Filtering for linear systems driven by fractional Brownian motion

Abstract

In this paper we study continuous time filtering for linear systems driven by fractional Brownian motion processes. We present the derivation of the optimum linear filter equations which involve a pair of functional-differential equations giving the error co-variance (matrix-valued) function and the filter. These equations are the appropriate substitutes of the matrix-Riccati differential equation arising in classical Kalman filtering. However the optimum filter has the classical appearance and, as usual, it is driven by the increments of the observed process. Our derivation is based on the same general principles as used in [5,6,7].