Learning characteristics of adaptive lattice filtering algorithms

This paper describes the performance and learning characteristics of the continuously adaptive lattice form for prediction-error filtering. Quantitative relationships are developed for convergence behavior, and procedures are described for selection of the adaptive weighting constant and filter order. Burg's algorithm is used to calculate the reflection coefficients of the filter. Based on this algorithm, two recursive relationships are developed to calculate the coefficients iteratively, one form assuming a stationary input signal, and a more complex form not making this assumption. A quantitative exposition of the convergence behavior in terms of an adaptive weighting constant is set down for these relationships for the first-order filter. Careful attention is given to the decoupling of higher filter orders, leading to the creation of a decoupling constant for the stationary signal case. Higher order convergence and the factors affecting it are examined, resulting in a procedure for choosing the adaptive weighting constant based on the input signal characteristics. Properties of the filter in the spectral domain are also examined. This leads to selection criteria for choosing the filter order, based on the signal characteristics. Application of the filter to the problem of radar clutter discrimination is presented and discussed.