GNSSAttitudeContext.java
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* http://www.apache.org/licenses/LICENSE-2.0
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* Unless required by applicable law or agreed to in writing, software
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package org.orekit.gnss.attitude;
import org.hipparchus.analysis.UnivariateFunction;
import org.hipparchus.analysis.differentiation.DSFactory;
import org.hipparchus.analysis.differentiation.DerivativeStructure;
import org.hipparchus.analysis.solvers.BracketingNthOrderBrentSolver;
import org.hipparchus.analysis.solvers.UnivariateSolverUtils;
import org.hipparchus.geometry.euclidean.threed.FieldVector3D;
import org.hipparchus.geometry.euclidean.threed.Vector3D;
import org.hipparchus.util.FastMath;
import org.hipparchus.util.FieldSinCos;
import org.hipparchus.util.SinCos;
import org.orekit.frames.Frame;
import org.orekit.frames.LOFType;
import org.orekit.frames.Transform;
import org.orekit.time.AbsoluteDate;
import org.orekit.time.FieldAbsoluteDate;
import org.orekit.time.TimeStamped;
import org.orekit.utils.ExtendedPVCoordinatesProvider;
import org.orekit.utils.FieldPVCoordinates;
import org.orekit.utils.PVCoordinates;
import org.orekit.utils.PVCoordinatesProvider;
import org.orekit.utils.TimeStampedAngularCoordinates;
import org.orekit.utils.TimeStampedPVCoordinates;
/**
* Boilerplate computations for GNSS attitude.
*
* <p>
* This class is intended to hold throw-away data pertaining to <em>one</em> call
* to {@link GNSSAttitudeProvider#getAttitude(org.orekit.utils.PVCoordinatesProvider,
* org.orekit.time.AbsoluteDate, org.orekit.frames.Frame) getAttitude}.
* </p>
*
* @author Luc Maisonobe
* @since 9.2
*/
class GNSSAttitudeContext implements TimeStamped {
/** Derivation order. */
private static final int ORDER = 2;
/** Time derivation factory. */
private static final DSFactory FACTORY = new DSFactory(1, ORDER);
/** Constant Y axis. */
private static final PVCoordinates PLUS_Y_PV =
new PVCoordinates(Vector3D.PLUS_J, Vector3D.ZERO, Vector3D.ZERO);
/** Constant Z axis. */
private static final PVCoordinates MINUS_Z_PV =
new PVCoordinates(Vector3D.MINUS_K, Vector3D.ZERO, Vector3D.ZERO);
/** Limit value below which we shoud use replace beta by betaIni. */
private static final double BETA_SIGN_CHANGE_PROTECTION = FastMath.toRadians(0.07);
/** Current date. */
private final AbsoluteDate date;
/** Current date. */
private final FieldAbsoluteDate<DerivativeStructure> dateDS;
/** Provider for Sun position. */
private final ExtendedPVCoordinatesProvider sun;
/** Provider for spacecraft position. */
private final PVCoordinatesProvider pvProv;
/** Inertial frame where velocity are computed. */
private final Frame inertialFrame;
/** Cosine of the angle between spacecraft and Sun direction. */
private final DerivativeStructure svbCos;
/** Morning/Evening half orbit indicator. */
private final boolean morning;
/** Relative orbit angle to turn center. */
private final DerivativeStructure delta;
/** Spacecraft angular velocity. */
private double muRate;
/** Limit cosine for the midnight turn. */
private double cNight;
/** Limit cosine for the noon turn. */
private double cNoon;
/** Turn time data. */
private TurnSpan turnSpan;
/** Simple constructor.
