mrpt::poses::CPose3DPDFGaussian Class Reference

Declares a class that represents a Probability Density function (PDF) of a 3D pose $p(\mathbf{x}) = [x ~ y ~ z ~ yaw ~ pitch ~ roll]^t$ . More...

#include <mrpt/poses/CPose3DPDFGaussian.h>

Inheritance diagram for mrpt::poses::CPose3DPDFGaussian:

List of all members.

Public Member Functions

CPose3DPDFGaussian ()

Default constructor.

CPose3DPDFGaussian (const CPose3D &init_Mean)

Constructor.

CPose3DPDFGaussian (const CPose3D &init_Mean, const CMatrixD &init_Cov)

Constructor.

CPose3DPDFGaussian (const CPosePDFGaussian &o)

Constructor from a Gaussian 2D pose PDF (sets to 0 the missing variables z,pitch, and roll).

void getMean (CPose3D &mean_pose) const

Returns an estimate of the pose, (the mean, or mathematical expectation of the PDF), computed as a weighted average over all m_particles.

void getCovarianceAndMean (CMatrixDouble66 &cov, CPose3D &mean_point) const

Returns an estimate of the pose covariance matrix (6x6 cov matrix) and the mean, both at once.

void copyFrom (const CPose3DPDF &o)

Copy operator, translating if necesary (for example, between particles and gaussian representations).

void copyFrom (const CPosePDF &o)

Copy operator, translating if necesary (for example, between particles and gaussian representations).

void saveToTextFile (const std::string &file) const

Save PDF's particles to a text file, containing the 3D pose in the first line, then the covariance matrix in next 3 lines.

void changeCoordinatesReference (const CPose3D &newReferenceBase)

This can be used to convert a PDF from local coordinates to global, providing the point (newReferenceBase) from which "to project" the current pdf.

void rotateCov (const double &ang)

Rotate the covariance matrix by replacing it by $\mathbf{R}~\mathbf{COV}~\mathbf{R}^t$ , where $\mathbf{R} = ...$ .

void drawSingleSample (CPose3D &outPart) const

Draws a single sample from the distribution.

void drawManySamples (size_t N, std::vector< vector_double > &outSamples) const

Draws a number of samples from the distribution, and saves as a list of 1x6 vectors, where each row contains a (x,y,phi) datum.

void bayesianFusion (CPose3DPDF &p1, CPose3DPDF &p2)

Bayesian fusion of two points gauss.

void inverse (CPose3DPDF &o) const

Returns a new PDF such as: NEW_PDF = (0,0,0) - THIS_PDF.

void operator+= (const CPose3D &Ap)

Makes: thisPDF = thisPDF + Ap, where "+" is pose composition (both the mean, and the covariance matrix are updated).

void operator+= (const CPose3DPDFGaussian &Ap)

Makes: thisPDF = thisPDF + Ap, where "+" is pose composition (both the mean, and the covariance matrix are updated) (see formulas on the top of this page).

double evaluatePDF (const CPose3D &x) const

Evaluates the PDF at a given point.

double evaluateNormalizedPDF (const CPose3D &x) const

Evaluates the ratio PDF(x) / PDF(MEAN), that is, the normalized PDF in the range [0,1].

double mahalanobisDistanceTo (const CPose3DPDFGaussian &theOther)

Computes the Mahalanobis distance between the centers of two Gaussians.

void getCovSubmatrix2D (CMatrixDouble &out_cov) const

Returns a 3x3 matrix with submatrix of the covariance for the variables (x,y,yaw) only.

Static Public Member Functions

static void jacobiansPoseComposition (const CPose3DPDFGaussian &x, const CPose3DPDFGaussian &u, CMatrixDouble66 &df_dx, CMatrixDouble66 &df_du)

This static method computes the pose composition Jacobians, with these formulas:.

Public Attributes

CPose3D mean

The mean value.

CMatrixDouble66 cov

The 6x6 covariance matrix.

Protected Member Functions

void assureSymmetry ()

Assures the symmetry of the covariance matrix (eventually certain operations in the math-coprocessor lead to non-symmetric matrixes!).

Detailed Description

Declares a class that represents a Probability Density function (PDF) of a 3D pose $p(\mathbf{x}) = [x ~ y ~ z ~ yaw ~ pitch ~ roll]^t$ .

This class implements that PDF using a mono-modal Gaussian distribution. See mrpt::poses::CPose3DPDF for more details.

