fr.cnes.sirius.patrius.forces.maneuvers

Class GatesModel

java.lang.Object

fr.cnes.sirius.patrius.forces.maneuvers.GatesModel

public class GatesModel
extends Object

This class implements a variation of the model proposed by C.R. Gates to represent the uncertainty on a maneuver's magnitude and direction.

The model implemented here differs from the one proposed by Gates in a few ways. Although no mention of it is made in the paper, the formulation proposed by Gates seems to rely on the small angles hypothesis. This is not the case of the formulation used here. In addition, this class only implements the shutoff error and the pointing error, that is, the errors on the maneuver's magnitude and direction which are proportional to ΔV. The uncertainty on the maneuver's direction is modeled as a spherical Gaussian distribution around the ΔV vector, while the uncertainty on the maneuver's magnitude is assumed to follow an uncorrelated Gaussian distribution.

Note that although the uncertainty on the maneuver's magnitude and direction is defined using the target ΔV vector, the latter is generally not the mean of the distribution (this is only the case if there is no uncertainty on the maneuver's direction). The mean perturbed maneuver can be computed using getMeanDeltaV(Vector3D) or getMeanDeltaV(Vector3D, double).

See:
A Simplified Model of Midcourse Maneuver Execution Errors
by C.R. Gates
Technical Report n°32-504, October 15, 1963
Jet Propulsion Laboratory (JPL)
California Institute of Technology, Pasadena, California.

Since:

4.7

Author:

GMV

Constructor Summary

Constructors

Constructor and Description
GatesModel(double sigmaMagnitudeIn, double sigmaDirectionIn) Constructor.

Method Summary

Modifier and Type	Method and Description
SymmetricMatrix	getCovarianceMatrix3x3(Vector3D deltaV) Computes the covariance matrix modeling the uncertainty on a maneuver's magnitude and direction.
static SymmetricMatrix	getCovarianceMatrix3x3(Vector3D deltaV, double sigmaMagnitude, double sigmaDirection) Computes the covariance matrix modeling the uncertainty on a maneuver's magnitude and direction.
SymmetricMatrix	getCovarianceMatrix6x6(Vector3D deltaV) Computes the covariance matrix modeling the uncertainty on an object's position and velocity induced by the uncertainty on a maneuver's magnitude and direction.
static SymmetricMatrix	getCovarianceMatrix6x6(Vector3D deltaV, double sigmaMagnitude, double sigmaDirection) Computes the covariance matrix modeling the uncertainty on an object's position and velocity induced by the uncertainty on a maneuver's magnitude and direction.
Vector3D	getMeanDeltaV(Vector3D deltaV) Computes the mean ΔV vector of the distribution modeling the uncertainty on a maneuver's magnitude and direction.
static Vector3D	getMeanDeltaV(Vector3D deltaV, double sigmaDirection) Computes the mean ΔV vector of the distribution modeling the uncertainty on a maneuver's magnitude and direction.
double	getSigmaDirection() Gets the standard deviation σD on the direction (in radians).
double	getSigmaMagnitude() Gets the standard deviation σM on the magnitude (in percent).

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

GatesModel

public GatesModel(double sigmaMagnitudeIn,
                  double sigmaDirectionIn)

Constructor.

The parameter σ_M defines the shutoff error, which is in the direction of ΔV and is proportional to its norm.
Such an error would result from scale-factor errors in the shutoff system.

The parameter σ_D defines the pointing error, which is proportional to the norm of ΔV.
Such an error would result from imperfect angular orientation of the thrust vector.

Parameters:

sigmaMagnitudeIn - the standard deviation σ_M on the magnitude (in percent)

sigmaDirectionIn - the standard deviation σ_D on the direction (in radians)

Method Detail

getSigmaMagnitude

public double getSigmaMagnitude()

Gets the standard deviation σ_M on the magnitude (in percent).

This parameter defines the shutoff error, which is in the direction of ΔV and is proportional to its norm.
Such an error would result from scale-factor errors in the shutoff system.

Returns:

the standard deviation on the magnitude (in percent)

getSigmaDirection

public double getSigmaDirection()

Gets the standard deviation σ_D on the direction (in radians).

This parameter defines the pointing error, which is orthogonal to ΔV and proportional to its norm.
Such an error would result from imperfect angular orientation of the thrust vector.

Returns:

the standard deviation on the direction (in radians)

getCovarianceMatrix3x3

public SymmetricMatrix getCovarianceMatrix3x3(Vector3D deltaV)

Computes the covariance matrix modeling the uncertainty on a maneuver's magnitude and direction.

This methods assumes the uncertainty on the maneuver's direction follows a spherical Gaussian distribution around the provided ΔV vector. The uncertainty on the maneuver's magnitude is assumed to follow an uncorrelated Gaussian distribution. Both uncertainties are proportional to the norm of ΔV.