* @param date current date
* @param sun provider for Sun position
* @param pvProv provider for spacecraft position
* @param inertialFrame inertial frame where velocity are computed
* @param turnSpan turn time data, if a turn has already been identified in the date neighborhood,
* null otherwise
*/
GNSSAttitudeContext(final AbsoluteDate date,
final ExtendedPVCoordinatesProvider sun, final PVCoordinatesProvider pvProv,
final Frame inertialFrame, final TurnSpan turnSpan) {
this.date = date;
this.dateDS = addDerivatives(date);
this.sun = sun;
this.pvProv = pvProv;
this.inertialFrame = inertialFrame;
final FieldPVCoordinates<DerivativeStructure> sunPVDS = sun.getPVCoordinates(dateDS, inertialFrame);
final TimeStampedPVCoordinates svPV = pvProv.getPVCoordinates(date, inertialFrame);
final FieldPVCoordinates<DerivativeStructure> svPVDS = svPV.toDerivativeStructurePV(FACTORY.getCompiler().getOrder());
this.svbCos = FieldVector3D.dotProduct(sunPVDS.getPosition(), svPVDS.getPosition()).
divide(sunPVDS.getPosition().getNorm().multiply(svPVDS.getPosition().getNorm()));
this.morning = Vector3D.dotProduct(svPV.getVelocity(), sunPVDS.getPosition().toVector3D()) >= 0.0;
this.muRate = svPV.getAngularVelocity().getNorm();
this.turnSpan = turnSpan;
final DerivativeStructure absDelta;
if (svbCos.getValue() <= 0) {
// night side
absDelta = inOrbitPlaneAbsoluteAngle(svbCos.acos().negate().add(FastMath.PI));
} else {
// Sun side
absDelta = inOrbitPlaneAbsoluteAngle(svbCos.acos());
}
delta = FastMath.copySign(absDelta, -absDelta.getPartialDerivative(1));
}
/** Convert a date, removing derivatives.
* @param d date to convert
* @return date without derivatives
*/
private AbsoluteDate removeDerivatives(final FieldAbsoluteDate<DerivativeStructure> d) {
return d.toAbsoluteDate();
}
/** Convert a date, adding derivatives.
* @param d date to convert
* @return date without derivatives
*/
private FieldAbsoluteDate<DerivativeStructure> addDerivatives(final AbsoluteDate d) {
return new FieldAbsoluteDate<>(FACTORY.getDerivativeField(), d).
shiftedBy(FACTORY.variable(0, 0.0));
}
/** Compute nominal yaw steering.
* @param d computation date
* @return nominal yaw steering
*/
public TimeStampedAngularCoordinates nominalYaw(final AbsoluteDate d) {
final PVCoordinates svPV = pvProv.getPVCoordinates(d, inertialFrame);
return new TimeStampedAngularCoordinates(d,
svPV.normalize(),
PVCoordinates.crossProduct(sun.getPVCoordinates(d, inertialFrame), svPV).normalize(),
MINUS_Z_PV,
PLUS_Y_PV,
1.0e-9);
}
/** Compute Sun elevation.
* @param d computation date
* @return Sun elevation
*/
public double beta(final AbsoluteDate d) {
final TimeStampedPVCoordinates svPV = pvProv.getPVCoordinates(d, inertialFrame);
return 0.5 * FastMath.PI - Vector3D.angle(sun.getPVCoordinates(d, inertialFrame).getPosition(), svPV.getMomentum());
}
/** Compute Sun elevation.
* @param d computation date
* @return Sun elevation
*/
private DerivativeStructure betaDS(final FieldAbsoluteDate<DerivativeStructure> d) {
final TimeStampedPVCoordinates svPV = pvProv.getPVCoordinates(removeDerivatives(d), inertialFrame);
final FieldPVCoordinates<DerivativeStructure> svPVDS = svPV.toDerivativeStructurePV(FACTORY.getCompiler().getOrder());
return FieldVector3D.angle(sun.getPVCoordinates(d, inertialFrame).getPosition(), svPVDS.getMomentum()).
negate().
add(0.5 * FastMath.PI);
}
/** Compute Sun elevation.
