Filtering for linear systems driven by fractional Brownian motion

Abstract

In this paper we study continuous time filtering for linear multidimensional 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 optimum error covariance (matrix-valued) functions and the optimum 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.