The formulas used for pose/uncertainty composition in the "CPose3DPDFGaussian::operator+=" and "CPose3DPDFGaussian::jacobiansPoseComposition":

We compose the pose "x" by adding "u" to it, obtaining "y":

$y = x \oplus u$

The mean of "y" is:

$\hat{y} = \left( \begin{array}{l} \hat{x}_x + R_{11}\hat{u}_x + R_{12}\hat{u}_y + R_{13}\hat{u}_z \\ \hat{x}_y + R_{21}\hat{u}_x + R_{22}\hat{u}_y + R_{23}\hat{u}_z \\ \hat{x}_z + R_{31}\hat{u}_x + R_{32}\hat{u}_y + R_{33}\hat{u}_z \\ \hat{x}_{yaw} + \hat{u}_{yaw} \\ \hat{x}_p + \hat{u}_p \\ \hat{x}_r + \hat{u}_r \end{array} \right)$

And its covariance:

$\Sigma_y = \frac{df}{dx} \Sigma_x \frac{df}{dx}^\top + \frac{df}{du} \Sigma_u \frac{df}{du}^\top$

With the Jacobians being computed by CPose3DPDFGaussian::jacobiansPoseComposition (see that method documentation for the exact formulas).

See also:: CPose3D, CPose3DPDF, CPose3DPDFParticles

Definition at line 76 of file CPose3DPDFGaussian.h.

Constructor & Destructor Documentation

mrpt::poses::CPose3DPDFGaussian::CPose3DPDFGaussian ( )

Default constructor.

mrpt::poses::CPose3DPDFGaussian::CPose3DPDFGaussian ( const CPose3D & init_Mean )

Constructor.

mrpt::poses::CPose3DPDFGaussian::CPose3DPDFGaussian	(	const CPose3D &	init_Mean,
		const CMatrixD &	init_Cov
	)

Constructor.

mrpt::poses::CPose3DPDFGaussian::CPose3DPDFGaussian ( const CPosePDFGaussian & o )

Constructor from a Gaussian 2D pose PDF (sets to 0 the missing variables z,pitch, and roll).

Member Function Documentation

void mrpt::poses::CPose3DPDFGaussian::assureSymmetry ( ) [protected]

Assures the symmetry of the covariance matrix (eventually certain operations in the math-coprocessor lead to non-symmetric matrixes!).

void mrpt::poses::CPose3DPDFGaussian::bayesianFusion	(	CPose3DPDF &	p1,
		CPose3DPDF &	p2
	)			`[virtual]`

Bayesian fusion of two points gauss.

distributions, then save the result in this object. The process is as follows:

(x1,S1): Mean and variance of the p1 distribution.
(x2,S2): Mean and variance of the p2 distribution.
(x,S): Mean and variance of the resulting distribution.

S = (S1^-1 + S2^-1)^-1; x = S * ( S1^-1*x1 + S2^-1*x2 );

Implements mrpt::poses::CPose3DPDF.

void mrpt::poses::CPose3DPDFGaussian::changeCoordinatesReference ( const CPose3D & newReferenceBase ) [virtual]

This can be used to convert a PDF from local coordinates to global, providing the point (newReferenceBase) from which "to project" the current pdf.

Result PDF substituted the currently stored one in the object.

Implements mrpt::utils::CProbabilityDensityFunction< CPose3D, 6 >.

void mrpt::poses::CPose3DPDFGaussian::copyFrom ( const CPosePDF & o )

Copy operator, translating if necesary (for example, between particles and gaussian representations).

void mrpt::poses::CPose3DPDFGaussian::copyFrom ( const CPose3DPDF & o ) [virtual]

Copy operator, translating if necesary (for example, between particles and gaussian representations).

Implements mrpt::poses::CPose3DPDF.

void mrpt::poses::CPose3DPDFGaussian::drawManySamples	(	size_t	N,
		std::vector< vector_double > &	outSamples
	)			const `[virtual]`

Draws a number of samples from the distribution, and saves as a list of 1x6 vectors, where each row contains a (x,y,phi) datum.

Reimplemented from mrpt::utils::CProbabilityDensityFunction< CPose3D, 6 >.

void mrpt::poses::CPose3DPDFGaussian::drawSingleSample ( CPose3D & outPart ) const

Draws a single sample from the distribution.

double mrpt::poses::CPose3DPDFGaussian::evaluateNormalizedPDF ( const CPose3D & x ) const

Evaluates the ratio PDF(x) / PDF(MEAN), that is, the normalized PDF in the range [0,1].

double mrpt::poses::CPose3DPDFGaussian::evaluatePDF ( const CPose3D & x ) const

Evaluates the PDF at a given point.

void mrpt::poses::CPose3DPDFGaussian::getCovarianceAndMean	(	CMatrixDouble66 &	cov,
		CPose3D &	mean_point
	)			const

Returns an estimate of the pose covariance matrix (6x6 cov matrix) and the mean, both at once.