* @return Sun elevation
*/
public DerivativeStructure betaDS() {
return betaDS(dateDS);
}
/** {@inheritDoc} */
@Override
public AbsoluteDate getDate() {
return date;
}
/** Get the turn span.
* @return turn span, may be null if context is outside of turn
*/
public TurnSpan getTurnSpan() {
return turnSpan;
}
/** Get the cosine of the angle between spacecraft and Sun direction.
* @return cosine of the angle between spacecraft and Sun direction.
*/
public double getSVBcos() {
return svbCos.getValue();
}
/** Get a Sun elevation angle that does not change sign within the turn.
* <p>
* This method either returns the current beta or replaces it with the
* value at turn start, so the sign remains constant throughout the
* turn. As of 9.2, it is used for GPS, Glonass and Galileo.
* </p>
* @return secured Sun elevation angle
* @see #beta(AbsoluteDate)
* @see #betaDS(FieldAbsoluteDate)
*/
public double getSecuredBeta() {
final double beta = beta(getDate());
return FastMath.abs(beta) < BETA_SIGN_CHANGE_PROTECTION ?
beta(turnSpan.getTurnStartDate()) :
beta;
}
/** Check if a linear yaw model is still active or if we already reached target yaw.
* @param linearPhi value of the linear yaw model
* @param phiDot slope of the linear yaw model
* @return true if linear model is still active
*/
public boolean linearModelStillActive(final double linearPhi, final double phiDot) {
final double dt0 = turnSpan.getTurnEndDate().durationFrom(date);
final UnivariateFunction yawReached = dt -> {
final AbsoluteDate t = date.shiftedBy(dt);
final Vector3D pSun = sun.getPVCoordinates(t, inertialFrame).getPosition();
final PVCoordinates pv = pvProv.getPVCoordinates(t, inertialFrame);
final Vector3D pSat = pv.getPosition();
final Vector3D targetX = Vector3D.crossProduct(pSat, Vector3D.crossProduct(pSun, pSat)).normalize();
final double phi = linearPhi + dt * phiDot;
final SinCos sc = FastMath.sinCos(phi);
final Vector3D pU = pv.getPosition().normalize();
final Vector3D mU = pv.getMomentum().normalize();
final Vector3D omega = new Vector3D(-phiDot, pU);
final Vector3D currentX = new Vector3D(-sc.sin(), mU, -sc.cos(), Vector3D.crossProduct(pU, mU));
final Vector3D currentXDot = Vector3D.crossProduct(omega, currentX);
return Vector3D.dotProduct(targetX, currentXDot);
};
final double fullTurn = 2 * FastMath.PI / FastMath.abs(phiDot);
final double dtMin = FastMath.min(turnSpan.getTurnStartDate().durationFrom(date), dt0 - 60.0);
final double dtMax = FastMath.max(dtMin + fullTurn, dt0 + 60.0);
double[] bracket = UnivariateSolverUtils.bracket(yawReached, dt0,
dtMin, dtMax, fullTurn / 100, 1.0, 100);
if (yawReached.value(bracket[0]) <= 0.0) {
// we have bracketed the wrong crossing
bracket = UnivariateSolverUtils.bracket(yawReached, 0.5 * (bracket[0] + bracket[1] + fullTurn),
bracket[1], bracket[1] + fullTurn, fullTurn / 100, 1.0, 100);
}
final double dt = new BracketingNthOrderBrentSolver(1.0e-3, 5).
solve(100, yawReached, bracket[0], bracket[1]);
turnSpan.updateEnd(date.shiftedBy(dt), date);
return dt > 0.0;
}
/** Set up the midnight/noon turn region.
