Title :
Kronecker Product Based Second Order Approximation of Mean Value and Covariance Matrix in Nonlinear Transformations
Author :
Manolakis, Dimitris E.
Author_Institution :
Dept of Autom., Alexander Technol. Educ. Inst. of Thessaloniki, Thessaloniki, Greece
Abstract :
This paper derives new formulae for the approximations of the mean value and the covariance matrix of a random vector which is derived as a nonlinear transformation of another random vector. Towards this purpose, it is first proposed to formulate the Taylor series expansion by using Kronecker product operators along with partial derivatives block matrices. This formulation facilitates the mathematical manipulation of higher order terms in multidimensional systems. The final expressions for the mean value and covariance matrix are simple in block matrix notation, convenient and easy to implement. The analytical expressions are evaluated and verified in a typical nonlinear transformation faced in navigation systems.
Keywords :
Kalman filters; approximation theory; covariance matrices; nonlinear filters; Kronecker product based second order approximation; Taylor series expansion; block matrix notation; covariance matrix; extended Kalman filtering; mathematical manipulation; mean value approximation; multidimensional systems; navigation systems; nonlinear transformation; partial derivatives block matrices; random vector; Approximation methods; Covariance matrix; Filtering theory; Multidimensional systems; Nonlinear systems; Taylor series; Covariance matrix; Kronecker product; Taylor series; extended Kalman filtering; mean value; nonlinear systems;
Journal_Title :
Signal Processing Letters, IEEE
DOI :
10.1109/LSP.2010.2093128
