On the Approximation of Optimal Realizable Linear Filters Using a Karhunen-Loève Expansion

Abstract

The Karhunen-Loève expansion of a random process is used to derive the impulse response of the optimal realizable linear estimator for the process. The expansion is truncated to yield an approximate state-variable model of the process in terms of the first N eigenvalues and eigenfunctions. The Kalmaa-Bucy filter for this model provides an approximate realizable linear estimator which approaches the optimal one as N → ∞. A bound on the truncation error is obtained. Show more