Nonlinear filtering using the wavelet transform

Abstract

We present a fast nonlinear filtering algorithm that propagates the entire underlying conditional probability density functions recursively in a computationally efficient manner using the discrete wavelet transform. With the multiresolution analysis capability offered by the wavelet transform, we can speed up the computation by ignoring the high-frequency details of the probability density function up to a certain level. The level of the wavelet decomposition can be determined at each time step adaptively. According to our simulation, the proposed algorithm appears to be potentially more accurate than the widely used extended Kalman filter. (C) 2000 Elsevier Science B.V. All rights reserved.