* @param cosNight limit cosine for the midnight turn
* @param cosNoon limit cosine for the noon turn
* @return true if spacecraft is in the midnight/noon turn region
*/
public boolean setUpTurnRegion(final double cosNight, final double cosNoon) {
this.cNight = cosNight;
this.cNoon = cosNoon;
if (svbCos.getValue() < cNight || svbCos.getValue() > cNoon) {
// we are within turn triggering zone
return true;
} else {
// we are outside of turn triggering zone,
// but we may still be trying to recover nominal attitude at the end of a turn
return inTurnTimeRange();
}
}
/** Get the relative orbit angle to turn center.
* @return relative orbit angle to turn center
*/
public DerivativeStructure getDeltaDS() {
return delta;
}
/** Get the orbit angle since solar midnight.
* @return orbit angle since solar midnight
*/
public double getOrbitAngleSinceMidnight() {
final double absAngle = inOrbitPlaneAbsoluteAngle(FastMath.PI - FastMath.acos(svbCos.getValue()));
return morning ? absAngle : -absAngle;
}
/** Check if spacecraft is in the half orbit closest to Sun.
* @return true if spacecraft is in the half orbit closest to Sun
*/
public boolean inSunSide() {
return svbCos.getValue() > 0;
}
/** Get yaw at turn start.
* @param sunBeta Sun elevation above orbital plane
* (it <em>may</em> be different from {@link #getBeta()} in
* some special cases)
* @return yaw at turn start
*/
public double getYawStart(final double sunBeta) {
final double halfSpan = 0.5 * turnSpan.getTurnDuration() * muRate;
return computePhi(sunBeta, FastMath.copySign(halfSpan, svbCos.getValue()));
}
/** Get yaw at turn end.
* @param sunBeta Sun elevation above orbital plane
* (it <em>may</em> be different from {@link #getBeta()} in
* some special cases)
* @return yaw at turn end
*/
public double getYawEnd(final double sunBeta) {
final double halfSpan = 0.5 * turnSpan.getTurnDuration() * muRate;
return computePhi(sunBeta, FastMath.copySign(halfSpan, -svbCos.getValue()));
}
/** Compute yaw rate.
* @param sunBeta Sun elevation above orbital plane
* (it <em>may</em> be different from {@link #getBeta()} in
* some special cases)
* @return yaw rate
*/
public double yawRate(final double sunBeta) {
return (getYawEnd(sunBeta) - getYawStart(sunBeta)) / turnSpan.getTurnDuration();
}
/** Get the spacecraft angular velocity.
* @return spacecraft angular velocity
*/
public double getMuRate() {
return muRate;
}
/** Project a spacecraft/Sun angle into orbital plane.
* <p>
* This method is intended to find the limits of the noon and midnight
* turns in orbital plane. The return angle is signed, depending on the
* spacecraft being before or after turn middle point.
* </p>
* @param angle spacecraft/Sun angle (or spacecraft/opposite-of-Sun)
* @return angle projected into orbital plane, always positive
*/
private DerivativeStructure inOrbitPlaneAbsoluteAngle(final DerivativeStructure angle) {
return FastMath.acos(FastMath.cos(angle).divide(FastMath.cos(beta(getDate()))));
}
/** Project a spacecraft/Sun angle into orbital plane.
* <p>
* This method is intended to find the limits of the noon and midnight
* turns in orbital plane. The return angle is always positive. The
* correct sign to apply depends on the spacecraft being before or
* after turn middle point.
* </p>
* @param angle spacecraft/Sun angle (or spacecraft/opposite-of-Sun)
* @return angle projected into orbital plane, always positive
*/
public double inOrbitPlaneAbsoluteAngle(final double angle) {
return FastMath.acos(FastMath.cos(angle) / FastMath.cos(beta(getDate())));
}
/** Compute yaw.
* @param sunBeta Sun elevation above orbital plane
* (it <em>may</em> be different from {@link #getBeta()} in
* some special cases)
* @param inOrbitPlaneAngle in orbit angle between spacecraft
* and Sun (or opposite of Sun) projection
* @return yaw angle
*/
public double computePhi(final double sunBeta, final double inOrbitPlaneAngle) {
return FastMath.atan2(-FastMath.tan(sunBeta), FastMath.sin(inOrbitPlaneAngle));
}
/** Set turn half span and compute corresponding turn time range.
