SemiAnalyticalUnscentedKalmanModel.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.estimation.sequential;
import org.hipparchus.filtering.kalman.ProcessEstimate;
import org.hipparchus.filtering.kalman.unscented.UnscentedEvolution;
import org.hipparchus.filtering.kalman.unscented.UnscentedKalmanFilter;
import org.hipparchus.filtering.kalman.unscented.UnscentedProcess;
import org.hipparchus.linear.ArrayRealVector;
import org.hipparchus.linear.MatrixUtils;
import org.hipparchus.linear.RealMatrix;
import org.hipparchus.linear.RealVector;
import org.hipparchus.util.FastMath;
import org.orekit.estimation.measurements.EstimatedMeasurement;
import org.orekit.estimation.measurements.ObservedMeasurement;
import org.orekit.orbits.Orbit;
import org.orekit.orbits.OrbitType;
import org.orekit.orbits.PositionAngleType;
import org.orekit.propagation.PropagationType;
import org.orekit.propagation.SpacecraftState;
import org.orekit.propagation.conversion.DSSTPropagatorBuilder;
import org.orekit.propagation.semianalytical.dsst.DSSTPropagator;
import org.orekit.propagation.semianalytical.dsst.forces.DSSTForceModel;
import org.orekit.propagation.semianalytical.dsst.forces.ShortPeriodTerms;
import org.orekit.propagation.semianalytical.dsst.utilities.AuxiliaryElements;
import org.orekit.time.AbsoluteDate;
import org.orekit.time.ChronologicalComparator;
import org.orekit.utils.ParameterDriver;
import org.orekit.utils.ParameterDriversList;
import org.orekit.utils.ParameterDriversList.DelegatingDriver;
import java.util.ArrayList;
import java.util.Comparator;
import java.util.List;
/** Class defining the process model dynamics to use with a {@link SemiAnalyticalUnscentedKalmanEstimator}.
* @author Gaëtan Pierre
* @author Bryan Cazabonne
* @since 11.3
*/
public class SemiAnalyticalUnscentedKalmanModel implements KalmanEstimation, UnscentedProcess<MeasurementDecorator>, SemiAnalyticalProcess {
/** Initial builder for propagator. */
private final DSSTPropagatorBuilder builder;
/** Estimated orbital parameters. */
private final ParameterDriversList estimatedOrbitalParameters;
/** Estimated propagation parameters. */
private final ParameterDriversList estimatedPropagationParameters;
/** Estimated measurements parameters. */
private final ParameterDriversList estimatedMeasurementsParameters;
/** Provider for covariance matrice. */
private final CovarianceMatrixProvider covarianceMatrixProvider;
/** Process noise matrix provider for measurement parameters. */
private final CovarianceMatrixProvider measurementProcessNoiseMatrix;
/** Position angle type used during orbit determination. */
private final PositionAngleType angleType;
/** Orbit type used during orbit determination. */
private final OrbitType orbitType;
/** Current corrected estimate. */
private ProcessEstimate correctedEstimate;
/** Observer to retrieve current estimation info. */
private KalmanObserver observer;
/** Current number of measurement. */
private int currentMeasurementNumber;
/** Current date. */
private AbsoluteDate currentDate;
/** Nominal mean spacecraft state. */
private SpacecraftState nominalMeanSpacecraftState;
/** Previous nominal mean spacecraft state. */
private SpacecraftState previousNominalMeanSpacecraftState;
/** Predicted osculating spacecraft state. */
private SpacecraftState predictedSpacecraftState;
/** Corrected mean spacecraft state. */
private SpacecraftState correctedSpacecraftState;
/** Predicted measurement. */
private EstimatedMeasurement<?> predictedMeasurement;
/** Corrected measurement. */
private EstimatedMeasurement<?> correctedMeasurement;
/** Predicted mean element filter correction. */
private RealVector predictedFilterCorrection;
/** Corrected mean element filter correction. */
private RealVector correctedFilterCorrection;
/** Propagators for the reference trajectories, up to current date. */
private DSSTPropagator dsstPropagator;
/** Short period terms for the nominal mean spacecraft state. */
private RealVector shortPeriodicTerms;
/** Unscented Kalman process model constructor (package private).
