowDimension(); ++i) {
for (int j = 0; j < covariances.getColumnDimension(); ++j) {
covariances.setEntry(i, j, scale[i] * scale[j] * covariances.getEntry(i, j));
}
}
return covariances;
}
/** Get the number of iterations used for last estimation.
* @return number of iterations used for last estimation
* @see #setMaxIterations(int)
*/
public int getIterationsCount() {
return iterationsCounter.getCount();
}
/** Get the number of evaluations used for last estimation.
* @return number of evaluations used for last estimation
* @see #setMaxEvaluations(int)
*/
public int getEvaluationsCount() {
return evaluationsCounter.getCount();
}
/** Wrapper used to tap the various counters. */
private class TappedLSProblem implements LeastSquaresProblem {
/** Underlying problem. */
private final LeastSquaresProblem problem;
/** Multivariate function model. */
private final AbstractBatchLSModel model;
/** Estimated orbital parameters. */
private final ParameterDriversList estimatedOrbitalParameters;
/** Estimated propagator parameters. */
private final ParameterDriversList estimatedPropagatorParameters;
/** Estimated measurements parameters. */
private final ParameterDriversList estimatedMeasurementsParameters;
/** Simple constructor.
* @param problem underlying problem
* @param model multivariate function model
* @param estimatedOrbitalParameters estimated orbital parameters
* @param estimatedPropagatorParameters estimated propagator parameters
* @param estimatedMeasurementsParameters estimated measurements parameters
*/
TappedLSProblem(final LeastSquaresProblem problem,
final AbstractBatchLSModel model,
final ParameterDriversList estimatedOrbitalParameters,
final ParameterDriversList estimatedPropagatorParameters,
final ParameterDriversList estimatedMeasurementsParameters) {
this.problem = problem;
this.model = model;
this.estimatedOrbitalParameters = estimatedOrbitalParameters;
this.estimatedPropagatorParameters = estimatedPropagatorParameters;
this.estimatedMeasurementsParameters = estimatedMeasurementsParameters;
}
/** {@inheritDoc} */
@Override
public Incrementor getEvaluationCounter() {
// tap the evaluations counter
BatchLSEstimator.this.evaluationsCounter = problem.getEvaluationCounter();
model.setEvaluationsCounter(BatchLSEstimator.this.evaluationsCounter);
return BatchLSEstimator.this.evaluationsCounter;
}
/** {@inheritDoc} */
@Override
public Incrementor getIterationCounter() {
// tap the iterations counter
BatchLSEstimator.this.iterationsCounter = problem.getIterationCounter();
model.setIterationsCounter(BatchLSEstimator.this.iterationsCounter);
return BatchLSEstimator.this.iterationsCounter;
}
/** {@inheritDoc} */
@Override
public ConvergenceChecker<Evaluation> getConvergenceChecker() {
return problem.getConvergenceChecker();
}
/** {@inheritDoc} */
@Override
public RealVector getStart() {
return problem.getStart();
}
/** {@inheritDoc} */
@Override
public int getObservationSize() {
return problem.getObservationSize();
}
/** {@inheritDoc} */
@Override
public int getParameterSize() {
return problem.getParameterSize();
}
/** {@inheritDoc} */
@Override
public Evaluation evaluate(final RealVector point) {
// perform the evaluation
final Evaluation evaluation = problem.evaluate(point);
// notify the observer
if (observer != null) {
observer.evaluationPerformed(iterationsCounter.getCount(),
evaluationsCounter.getCount(),
orbits,
estimatedOrbitalParameters,
estimatedPropagatorParameters,
estimatedMeasurementsParameters,
new Provider(),
evaluation);
}
return evaluation;
}
}
/** Provider for evaluations. */
private class Provider implements EstimationsProvider {
/** Sorted estimations. */
private EstimatedMeasurement<?>[] sortedEstimations;
/** {@inheritDoc} */
@Override
public int getNumber() {
return estimations.size();
}
/** {@inheritDoc} */
@Override
public EstimatedMeasurement<?> getEstimatedMeasurement(final int index) {
// safety checks
if (index < 0 || index >= estimations.size()) {
throw new OrekitException(LocalizedCoreFormats.OUT_OF_RANGE_SIMPLE,
index, 0, estimations.size());
}
if (sortedEstimations == null) {
// lazy evaluation of the sorted array
sortedEstimations = new EstimatedMeasurement<?>[estimations.size()];
int i = 0;
for (final Map.Entry<ObservedMeasurement<?>, EstimatedMeasurement<?>> entry : estimations.entrySet()) {
sortedEstimations[i++] = entry.getValue();
}
// sort the array, primarily chronologically
Arrays.sort(sortedEstimations, 0, sortedEstimations.length, Comparator.naturalOrder());
}
return sortedEstimations[index];
}
}
/** Validator for estimated parameters. */
private static class Validator implements ParameterValidator {
/** Estimated orbital parameters. */
private final ParameterDriversList estimatedOrbitalParameters;
/** Estimated propagator parameters. */
private final ParameterDriversList estimatedPropagatorParameters;
/** Estimated measurements parameters. */
private final ParameterDriversList estimatedMeasurementsParameters;
/** Simple constructor.
* @param estimatedOrbitalParameters estimated orbital parameters
* @param estimatedPropagatorParameters estimated propagator parameters
* @param estimatedMeasurementsParameters estimated measurements parameters
*/
Validator(final ParameterDriversList estimatedOrbitalParameters,
final ParameterDriversList estimatedPropagatorParameters,
final ParameterDriversList estimatedMeasurementsParameters) {
this.estimatedOrbitalParameters = estimatedOrbitalParameters;
this.estimatedPropagatorParameters = estimatedPropagatorParameters;
this.estimatedMeasurementsParameters = estimatedMeasurementsParameters;
}
/** {@inheritDoc} */
@Override
public RealVector validate(final RealVector params) {
int i = 0;
for (final ParameterDriver driver : estimatedOrbitalParameters.getDrivers()) {
// let the parameter handle min/max clipping
driver.setNormalizedValue(params.getEntry(i));
params.setEntry(i++, driver.getNormalizedValue());
}
for (final ParameterDriver driver : estimatedPropagatorParameters.getDrivers()) {
// let the parameter handle min/max clipping
driver.setNormalizedValue(params.getEntry(i));
params.setEntry(i++, driver.getNormalizedValue());
}
for (final ParameterDriver driver : estimatedMeasurementsParameters.getDrivers()) {
// let the parameter handle min/max clipping
driver.setNormalizedValue(params.getEntry(i));
params.setEntry(i++, driver.getNormalizedValue());
}
return params;
}
}
}