Sequential estimation and identification of reflection coefficients by minimax entropy inverse filtering

Abstract

The problem of inverse filtering is formulated as one of finding an optimal joint probability density function for a given sequence of observations. Using the joint entropy of N consecutive observations as a performance index, this paper develops a minimax entropy approach for sequentially estimating the reflection coefficients of a stationary random process from a short observation interval. For the second order discrete-time processes the resulting algorithm has a lattice type digital ladder structure which is quite desirable for its high computational efficiency, low error sensitivity, and stability. The algorithm can also be implemented in a parallel representation. A 4th order linear model example considered here shows excellent identification accuracy, particularly of the frequency peaks. Also, a procedure is described for determining the dimension of the best fitting linear model subject to a fidelity criterion.