* @param propagatorBuilder propagators builders used to evaluate the orbits.
* @param covarianceMatrixProvider provider for covariance matrix
* @param estimatedMeasurementParameters measurement parameters to estimate
* @param measurementProcessNoiseMatrix provider for measurement process noise matrix
*/
protected SemiAnalyticalUnscentedKalmanModel(final DSSTPropagatorBuilder propagatorBuilder,
final CovarianceMatrixProvider covarianceMatrixProvider,
final ParameterDriversList estimatedMeasurementParameters,
final CovarianceMatrixProvider measurementProcessNoiseMatrix) {
this.builder = propagatorBuilder;
this.angleType = propagatorBuilder.getPositionAngleType();
this.orbitType = propagatorBuilder.getOrbitType();
this.estimatedMeasurementsParameters = estimatedMeasurementParameters;
this.currentMeasurementNumber = 0;
this.currentDate = propagatorBuilder.getInitialOrbitDate();
this.covarianceMatrixProvider = covarianceMatrixProvider;
this.measurementProcessNoiseMatrix = measurementProcessNoiseMatrix;
// Number of estimated parameters
int columns = 0;
// Set estimated orbital parameters
this.estimatedOrbitalParameters = new ParameterDriversList();
for (final ParameterDriver driver : propagatorBuilder.getOrbitalParametersDrivers().getDrivers()) {
// Verify if the driver reference date has been set
if (driver.getReferenceDate() == null) {
driver.setReferenceDate(currentDate);
}
// Verify if the driver is selected
if (driver.isSelected()) {
estimatedOrbitalParameters.add(driver);
columns++;
}
}
// Set estimated propagation parameters
this.estimatedPropagationParameters = new ParameterDriversList();
final List<String> estimatedPropagationParametersNames = new ArrayList<>();
for (final ParameterDriver driver : propagatorBuilder.getPropagationParametersDrivers().getDrivers()) {
// Verify if the driver reference date has been set
if (driver.getReferenceDate() == null) {
driver.setReferenceDate(currentDate);
}
// Verify if the driver is selected
if (driver.isSelected()) {
estimatedPropagationParameters.add(driver);
final String driverName = driver.getName();
// Add the driver name if it has not been added yet
if (!estimatedPropagationParametersNames.contains(driverName)) {
estimatedPropagationParametersNames.add(driverName);
++columns;
}
}
}
estimatedPropagationParametersNames.sort(Comparator.naturalOrder());
// Set the estimated measurement parameters
for (final ParameterDriver parameter : estimatedMeasurementsParameters.getDrivers()) {
if (parameter.getReferenceDate() == null) {
parameter.setReferenceDate(currentDate);
}
++columns;
}
// Number of estimated measurement parameters
final int nbMeas = estimatedMeasurementParameters.getNbParams();
// Number of estimated dynamic parameters (orbital + propagation)
final int nbDyn = estimatedOrbitalParameters.getNbParams() +
estimatedPropagationParameters.getNbParams();
// Build the reference propagator
this.dsstPropagator = getEstimatedPropagator();
final SpacecraftState meanState = dsstPropagator.initialIsOsculating() ?
DSSTPropagator.computeMeanState(dsstPropagator.getInitialState(), dsstPropagator.getAttitudeProvider(), dsstPropagator.getAllForceModels()) :
dsstPropagator.getInitialState();
this.nominalMeanSpacecraftState = meanState;
this.predictedSpacecraftState = meanState;
this.correctedSpacecraftState = predictedSpacecraftState;
this.previousNominalMeanSpacecraftState = nominalMeanSpacecraftState;
// Initialize the estimated mean element filter correction
this.predictedFilterCorrection = MatrixUtils.createRealVector(columns);
this.correctedFilterCorrection = predictedFilterCorrection;
// Covariance matrix
final RealMatrix noiseK = MatrixUtils.createRealMatrix(nbDyn + nbMeas, nbDyn + nbMeas);
final RealMatrix noiseP = covarianceMatrixProvider.getInitialCovarianceMatrix(nominalMeanSpacecraftState);
noiseK.setSubMatrix(noiseP.getData(), 0, 0);
if (measurementProcessNoiseMatrix != null) {
final RealMatrix noiseM = measurementProcessNoiseMatrix.getInitialCovarianceMatrix(nominalMeanSpacecraftState);
noiseK.setSubMatrix(noiseM.getData(), nbDyn, nbDyn);
}
KalmanEstimatorUtil.checkDimension(noiseK.getRowDimension(),
propagatorBuilder.getOrbitalParametersDrivers(),
propagatorBuilder.getPropagationParametersDrivers(),
estimatedMeasurementsParameters);
// Initialize corrected estimate
this.correctedEstimate = new ProcessEstimate(0.0, correctedFilterCorrection, noiseK);
}
/** {@inheritDoc} */
@Override
public KalmanObserver getObserver() {
return observer;
}
/** Set the observer.
