Limited memory optimal filtering

Abstract

Linear and nonlinear optimal filters with limited memory length are developed. The filter output is the conditional probability density function and, in the linear Gaussian case, is the conditional mean and covariance matrix where the conditioning is only on a fixed amount of most recent data. This is related to maximum-likelihood least-squares estimation. These filters have application in problems where standard filters diverge due to dynamical model errors. This is demonstrated via numerical simulations.