* @param halfSpan half span of the turn region, as an angle in orbit plane
* @param endMargin margin in seconds after turn end
*/
public void setHalfSpan(final double halfSpan, final double endMargin) {
final AbsoluteDate start = date.shiftedBy((delta.getValue() - halfSpan) / muRate);
final AbsoluteDate end = date.shiftedBy((delta.getValue() + halfSpan) / muRate);
final AbsoluteDate estimationDate = getDate();
if (turnSpan == null) {
turnSpan = new TurnSpan(start, end, estimationDate, endMargin);
} else {
turnSpan.updateStart(start, estimationDate);
turnSpan.updateEnd(end, estimationDate);
}
}
/** Check if context is within turn range.
* @return true if context is within range extended by end margin
*/
public boolean inTurnTimeRange() {
return turnSpan != null && turnSpan.inTurnTimeRange(getDate());
}
/** Get elapsed time since turn start.
* @return elapsed time from turn start to current date
*/
public double timeSinceTurnStart() {
return getDate().durationFrom(turnSpan.getTurnStartDate());
}
/** Generate an attitude with turn-corrected yaw.
* @param yaw yaw value to apply
* @param yawDot yaw first time derivative
* @return attitude with specified yaw
*/
public TimeStampedAngularCoordinates turnCorrectedAttitude(final double yaw, final double yawDot) {
return turnCorrectedAttitude(FACTORY.build(yaw, yawDot, 0.0));
}
/** Generate an attitude with turn-corrected yaw.
* @param yaw yaw value to apply
* @return attitude with specified yaw
*/
public TimeStampedAngularCoordinates turnCorrectedAttitude(final DerivativeStructure yaw) {
// Earth pointing (Z aligned with position) with linear yaw (momentum with known cos/sin in the X/Y plane)
final PVCoordinates svPV = pvProv.getPVCoordinates(date, inertialFrame);
final Vector3D p = svPV.getPosition();
final Vector3D v = svPV.getVelocity();
final Vector3D a = svPV.getAcceleration();
final double r2 = p.getNormSq();
final double r = FastMath.sqrt(r2);
final Vector3D keplerianJerk = new Vector3D(-3 * Vector3D.dotProduct(p, v) / r2, a, -a.getNorm() / r, v);
final PVCoordinates velocity = new PVCoordinates(v, a, keplerianJerk);
final PVCoordinates momentum = PVCoordinates.crossProduct(svPV, velocity);
final FieldSinCos<DerivativeStructure> sc = FastMath.sinCos(yaw);
final DerivativeStructure c = sc.cos().negate();
final DerivativeStructure s = sc.sin().negate();
final Vector3D m0 = new Vector3D(s.getValue(), c.getValue(), 0.0);
final Vector3D m1 = new Vector3D(s.getPartialDerivative(1), c.getPartialDerivative(1), 0.0);
final Vector3D m2 = new Vector3D(s.getPartialDerivative(2), c.getPartialDerivative(2), 0.0);
return new TimeStampedAngularCoordinates(date,
svPV.normalize(), momentum.normalize(),
MINUS_Z_PV, new PVCoordinates(m0, m1, m2),
1.0e-9);
}
/** Compute Orbit Normal (ON) yaw.
* @return Orbit Normal yaw, using inertial frame as reference
*/
public TimeStampedAngularCoordinates orbitNormalYaw() {
final Transform t = LOFType.LVLH_CCSDS.transformFromInertial(date, pvProv.getPVCoordinates(date, inertialFrame));
return new TimeStampedAngularCoordinates(date,
t.getRotation(),
t.getRotationRate(),
t.getRotationAcceleration());
}
}