Efficient Algorithms for Adaptive Capon and APES Spectral Estimation

In this paper fast algorithms for adaptive Capon and amplitude and phase estimation (APES) methods for spectral analysis of time varying signals, are derived. Fast, stable, nonrecursive formulae are derived, based on time shifting properties of the pertinent variables. As a consequence, efficient frequency domain recursive least squares (RLS) based, as well as fast RLS based algorithms for the adaptive estimation of the power spectra are developed. Stability issues of the frequency domain estimators are considered, and stabilization procedures are proposed. The computational complexity of the proposed algorithms is lower than relevant existing methods. The performance of the proposed algorithms is demonstrated through extensive simulations.

[1]  Erik G. Larsson,et al.  Efficient time-recursive implementation of matched filterbank spectral estimators , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

[2]  Leon Cohen,et al.  Time Frequency Analysis: Theory and Applications , 1994 .

[3]  W. Alexander,et al.  The unbiased gradient type LS algorithm for adaptive spectrum estimation , 1990 .

[4]  Koeng-Mo Sung,et al.  On robust Kalman filtering with forgetting factor for sequential speech analysis , 1997, Signal Process..

[5]  Phillip A. Regalia,et al.  On the numerical stability and accuracy of the conventional recursive least squares algorithm , 1999, IEEE Trans. Signal Process..

[6]  Gregory E. Bottomley,et al.  A novel approach for stabilizing recursive least squares filters , 1991, IEEE Trans. Signal Process..

[7]  S. Lawrence Marple,et al.  Fast algorithms for least-squares-based minimum variance spectral estimation , 2008, Signal Process..

[8]  Petre Stoica,et al.  Spectral Analysis of Signals , 2009 .

[9]  Dirk T. M. Slock,et al.  The fast subsampled-updating recursive least-squares (FSU RLS) algorithm for adaptive filtering based on displacement structure and the FFT , 1994, Signal Process..

[10]  Jian Li,et al.  An adaptive filtering approach to spectral estimation and SAR imaging , 1996, IEEE Trans. Signal Process..

[11]  Silvia Conforto,et al.  Optimal estimation of power spectral density by means of a time-varying autoregressive approach , 1999, Signal Process..

[12]  Jacob Benesty,et al.  Recursive and Fast Recursive Capon Spectral Estimators , 2007, EURASIP J. Adv. Signal Process..

[13]  Erik G. Larsson,et al.  Fast Implementation of Two-Dimensional APES and CAPON Spectral Estimators , 2001, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221).

[14]  G. Lothian,et al.  Spectral Analysis , 1971, Nature.

[15]  T. Söderström,et al.  Adaptive instrumental variable methods for frequency estimation , 1992 .

[16]  Boaz Porat.  Second-order equivalence of rectangular and exponential windows in least-squares estimation of Gaussian autoregressive processes , 1985, IEEE Trans. Acoust. Speech Signal Process..

[17]  George V. Moustakides,et al.  Stabilizing the fast Kalman algorithms , 1989, IEEE Trans. Acoust. Speech Signal Process..

[18]  Uday B. Desai,et al.  A robust recursive least squares algorithm , 1997, IEEE Trans. Signal Process..

[19]  Jian Li,et al.  Efficient implementation of Capon and APES for spectral estimation , 1998 .

[20]  George-Othon Glentis,et al.  A fast algorithm for ∈R-1 factorization of Toeplitz matrices , 1995, Signal Process..

[21]  M. H. Verhaegen,et al.  Round-off error propagation in four generally-applicable, recursive, least-squares estimation schemes , 1989, Autom..

[22]  H..  Round-Off Error Propagation in Four Generally Applicable , Recursive , Least-Squares-Estimation Schemes , .

[23]  Anthony G. Constantinides,et al.  Underdetermined-order recursive least-squares adaptive filtering: the concept and algorithms , 1997, IEEE Trans. Signal Process..

[24]  George-Othon Glentis,et al.  Efficient fast recursive least-squares adaptive complex filtering using real valued arithmetic , 2005, Signal Process..

[25]  W. M. Carey,et al.  Digital spectral analysis: with applications , 1986 .

[26]  Jun Yu Li,et al.  Time-varying complex spectral analysis via recursive APES , 1998 .

[27]  Andreas Spanias,et al.  Adaptive modified covariance algorithms for spectral analysis , 2002, Signal Process..

[28]  George-Othon Glentis,et al.  Efficient least squares adaptive algorithms for FIR transversal filtering , 1999, IEEE Signal Process. Mag..

[29]  T. Kailath,et al.  Numerically stable fast transversal filters for recursive least squares adaptive filtering , 1991, IEEE Trans. Signal Process..

[30]  Bruce R. Musicus.  Fast MLM power spectrum estimation from uniformly spaced correlations , 1985, IEEE Trans. Acoust. Speech Signal Process..

[31]  George-Othon Glentis,et al.  A Fast Algorithm for APES and Capon Spectral Estimation , 2008, IEEE Transactions on Signal Processing.

[32]  Mehmet Tankut Özgen.  Extension of the Capon's spectral estimator to time-frequency analysis and to the analysis of polynomial-phase signals , 2003, Signal Process..

[33]  I. Gohberg,et al.  Complexity of multiplication with vectors for structured matrices , 1994 .

[34]  Y. Lim,et al.  A comment on the computational complexity of sliding FFT , 1992 .

[35]  J. Shynk.  Frequency-domain and multirate adaptive filtering , 1992, IEEE Signal Processing Magazine.

[36]  Francis Grenez,et al.  Time-frequency analysis and instantaneous frequency estimation using two-sided linear prediction , 2005, Signal Process..

[37]  Gerald Matz,et al.  Time-Frequency ARMA Models and Parameter Estimators for Underspread Nonstationary Random Processes , 2007, IEEE Transactions on Signal Processing.

[38]  Phillip A. Regalia,et al.  Numerical stability issues in fast least-squares adaptation algorithms , 1992 .

[39]  Satoru Goto,et al.  On-line spectral estimation of nonstationary time series based on AR model parameter estimation and order selection with a forgetting factor , 1995, IEEE Trans. Signal Process..

[40]  Lennart Ljung,et al.  Error propagation properties of recursive least-squares adaptation algorithms , 1985, Autom..

[41]  Steven Kay,et al.  Modern Spectral Estimation: Theory and Application , 1988 .