On the approximation of optimal realizable linear filters using a Karhunen-Loeve expansion (Corresp.)
Thomas E. Fortmann, Brian D. O. Anderson · IEEE Transactions on Information Theory · 1973
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 firstNeigenvalues and eigenfunctions. The Kalman-Bucy filter for this model provides an approximate realizable linear estimator which approaches the optimal one asN \rightarrow \infty. A bound on the truncation error is obtained.