Recursive algorithms of adaptive lattice filters adjustment

D. I. Lekhovytskiy; V. P. Riabukha; D. S. Rachkov; A. V. Semeniaka

doi:10.15222/TKEA2016.2-3.26

D. I. Lekhovytskiy Kharkiv National University of Radio Electronics, Kharkiv, Ukraine
V. P. Riabukha Kharkiv National University of Radio Electronics, Kharkiv, Ukraine
D. S. Rachkov Kharkiv National University of Radio Electronics, Kharkiv, Ukraine
A. V. Semeniaka Kharkiv National University of Radio Electronics, Kharkiv, Ukraine

DOI: https://doi.org/10.15222/TKEA2016.2-3.26

Keywords: space-time signal processing, adaptive lattice filter, Levinson’s generalized factorization, Cholesky multiplier, partial correlation coefficients, combined algorithm

Abstract

The authors analyse the algorithms intended for correction of adaptive lattice filters (ALF) parameters under K-rank (K ≥ 1) modification of estimate correlation matrix within a "sliding" over the time (range) data window. The drawbacks of methods that correct the ALF parameters based on K-fold utilization of known algorithms of rank-one (K = 1) modification are discussed. The combined algorithm (CA) of K-rank (K ≥ 1) modification is synthesized. Under considered conditions, the only one-fold utilization of the CA solves the task of ALF parameters correction. The paper demonstrates, that proposed CA reduces the computational complexity and enhances the numerical stability of procedure of ALF parameters correction as compared with the competing methods based on algorithms of rank-one modification.

References

B. Friedlander Lattice filters for adaptive processing. Proc. of the IEEE, 1982, vol. 70, iss. 8, pp. 829-867. http://dx.doi.org/10.1109/PROC.1982.12407

C.F.N. Cowan, P.M. Grant (Eds.) Adaptive Filters, Englewood Cliffs, NJ, Prentice-Hall, Inc., 1985, 308 p.

A.H. Sayed, Fundamentals of Adaptive Filtering, Hoboken, NJ: John Wiley & Sons, Inc., 2003, 1120 p.

D.I. Lekhovytskiy, S.B. Milovanov, I.D. Rakov, B.G. Sverdlov. Universal adaptive lattice filters. Adaptation for a given root of the estimating correlation matrix. Radiophysics and Quantum Electronics, 1992, vol. 35, no. 11-12, pp. 621-636.

D.I. Lekhovytskiy, Y.I. Abramovich. Adaptive lattice filters for band-inverse (TVAR) covariance matrix approximations: theory and practical applications. Proc. of the Int. Radar Symposium 2009, Hamburg, Germany, pp. 535—539.

H. Lev-Ari, T. Kailath. Schur and Levinson algorithms for nonstationary processes. Proc. of the IEEE Int. Conf. Acoustics, Speech and Signal Processing, 1981, Atlanta, USA, vol. 6, pp. 860-864.

K.C. Sharman, T.S. Durrani. Spatial lattice filter for high-resolution spectral analysis of array data. IEEE Proc. F Communications, Radar and Signal Processing, 1983, vol. 130, no. 3, pp. 279-287.

Y.I. Abramovich. A controlled method for adaptive optimization of filters using the criterion of maximum SNR. Radio Eng. Electron. Phys., 1981, vol. 26, no. 3, pp. 87-95.

D.I. Lekhovytskiy. Thirty years experience in development of adaptive lattice filters theory, techniques and testing in Kharkiv. Proc. of the VIII Int. Conf. Antenna Theory and Techniques, 2011, Kyiv, Ukraine, pp. 51-56.

V. Efremov, U. Laurukevich, D. Lekhovytskiy, I. Vylegzhanin, B. Vovshin. Results of theoretical and experimental investigations of meteorological formations power spectrum using “superresolution” methods. Proc. of the Int. Radar Symposium 2009, Hamburg, Germany, pp. 777-784.