MatrixKalmanFilter Class Reference [Auxilliary Tools]

Auxilliary Tool: A Kalman Filter for estimating the values of a matrix, which is like doing online linear regression from a probability theory perspective. More...

#include <MatrixKalmanFilter.h>

List of all members.

Public Member Functions
MatrixKalmanFilter &	operator= (const MatrixKalmanFilter &rhs)
	Assignment Operator. Perform a deep copy of another MatrixKalmanFilter.
	MatrixKalmanFilter (const MatrixKalmanFilter &copy)
	Copy Constructor. Perform a deep copy of another MatrixKalmanFilter.
	MatrixKalmanFilter ()
	Default Constructor. Initializes a trivial Matrix Kalman Filter with one state and one observation (i.e. it would estimate a scalar value).
	MatrixKalmanFilter (size_t numStates, size_t numObs=1)
	Main Constructor. Initialize with numStates (size of the input vector x) and numObs (size of the output vector y in xC=y).
virtual	~MatrixKalmanFilter ()
	Destructor.
void	setMuPrior (double val=0.0)
	Set the mean of the estimate of C to have each element with identical value.
void	setSigmaPrior (double diagval=1.0)
	Set the uncertainty in the estimate of C to a diagonal matrix with identical values along the diagonal.
void	setR (double diagval=0.0)
	Set R, the drift in the estimate of C, to a diagonal matrix with identical values along the diagonal.
void	setQ (double diagval=1.0)
	Set Q, the noise in observations y, to a diagonal matrix with identical values along the diagonal.
void	setMuPrior (const cv::Mat &muPrior)
	Set the mean of the estimate of C to a specific matrix.
void	setSigmaPrior (const cv::Mat &sigmaPrior)
	Set the uncertainty in the estimate of C to a specific matrix.
void	setR (const cv::Mat &rVal)
	Set R, the drift in the estimate of C, to a specific matrix.
void	setQ (const cv::Mat &qVal)
	Set Q, the noise in observations y, to a specific matrix.
void	setQDiag (const cv::Mat &qVal)
	Set Q, the noise in observations y, to be a diagonal matrix with values given by the vector qVal. qVal must have numObsx1 elements.
void	setNumStatesAndObs (size_t numStates=1, size_t numObs=1)
	Reinitialize this MatrixKalmanFilter to have a new number of states and observations. This resets all default values for Mu, Sigma, Q, and R.
void	getObsMean (const cv::Mat &x, cv::Mat &y)
	Compute the expected value of y given x and the current estimate of C, i.e. Cx = y.
double	obsLogLikelihood (const cv::Mat &x, const cv::Mat &y)
	Compute log likelihood of y given x, based on the current mean and variance in the estimate of C.
likelihood	modelLogLikelihood (const cv::Mat &x, const cv::Mat &y)
	Compute log likelihood of y given x, based on the current mean and variance in the estimate of C.
void	updateModel (const cv::Mat &x, const cv::Mat &y)
	Update the current mean and variance in the estimate of C based on a newly observed input (x) and output (y)
void	rectify ()
	Rectify the estimate of C so that no elements are less than 0. Calling this after updateModel will approximate non-negative matrix factorization.
Public Attributes
cv::Mat	mu
	The vectorized mean of the current C estimate, row major. This vector has size (numStates * numObs) x 1. This is the actual underlying estimate data. It is exposed for convenient inspection. Don't modify it.
cv::Mat	Sigma
	The covariance matrix for the current C estimate. This vector has size (numStates * numObs) x (numStates * numObs) . This is the actual underlying estimate data. It is exposed for convenient inspection. Don't modify it.
Friends
std::ostream &	operator<< (std::ostream &ofs, const MatrixKalmanFilter &feat)
	Write to a file.
std::istream &	operator>> (std::istream &ifs, MatrixKalmanFilter &feat)
	Read from a file.

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Detailed Description

Auxilliary Tool: A Kalman Filter for estimating the values of a matrix, which is like doing online linear regression from a probability theory perspective.

Linear Regression problems take the form Cx = y. x and y are observed, and C must be inferred from data. The Kalman Filter gives a Mean estimate of the values of C's elements, and maintains a covariance matrix Sigma of uncertainties on those estimates.

There are many parameters to a Kalman Filter that may be set:

It is useful to think of there being a stochastic relation between Cx and y, specifically y is drawn from a normal distribution with mean Cx and Covariance Q.

It is also useful to think of there being a drift in C, i.e. its values may change over time. This drift is 0 mean, and has covariance R. If R is 0, you are making a strong assertion that the elements of C will never change.

Finally, you may set a prior mean estimate Mu of C, and a prior uncertainty, Sigma.

Author:

Nicholas Butko

Date:

2010 version 0.4

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Constructor & Destructor Documentation

MatrixKalmanFilter::MatrixKalmanFilter	(	size_t	numStates,
		size_t	numObs = 1
	)

Main Constructor. Initialize with numStates (size of the input vector x) and numObs (size of the output vector y in xC=y).

MuPrior, SigmaPrior, R, and Q are set to default values. Use setter functions to modify them.

Parameters:

numStates	The number of inputs, i.e. the length of the vector x in Cx=y, when we are trying to estimate C. The matrix C has size numStates x numObs.
numObs	The number of outputs, i.e. the length of the vector y in Cx=y.The matrix C has size numStates x numObs.

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Member Function Documentation

void MatrixKalmanFilter::getObsMean	(	const cv::Mat &	x,
		cv::Mat &	y
	)

Compute the expected value of y given x and the current estimate of C, i.e. Cx = y.

Parameters:

x	Input vector
y	Output vector: computation is passed back out by y.

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

• /Users/nick/projects/NickThesis/Code/OpenCV/src/MatrixKalmanFilter.h
• /Users/nick/projects/NickThesis/Code/OpenCV/src/MatrixKalmanFilter.cpp