A Generalised Mixed Norm Stochastic Gradient Algorithm

A novel stochastic gradient algorithm for finite impulse response (FIR) adaptive filters, termed the least sum of exponentials (LSE), is introduced. In order to provide a generalisation of the class of weighted mixed norm algorithms and at the same time avoid problems associated with a large number of free paramaters of such algorithms, LSE is derived by minimising a sum of error exponentials. A rigourous mathematical analysis is provided, resulting in closed form expressions for the optimal weights and the upper bound of the learning rate. The analysis is supported by simulations in a system identification setting.

[1]  J. Chambers,et al.  A robust mixed-norm adaptive filter algorithm , 1997, IEEE Signal Processing Letters.

[2]  S. Thomas Alexander,et al.  Adaptive Signal Processing , 1986, Texts and Monographs in Computer Science.

[3]  C. Richard Johnson,et al.  Exploiting sparsity in adaptive filters , 2002, IEEE Trans. Signal Process..

[4]  Manfred K. Warmuth,et al.  Exponentiated Gradient Versus Gradient Descent for Linear Predictors , 1997, Inf. Comput..

[5]  Danilo P. Mandic,et al.  A normalized mixed-norm adaptive filtering algorithm robust under impulsive noise interference , 2003, 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)..

[6]  Allan Kardec Barros,et al.  An algorithm based on the even moments of the error , 2003, 2003 IEEE XIII Workshop on Neural Networks for Signal Processing (IEEE Cat. No.03TH8718).

[7]  S. Lim.  Combined LMS / F algorithm , 2022 .

[8]  Jacob Benesty,et al.  An exponentiated gradient adaptive algorithm for blind identification of sparse SIMO systems , 2004, 2004 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[9]  Bernard Widrow,et al.  The least mean fourth (LMF) adaptive algorithm and its family , 1984, IEEE Trans. Inf. Theory.

[10]  Anthony G. Constantinides,et al.  LMS+F algorithm , 1995 .

[11]  Anthony G. Constantinides,et al.  Least-mean kurtosis: a novel higher-order statistics based adaptive filtering algorithm , 1994 .

[12]  Neil J. Bershad,et al.  Analysis of the normalized LMS algorithm with Gaussian inputs , 1986, IEEE Trans. Acoust. Speech Signal Process..