* @param observer the observer
*/
public void setObserver(final KalmanObserver observer) {
this.observer = observer;
}
/** Get the current corrected estimate.
* <p>
* For the Unscented Semi-analytical Kalman Filter
* it corresponds to the corrected filter correction.
* In other words, it doesn't represent an orbital state.
* </p>
* @return current corrected estimate
*/
public ProcessEstimate getEstimate() {
return correctedEstimate;
}
/** Process measurements.
* @param observedMeasurements the list of measurements to process
* @param filter Unscented Kalman Filter
* @return estimated propagator
*/
public DSSTPropagator processMeasurements(final List<ObservedMeasurement<?>> observedMeasurements,
final UnscentedKalmanFilter<MeasurementDecorator> filter) {
// Sort the measurement
observedMeasurements.sort(new ChronologicalComparator());
final AbsoluteDate tStart = observedMeasurements.get(0).getDate();
final AbsoluteDate tEnd = observedMeasurements.get(observedMeasurements.size() - 1).getDate();
final double overshootTimeRange = FastMath.nextAfter(tEnd.durationFrom(tStart),
Double.POSITIVE_INFINITY);
// Initialize step handler and set it to a parallelized propagator
final SemiAnalyticalMeasurementHandler stepHandler = new SemiAnalyticalMeasurementHandler(this, filter, observedMeasurements, builder.getInitialOrbitDate(), true);
dsstPropagator.getMultiplexer().add(stepHandler);
dsstPropagator.propagate(tStart, tStart.shiftedBy(overshootTimeRange));
// Return the last estimated propagator
return getEstimatedPropagator();
}
/** Get the propagator estimated with the values set in the propagator builder.
* @return propagator based on the current values in the builder
*/
public DSSTPropagator getEstimatedPropagator() {
// Return propagator built with current instantiation of the propagator builder
return (DSSTPropagator) builder.buildPropagator();
}
/** {@inheritDoc} */
@Override
public UnscentedEvolution getEvolution(final double previousTime, final RealVector[] sigmaPoints,
final MeasurementDecorator measurement) {
// Set a reference date for all measurements parameters that lack one (including the not estimated ones)
final ObservedMeasurement<?> observedMeasurement = measurement.getObservedMeasurement();
for (final ParameterDriver driver : observedMeasurement.getParametersDrivers()) {
if (driver.getReferenceDate() == null) {
driver.setReferenceDate(builder.getInitialOrbitDate());
}
}
// Increment measurement number
++currentMeasurementNumber;
// Update the current date
currentDate = measurement.getObservedMeasurement().getDate();
// STM for the prediction of the filter correction
final RealMatrix stm = getStm();
// Predicted states
final RealVector[] predictedStates = new RealVector[sigmaPoints.length];
for (int k = 0; k < sigmaPoints.length; ++k) {
// Predict filter correction for the current sigma point
final RealVector predicted = stm.operate(sigmaPoints[k]);
predictedStates[k] = predicted;
}
// Number of estimated measurement parameters
final int nbMeas = getNumberSelectedMeasurementDrivers();
// Number of estimated dynamic parameters (orbital + propagation)
final int nbDyn = getNumberSelectedOrbitalDrivers() + getNumberSelectedPropagationDrivers();
// Covariance matrix
final RealMatrix noiseK = MatrixUtils.createRealMatrix(nbDyn + nbMeas, nbDyn + nbMeas);
final RealMatrix noiseP = covarianceMatrixProvider.getProcessNoiseMatrix(previousNominalMeanSpacecraftState, nominalMeanSpacecraftState);
noiseK.setSubMatrix(noiseP.getData(), 0, 0);
if (measurementProcessNoiseMatrix != null) {
final RealMatrix noiseM = measurementProcessNoiseMatrix.getProcessNoiseMatrix(previousNominalMeanSpacecraftState, nominalMeanSpacecraftState);
noiseK.setSubMatrix(noiseM.getData(), nbDyn, nbDyn);
}
// Verify dimension
KalmanEstimatorUtil.checkDimension(noiseK.getRowDimension(),