Parameters:

deltaV - the maneuver's ΔV (in any frame)

Returns:

a 3-by-3 covariance matrix modeling the uncertainty on the maneuver's magnitude and direction (in the same frame as ΔV)

Throws:

MathArithmeticException - if the norm of the provided ΔV vector is close to zero (<ε), but not exactly equal to zero

getCovarianceMatrix6x6

public SymmetricMatrix getCovarianceMatrix6x6(Vector3D deltaV)

Computes the covariance matrix modeling the uncertainty on an object's position and velocity induced by the uncertainty on a maneuver's magnitude and direction.

This methods assumes the uncertainty on the maneuver's direction follows a spherical Gaussian distribution around the provided ΔV vector. The uncertainty on the maneuver's magnitude is assumed to follow an uncorrelated Gaussian distribution. Both uncertainties are proportional to the norm of ΔV.

Parameters:

deltaV - the maneuver's ΔV (in any frame)

Returns:

a 6-by-6 covariance matrix modeling the uncertainty on an object's position and velocity induced by the uncertainty on the maneuver's magnitude and direction (in the same frame as ΔV)

Throws:

MathArithmeticException - if the norm of the provided ΔV vector is close to zero (<ε), but not exactly equal to zero

getMeanDeltaV

public Vector3D getMeanDeltaV(Vector3D deltaV)

Computes the mean ΔV vector of the distribution modeling the uncertainty on a maneuver's magnitude and direction.

This methods assumes the uncertainty on the maneuver's direction follows a spherical Gaussian distribution around the provided ΔV vector. The uncertainty on the maneuver's magnitude is assumed to follow an uncorrelated Gaussian distribution. Both uncertainties are proportional to the norm of ΔV.

Parameters:

deltaV - the maneuver's ΔV (in any frame)

Returns:

the mean ΔV vector of the distribution modeling the uncertainty on a maneuver's magnitude and direction.

Throws:

MathArithmeticException - if the norm of the provided ΔV vector is close to zero (<ε), but not exactly equal to zero

getCovarianceMatrix3x3

public static SymmetricMatrix getCovarianceMatrix3x3(Vector3D deltaV,
                                                     double sigmaMagnitude,
                                                     double sigmaDirection)

Computes the covariance matrix modeling the uncertainty on a maneuver's magnitude and direction.

This methods assumes the uncertainty on the maneuver's direction follows a spherical Gaussian distribution around the provided ΔV vector. The uncertainty on the maneuver's magnitude is assumed to follow an uncorrelated Gaussian distribution. Both uncertainties are proportional to the norm of ΔV.

Parameters:

deltaV - the maneuver's ΔV (in any frame)

sigmaMagnitude - the standard deviation on the magnitude (in percents)

sigmaDirection - the standard deviation on the direction (in radians)

Returns:

a 3-by-3 covariance matrix modeling the uncertainty on the maneuver's magnitude and direction (in the same frame as ΔV)

Throws:

MathArithmeticException - if the norm of the provided ΔV vector is close to zero (<ε), but not exactly equal to zero

getCovarianceMatrix6x6

public static SymmetricMatrix getCovarianceMatrix6x6(Vector3D deltaV,
                                                     double sigmaMagnitude,
                                                     double sigmaDirection)

Computes the covariance matrix modeling the uncertainty on an object's position and velocity induced by the uncertainty on a maneuver's magnitude and direction.

This methods assumes the uncertainty on the maneuver's direction follows a spherical Gaussian distribution around the provided ΔV vector. The uncertainty on the maneuver's magnitude is assumed to follow an uncorrelated Gaussian distribution. Both uncertainties are proportional to the norm of ΔV.

Parameters:

deltaV - the maneuver's ΔV (in any frame)

sigmaMagnitude - the standard deviation on the magnitude (in percents)

sigmaDirection - the standard deviation on the direction (in radians)

Returns:

a 6-by-6 covariance matrix modeling the uncertainty on an object's position and velocity induced by the uncertainty on the maneuver's magnitude and direction (in the same frame as ΔV)

Throws:

MathArithmeticException - if the norm of the provided ΔV vector is close to zero (<ε), but not exactly equal to zero

getMeanDeltaV

public static Vector3D getMeanDeltaV(Vector3D deltaV,
                                     double sigmaDirection)

Computes the mean ΔV vector of the distribution modeling the uncertainty on a maneuver's magnitude and direction.

This methods assumes the uncertainty on the maneuver's direction follows a spherical Gaussian distribution around the provided ΔV vector. The uncertainty on the maneuver's magnitude is assumed to follow an uncorrelated Gaussian distribution. Both uncertainties are proportional to the norm of ΔV.

Parameters:

deltaV - the maneuver's ΔV (in any frame)

sigmaDirection - the standard deviation on the direction (in radians)

Returns:

the mean ΔV vector of the distribution modeling the uncertainty on a maneuver's magnitude and direction

Throws:

MathArithmeticException - if the norm of the provided ΔV vector is close to zero (<ε), but not exactly equal to zero