Adaptive lattice filters for systems of space-time processing of non-stationary Gaussian processes

David I. Lekhovytskiy

doi:10.3103/S0735272718110018

Authors

David I. Lekhovytskiy Kvant Radar Systems Scientific Research Institute, Ukraine https://orcid.org/0000-0001-7519-3239

DOI:

https://doi.org/10.3103/S0735272718110018

Keywords:

space-time processing, adaptive lattice filter, estimate correlation matrix, K-rank modification, combined algorithm, computational complexity, numerical stability, finite capacity, digital signal processor

Abstract

Adaptive systems protecting pulse radars from non-stationary in time (range) clutter echoes are usually tuned using training vectors composed of complex amplitudes of input signals and comprising a finite-length “sliding window” of data. From any current range gate to a subsequent one, a training sample is partially updated (or modified) by means of excluding the “old” training vectors (correspond to the current range gate) and including the “new” ones (correspond to the next range gate). As a consequence, respective estimates of adaptive system parameters are corrected according to a modified sample correlation matrix (CM), which is typically a sum of an initial CM and a modifying matrix of rank K ≥ 1. In this case it is possible to avoid re-computing these parameters based on a new training sample of full size and, instead of this, we correct them in an “economical” way employing K-rank modification of a matrix inverse to the CM estimate.

This paper is devoted to comparative analysis of various (K ≥ 1)-rank modification algorithms that correct the parameters of adaptive lattice filters (ALF). Main attention is paid to synthesis as well as theoretical and experimental study of algorithms of direct (K > 1)-rank modification of the ALF parameters. These algorithms attain the said objective omitting the K-fold application of known rank-one (K = 1) modification algorithms. We also synthesize a combined algorithm (CA) of (K ≥ 1)-rank modification of the ALF parameters that is more computationally simple and more numerically robust compared to known algorithms. The ALF employing the CA can serve as an effective tool for solving various tasks of space-time adaptive signal processing in pulse radars of different purpose.

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