builder.getOrbitalParametersDrivers(),
builder.getPropagationParametersDrivers(),
estimatedMeasurementsParameters);
// Return
return new UnscentedEvolution(measurement.getTime(), predictedStates, noiseK);
}
/** {@inheritDoc} */
@Override
public RealVector[] getPredictedMeasurements(final RealVector[] predictedSigmaPoints, final MeasurementDecorator measurement) {
// Observed measurement
final ObservedMeasurement<?> observedMeasurement = measurement.getObservedMeasurement();
// Initialize arrays of predicted states and measurements
final RealVector[] predictedMeasurements = new RealVector[predictedSigmaPoints.length];
// Loop on sigma points
for (int k = 0; k < predictedSigmaPoints.length; ++k) {
// Calculate the predicted osculating elements for the current mean state
final RealVector osculating = computeOsculatingElements(predictedSigmaPoints[k], nominalMeanSpacecraftState, shortPeriodicTerms);
final Orbit osculatingOrbit = orbitType.mapArrayToOrbit(osculating.toArray(), null, angleType,
currentDate, builder.getMu(), builder.getFrame());
// Then, estimate the measurement
final EstimatedMeasurement<?> estimated = observedMeasurement.estimate(currentMeasurementNumber,
currentMeasurementNumber,
new SpacecraftState[] {
new SpacecraftState(osculatingOrbit)
});
predictedMeasurements[k] = new ArrayRealVector(estimated.getEstimatedValue());
}
// Return
return predictedMeasurements;
}
/** {@inheritDoc} */
@Override
public RealVector getInnovation(final MeasurementDecorator measurement, final RealVector predictedMeas,
final RealVector predictedState, final RealMatrix innovationCovarianceMatrix) {
// Predicted filter correction
predictedFilterCorrection = predictedState;
// Predicted measurement
final RealVector osculating = computeOsculatingElements(predictedFilterCorrection, nominalMeanSpacecraftState, shortPeriodicTerms);
final Orbit osculatingOrbit = orbitType.mapArrayToOrbit(osculating.toArray(), null, angleType,
currentDate, builder.getMu(), builder.getFrame());
predictedSpacecraftState = new SpacecraftState(osculatingOrbit);
predictedMeasurement = measurement.getObservedMeasurement().estimate(currentMeasurementNumber, currentMeasurementNumber, getPredictedSpacecraftStates());
predictedMeasurement.setEstimatedValue(predictedMeas.toArray());
// Apply the dynamic outlier filter, if it exists
KalmanEstimatorUtil.applyDynamicOutlierFilter(predictedMeasurement, innovationCovarianceMatrix);
// Compute the innovation vector (not normalized for unscented Kalman filter)
return KalmanEstimatorUtil.computeInnovationVector(predictedMeasurement);
}
/** {@inheritDoc} */
@Override
public void finalizeEstimation(final ObservedMeasurement<?> observedMeasurement,
final ProcessEstimate estimate) {
// Update the process estimate
correctedEstimate = estimate;
// Corrected filter correction
correctedFilterCorrection = estimate.getState();
// Update the previous nominal mean spacecraft state
previousNominalMeanSpacecraftState = nominalMeanSpacecraftState;
// Update the previous nominal mean spacecraft state
// Calculate the corrected osculating elements
final RealVector osculating = computeOsculatingElements(correctedFilterCorrection, nominalMeanSpacecraftState, shortPeriodicTerms);
final Orbit osculatingOrbit = orbitType.mapArrayToOrbit(osculating.toArray(), null, builder.getPositionAngleType(),
currentDate, builder.getMu(), builder.getFrame());
// Compute the corrected measurements
correctedSpacecraftState = new SpacecraftState(osculatingOrbit);
correctedMeasurement = observedMeasurement.estimate(currentMeasurementNumber,
currentMeasurementNumber,
getCorrectedSpacecraftStates());
// Call the observer if the user add one
if (observer != null) {
observer.evaluationPerformed(this);
}
}
/** Get the state transition matrix used to predict the filter correction.
