Some new non-Riccati algorithms for continuous-time Kalman-Bucy filtering

In this paper we consider the problem of determining the error covariance matrix (and hence the gain) in Kalman-Bucy filtering, utilizing the smallest possible number of time-invariant, first-order differential equations. The traditional method requires the solution of a matrix Riccati equation containing 1/2n(n+1) such equations. Here we demonstrate that, under certain conditions, onlypn equations are needed, wherep is a number which often is much smaller thann. This is an improvement on the previous non-Riccati algorithms developed by Kailath and Lindquist. The reduction is achieved by exploiting certain time-invariant integrals of this system. This paper complements our previous papers 11, 12] in that the present method is more direct.This work was supported by the National Science Foundation under grant MPS 75-07028.