The Design of Chandrasekhar-Type Filters and Smoothers

Abstract

This paper designs two types of Chandrasekhar-type filters and smoothers (type I and II) by deriving the initial-value solutions to the Fredholm integral equations of the second kind which describe the linear least-squares estimates of stationary stochastic signals in the presence of white Gaussian noises. The covariance kernels of the Fredholm integral equations are assumed to be semi-degenerate form given by the sum of weighted exponential functions. Firstly, the Kailath-Geesey and Casti-Kalaba filtering algorithms which belong to the recursive Wiener filters are briefly reviewed. Secondly, two types of Chandrasekhar-type filters and smoothers are given in connection with these algorithms. Also, several interesting results on type II of the Chandrasekhar-type algorithms are presented.