See also:: getMean

void mrpt::poses::CPose3DPDFGaussian::getCovSubmatrix2D ( CMatrixDouble & out_cov ) const

Returns a 3x3 matrix with submatrix of the covariance for the variables (x,y,yaw) only.

void mrpt::poses::CPose3DPDFGaussian::getMean ( CPose3D & mean_pose ) const

Returns an estimate of the pose, (the mean, or mathematical expectation of the PDF), computed as a weighted average over all m_particles.

See also:: getCovariance

void mrpt::poses::CPose3DPDFGaussian::inverse ( CPose3DPDF & o ) const [virtual]

Returns a new PDF such as: NEW_PDF = (0,0,0) - THIS_PDF.

Implements mrpt::poses::CPose3DPDF.

static void mrpt::poses::CPose3DPDFGaussian::jacobiansPoseComposition	(	const CPose3DPDFGaussian &	x,
		const CPose3DPDFGaussian &	u,
		CMatrixDouble66 &	df_dx,
		CMatrixDouble66 &	df_du
	)			`[static]`

This static method computes the pose composition Jacobians, with these formulas:.

        df_dx =
        [ 1, 0, 0, -sin(yaw)*cos(p)*xu+(-sin(yaw)*sin(p)*sin(r)-cos(yaw)*cos(r))*yu+(-sin(yaw)*sin(p)*cos(r)+cos(yaw)*sin(r))*zu, -cos(yaw)*sin(p)*xu+cos(yaw)*cos(p)*sin(r)*yu+cos(yaw)*cos(p)*cos(r)*zu, (cos(yaw)*sin(p)*cos(r)+sin(yaw)*sin(r))*yu+(-cos(yaw)*sin(p)*sin(r)+sin(yaw)*cos(r))*zu]
        [ 0, 1, 0,    cos(yaw)*cos(p)*xu+(cos(yaw)*sin(p)*sin(r)-sin(yaw)*cos(r))*yu+(cos(yaw)*sin(p)*cos(r)+sin(yaw)*sin(r))*zu, -sin(yaw)*sin(p)*xu+sin(yaw)*cos(p)*sin(r)*yu+sin(yaw)*cos(p)*cos(r)*zu, (sin(yaw)*sin(p)*cos(r)-cos(yaw)*sin(r))*yu+(-sin(yaw)*sin(p)*sin(r)-cos(yaw)*cos(r))*zu]
        [ 0, 0, 1,                                                                                                             0, -cos(p)*xu-sin(p)*sin(r)*yu-sin(p)*cos(r)*zu,                            cos(p)*cos(r)*yu-cos(p)*sin(r)*zu]
        [ 0, 0, 0, 1, 0, 0]
        [ 0, 0, 0, 0, 1, 0]
        [ 0, 0, 0, 0, 0, 1]

        df_du =
        [ cos(yaw)*cos(p), cos(yaw)*sin(p)*sin(r)-sin(yaw)*cos(r), cos(yaw)*sin(p)*cos(r)+sin(yaw)*sin(r), 0, 0, 0]
        [ sin(yaw)*cos(p), sin(yaw)*sin(p)*sin(r)+cos(yaw)*cos(r), sin(yaw)*sin(p)*cos(r)-cos(yaw)*sin(r), 0, 0, 0]
        [ -sin(p),         cos(p)*sin(r),                          cos(p)*cos(r),                          0, 0, 0]
        [ 0, 0, 0, 1, 0, 0]
        [ 0, 0, 0, 0, 1, 0]
        [ 0, 0, 0, 0, 0, 1]

double mrpt::poses::CPose3DPDFGaussian::mahalanobisDistanceTo ( const CPose3DPDFGaussian & theOther )

Computes the Mahalanobis distance between the centers of two Gaussians.

The variables with a variance exactly equal to 0 are not taken into account in the process, but "infinity" is returned if the corresponding elements are not exactly equal.

void mrpt::poses::CPose3DPDFGaussian::operator+= ( const CPose3DPDFGaussian & Ap )

Makes: thisPDF = thisPDF + Ap, where "+" is pose composition (both the mean, and the covariance matrix are updated) (see formulas on the top of this page).

void mrpt::poses::CPose3DPDFGaussian::operator+= ( const CPose3D & Ap )

Makes: thisPDF = thisPDF + Ap, where "+" is pose composition (both the mean, and the covariance matrix are updated).

void mrpt::poses::CPose3DPDFGaussian::rotateCov ( const double & ang )

Rotate the covariance matrix by replacing it by $\mathbf{R}~\mathbf{COV}~\mathbf{R}^t$ , where $\mathbf{R} = ...$ .

void mrpt::poses::CPose3DPDFGaussian::saveToTextFile ( const std::string & file ) const [virtual]

Save PDF's particles to a text file, containing the 3D pose in the first line, then the covariance matrix in next 3 lines.