* <p>
* The state transition matrix is not computed by the DSST propagator.
* It is analytically calculated considering Keplerian contribution only
* </p>
* @return the state transition matrix used to predict the filter correction
*/
private RealMatrix getStm() {
// initialize the STM
final int nbDym = getNumberSelectedOrbitalDrivers() + getNumberSelectedPropagationDrivers();
final int nbMeas = getNumberSelectedMeasurementDrivers();
final RealMatrix stm = MatrixUtils.createRealIdentityMatrix(nbDym + nbMeas);
// State transition matrix using Keplerian contribution only
final double mu = builder.getMu();
final double sma = previousNominalMeanSpacecraftState.getA();
final double dt = currentDate.durationFrom(previousNominalMeanSpacecraftState.getDate());
final double contribution = -1.5 * dt * FastMath.sqrt(mu / FastMath.pow(sma, 5));
stm.setEntry(5, 0, contribution);
// Return
return stm;
}
/** {@inheritDoc} */
@Override
public void finalizeOperationsObservationGrid() {
// Update parameters
updateParameters();
}
/** {@inheritDoc} */
@Override
public ParameterDriversList getEstimatedOrbitalParameters() {
return estimatedOrbitalParameters;
}
/** {@inheritDoc} */
@Override
public ParameterDriversList getEstimatedPropagationParameters() {
return estimatedPropagationParameters;
}
/** {@inheritDoc} */
@Override
public ParameterDriversList getEstimatedMeasurementsParameters() {
return estimatedMeasurementsParameters;
}
/** {@inheritDoc}
* <p>
* Predicted state is osculating.
* </p>
*/
@Override
public SpacecraftState[] getPredictedSpacecraftStates() {
return new SpacecraftState[] {predictedSpacecraftState};
}
/** {@inheritDoc}
* <p>
* Corrected state is osculating.
* </p>
*/
@Override
public SpacecraftState[] getCorrectedSpacecraftStates() {
return new SpacecraftState[] {correctedSpacecraftState};
}
/** {@inheritDoc} */
@Override
public RealVector getPhysicalEstimatedState() {
// Method {@link ParameterDriver#getValue()} is used to get
// the physical values of the state.
// The scales'array is used to get the size of the state vector
final RealVector physicalEstimatedState = new ArrayRealVector(getEstimate().getState().getDimension());
int i = 0;
for (final DelegatingDriver driver : getEstimatedOrbitalParameters().getDrivers()) {
physicalEstimatedState.setEntry(i++, driver.getValue());
}
for (final DelegatingDriver driver : getEstimatedPropagationParameters().getDrivers()) {
physicalEstimatedState.setEntry(i++, driver.getValue());
}
for (final DelegatingDriver driver : getEstimatedMeasurementsParameters().getDrivers()) {
physicalEstimatedState.setEntry(i++, driver.getValue());
}
return physicalEstimatedState;
}
/** {@inheritDoc} */
@Override
public RealMatrix getPhysicalEstimatedCovarianceMatrix() {
return correctedEstimate.getCovariance();
}
/** {@inheritDoc} */
@Override
public RealMatrix getPhysicalStateTransitionMatrix() {
return null;
}
/** {@inheritDoc} */
@Override
public RealMatrix getPhysicalMeasurementJacobian() {
return null;
}
/** {@inheritDoc} */
@Override
public RealMatrix getPhysicalInnovationCovarianceMatrix() {
return correctedEstimate.getInnovationCovariance();
}
/** {@inheritDoc} */
@Override
public RealMatrix getPhysicalKalmanGain() {
return correctedEstimate.getKalmanGain();
}
/** {@inheritDoc} */
@Override
public int getCurrentMeasurementNumber() {
return currentMeasurementNumber;
}
/** {@inheritDoc} */
@Override
public AbsoluteDate getCurrentDate() {
return currentDate;
}
/** {@inheritDoc} */
@Override
public EstimatedMeasurement<?> getPredictedMeasurement() {
return predictedMeasurement;
}
/** {@inheritDoc} */
@Override
public EstimatedMeasurement<?> getCorrectedMeasurement() {
