frc::S3SigmaPoints< States > Class Template Reference

Generates sigma points and weights according to Papakonstantinou's paper[1] for the UnscentedKalmanFilter class. More...

#include <frc/estimator/S3SigmaPoints.h>

Public Member Functions
	S3SigmaPoints (double alpha=1e-3, double beta=2)
	Constructs a generator for Papakonstantinou sigma points.
Matrixd< States, NumSigmas >	SquareRootSigmaPoints (const Vectord< States > &x, const Matrixd< States, States > &S) const
	Computes the sigma points for an unscented Kalman filter given the mean (x) and square-root covariance (S) of the filter.
const Vectord< NumSigmas > &	Wm () const
	Returns the weight for each sigma point for the mean.
double	Wm (int i) const
	Returns an element of the weight for each sigma point for the mean.
const Vectord< NumSigmas > &	Wc () const
	Returns the weight for each sigma point for the covariance.
double	Wc (int i) const
	Returns an element of the weight for each sigma point for the covariance.

Static Public Attributes
static constexpr int	NumSigmas = States + 2

Detailed Description

template<int States>
class frc::S3SigmaPoints< States >

Generates sigma points and weights according to Papakonstantinou's paper[1] for the UnscentedKalmanFilter class.

It parameterizes the sigma points using alpha and beta terms. Unless you know better, this should be your default choice due to its high accuracy and performance.

[1] K. Papakonstantinou "A Scaled Spherical Simplex Filter (S3F) with a decreased n + 2 sigma points set size and equivalent 2n + 1 Unscented Kalman Filter (UKF) accuracy"

Template Parameters

States

The dimenstionality of the state. States + 2 weights will be generated.

Constructor & Destructor Documentation

S3SigmaPoints()

template<int States>

frc::S3SigmaPoints< States >::S3SigmaPoints ( double alpha = 1e-3, double beta = 2 )

inlineexplicit

Constructs a generator for Papakonstantinou sigma points.

Parameters

alpha	Determines the spread of the sigma points around the mean. Usually a small positive value (1e-3).
beta	Incorporates prior knowledge of the distribution of the mean. For Gaussian distributions, beta = 2 is optimal.

Member Function Documentation

SquareRootSigmaPoints()

template<int States>

Matrixd< States, NumSigmas > frc::S3SigmaPoints< States >::SquareRootSigmaPoints ( const Vectord< States > & x, const Matrixd< States, States > & S ) const

inline

Computes the sigma points for an unscented Kalman filter given the mean (x) and square-root covariance (S) of the filter.

Parameters

x	An array of the means.
S	Square-root covariance of the filter.

Returns

Two dimensional array of sigma points. Each column contains all of the sigmas for one dimension in the problem space. Ordered by Xi_0, Xi_{1..n+1}.

Wc() [1/2]

template<int States>

const Vectord< NumSigmas > & frc::S3SigmaPoints< States >::Wc ( ) const

inline

Returns the weight for each sigma point for the covariance.

Wc() [2/2]

template<int States>

double frc::S3SigmaPoints< States >::Wc ( int i ) const

inline

Returns an element of the weight for each sigma point for the covariance.

Parameters

i	Element of vector to return.

Wm() [1/2]

template<int States>

const Vectord< NumSigmas > & frc::S3SigmaPoints< States >::Wm ( ) const

inline

Returns the weight for each sigma point for the mean.

Wm() [2/2]

template<int States>

double frc::S3SigmaPoints< States >::Wm ( int i ) const

inline

Returns an element of the weight for each sigma point for the mean.

Parameters

i	Element of vector to return.

Member Data Documentation

NumSigmas

template<int States>

int frc::S3SigmaPoints< States >::NumSigmas = States + 2

staticconstexpr

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The documentation for this class was generated from the following file:

• frc/estimator/S3SigmaPoints.h