Implements mrpt::utils::CProbabilityDensityFunction< CPose3D, 6 >.

Member Data Documentation

CMatrixDouble66 mrpt::poses::CPose3DPDFGaussian::cov

The 6x6 covariance matrix.

Definition at line 109 of file CPose3DPDFGaussian.h.

CPose3D mrpt::poses::CPose3DPDFGaussian::mean

The mean value.

Definition at line 105 of file CPose3DPDFGaussian.h.


Public Member Functions
	CPose3DPDFGaussian ()
	Default constructor.
	CPose3DPDFGaussian (const CPose3D &init_Mean)
	Constructor.
	CPose3DPDFGaussian (const CPose3D &init_Mean, const CMatrixD &init_Cov)
	Constructor.
	CPose3DPDFGaussian (const CPosePDFGaussian &o)
	Constructor from a Gaussian 2D pose PDF (sets to 0 the missing variables z,pitch, and roll).
void	getMean (CPose3D &mean_pose) const
	Returns an estimate of the pose, (the mean, or mathematical expectation of the PDF), computed as a weighted average over all m_particles.
void	getCovarianceAndMean (CMatrixDouble66 &cov, CPose3D &mean_point) const
	Returns an estimate of the pose covariance matrix (6x6 cov matrix) and the mean, both at once.
void	copyFrom (const CPose3DPDF &o)
	Copy operator, translating if necesary (for example, between particles and gaussian representations).
void	copyFrom (const CPosePDF &o)
	Copy operator, translating if necesary (for example, between particles and gaussian representations).
void	saveToTextFile (const std::string &file) const
	Save PDF's particles to a text file, containing the 3D pose in the first line, then the covariance matrix in next 3 lines.
void	changeCoordinatesReference (const CPose3D &newReferenceBase)
	This can be used to convert a PDF from local coordinates to global, providing the point (newReferenceBase) from which "to project" the current pdf.
void	rotateCov (const double &ang)
	Rotate the covariance matrix by replacing it by $\mathbf{R}~\mathbf{COV}~\mathbf{R}^t$ , where $\mathbf{R} = ...$ .
void	drawSingleSample (CPose3D &outPart) const
	Draws a single sample from the distribution.
void	drawManySamples (size_t N, std::vector< vector_double > &outSamples) const
	Draws a number of samples from the distribution, and saves as a list of 1x6 vectors, where each row contains a (x,y,phi) datum.
void	bayesianFusion (CPose3DPDF &p1, CPose3DPDF &p2)
	Bayesian fusion of two points gauss.
void	inverse (CPose3DPDF &o) const
	Returns a new PDF such as: NEW_PDF = (0,0,0) - THIS_PDF.
void	operator+= (const CPose3D &Ap)
	Makes: thisPDF = thisPDF + Ap, where "+" is pose composition (both the mean, and the covariance matrix are updated).
void	operator+= (const CPose3DPDFGaussian &Ap)
	Makes: thisPDF = thisPDF + Ap, where "+" is pose composition (both the mean, and the covariance matrix are updated) (see formulas on the top of this page).
double	evaluatePDF (const CPose3D &x) const
	Evaluates the PDF at a given point.
double	evaluateNormalizedPDF (const CPose3D &x) const
	Evaluates the ratio PDF(x) / PDF(MEAN), that is, the normalized PDF in the range [0,1].
double	mahalanobisDistanceTo (const CPose3DPDFGaussian &theOther)
	Computes the Mahalanobis distance between the centers of two Gaussians.
void	getCovSubmatrix2D (CMatrixDouble &out_cov) const
	Returns a 3x3 matrix with submatrix of the covariance for the variables (x,y,yaw) only.
Static Public Member Functions
static void	jacobiansPoseComposition (const CPose3DPDFGaussian &x, const CPose3DPDFGaussian &u, CMatrixDouble66 &df_dx, CMatrixDouble66 &df_du)
	This static method computes the pose composition Jacobians, with these formulas:.
Public Attributes
CPose3D	mean
	The mean value.
CMatrixDouble66	cov
	The 6x6 covariance matrix.
Protected Member Functions
void	assureSymmetry ()
	Assures the symmetry of the covariance matrix (eventually certain operations in the math-coprocessor lead to non-symmetric matrixes!).