return correctedMeasurement;
}
/** {@inheritDoc} */
@Override
public void updateNominalSpacecraftState(final SpacecraftState nominal) {
this.nominalMeanSpacecraftState = nominal;
// Short period terms
shortPeriodicTerms = new ArrayRealVector(dsstPropagator.getShortPeriodTermsValue(nominalMeanSpacecraftState));
// Update the builder with the nominal mean elements orbit
builder.resetOrbit(nominal.getOrbit(), PropagationType.MEAN);
}
/** {@inheritDoc} */
@Override
public void updateShortPeriods(final SpacecraftState state) {
// Loop on DSST force models
for (final DSSTForceModel model : dsstPropagator.getAllForceModels()) {
model.updateShortPeriodTerms(model.getParameters(), state);
}
}
/** {@inheritDoc} */
@Override
public void initializeShortPeriodicTerms(final SpacecraftState meanState) {
final List<ShortPeriodTerms> shortPeriodTerms = new ArrayList<>();
for (final DSSTForceModel force : builder.getAllForceModels()) {
shortPeriodTerms.addAll(force.initializeShortPeriodTerms(new AuxiliaryElements(meanState.getOrbit(), 1), PropagationType.OSCULATING, force.getParameters()));
}
dsstPropagator.setShortPeriodTerms(shortPeriodTerms);
}
/** Compute the predicted osculating elements.
* @param filterCorrection physical kalman filter correction
* @param meanState mean spacecraft state
* @param shortPeriodTerms short period terms for the given mean state
* @return the predicted osculating element
*/
private RealVector computeOsculatingElements(final RealVector filterCorrection,
final SpacecraftState meanState,
final RealVector shortPeriodTerms) {
// Convert the input predicted mean state to a SpacecraftState
final RealVector stateVector = toRealVector(meanState);
// Return
return stateVector.add(filterCorrection).add(shortPeriodTerms);
}
/** Convert a SpacecraftState to a RealVector.
* @param state the input SpacecraftState
* @return the corresponding RealVector
*/
private RealVector toRealVector(final SpacecraftState state) {
// Convert orbit to array
final double[] stateArray = new double[6];
orbitType.mapOrbitToArray(state.getOrbit(), angleType, stateArray, null);
// Return the RealVector
return new ArrayRealVector(stateArray);
}
/** Get the number of estimated orbital parameters.
* @return the number of estimated orbital parameters
*/
public int getNumberSelectedOrbitalDrivers() {
return estimatedOrbitalParameters.getNbParams();
}
/** Get the number of estimated propagation parameters.
* @return the number of estimated propagation parameters
*/
public int getNumberSelectedPropagationDrivers() {
return estimatedPropagationParameters.getNbParams();
}
/** Get the number of estimated measurement parameters.
* @return the number of estimated measurement parameters
*/
public int getNumberSelectedMeasurementDrivers() {
return estimatedMeasurementsParameters.getNbParams();
}
/** Update the estimated parameters after the correction phase of the filter.
* The min/max allowed values are handled by the parameter themselves.
*/
private void updateParameters() {
final RealVector correctedState = correctedEstimate.getState();
int i = 0;
for (final DelegatingDriver driver : getEstimatedOrbitalParameters().getDrivers()) {
// let the parameter handle min/max clipping
driver.setValue(driver.getValue() + correctedState.getEntry(i++));
}
for (final DelegatingDriver driver : getEstimatedPropagationParameters().getDrivers()) {
// let the parameter handle min/max clipping
driver.setValue(driver.getValue() + correctedState.getEntry(i++));
}
for (final DelegatingDriver driver : getEstimatedMeasurementsParameters().getDrivers()) {
// let the parameter handle min/max clipping
driver.setValue(driver.getValue() + correctedState.getEntry(i++));
}
}
}