Adaptive linear prediction filters based on maximum a posteriori estimation

In this paper, we develop adaptive linear prediction filters in the framework of maximum a posteriori (MAP) estimation. It is shown how priors can be used to regularize the solution and references to known algorithms are made. The adaptive filters are suitable for implementation in real-time and by simulation with an adaptive line enhancer (ALE), it is shown how the parameters of the estimation problem affect the convergence of the adaptive filter. The adaptive line enhancer (ALE) is a widely used adaptive filter to separate periodic signals from additive background noise where it has traditionally been implemented using the least-mean-square (LMS) or recursive-least-square (RLS) filter. The derived algorithms can generally be used in any adaptive filter application with a desired target signal.

[1]  Stephen J. Wright,et al.  Numerical Optimization (Springer Series in Operations Research and Financial Engineering) , 2000 .

[2]  Marc Moonen,et al.  Sparse Linear Prediction and Its Applications to Speech Processing , 2012, IEEE Transactions on Audio, Speech, and Language Processing.

[3]  B. Widrow,et al.  Adaptive noise cancelling: Principles and applications , 1975 .

[4]  Toon van Waterschoot,et al.  Fast algorithms for high-order sparse linear prediction with applications to speech processing , 2016, Speech Commun..

[5]  Christopher M. Bishop,et al.  Pattern Recognition and Machine Learning (Information Science and Statistics) , 2006 .

[6]  K.Venkatesh Prasad,et al.  Fundamentals of statistical signal processing: Estimation theory: by Steven M. KAY; Prentice Hall signal processing series; Prentice Hall; Englewood Cliffs, NJ, USA; 1993; xii + 595 pp.; $65; ISBN: 0-13-345711-7 , 1994 .

[7]  Dong-Yan Huang,et al.  Maximum a Posteriori based Adaptive Algorithms , 2007, 2007 Conference Record of the Forty-First Asilomar Conference on Signals, Systems and Computers.

[8]  Simon Haykin,et al.  Proportionate Adaptation: New Paradigms in Adaptive Filters , 2005 .

[9]  Steven Kay,et al.  Fundamentals Of Statistical Signal Processing , 2001 .

[10]  Ali H. Sayed,et al.  Fundamentals Of Adaptive Filtering , 2003 .

[11]  John H. L. Hansen,et al.  Discrete-Time Processing of Speech Signals , 1993 .

[12]  Ieee Staff.  2017 25th European Signal Processing Conference (EUSIPCO) , 2017 .

[13]  S. Kay.  Fundamentals of statistical signal processing: estimation theory , 1993 .

[14]  Marc Moonen,et al.  Optimally regularized adaptive filtering algorithms for room acoustic signal enhancement , 2008, Signal Process..

[15]  M. Bellanger.  Adaptive filter theory: by Simon Haykin, McMaster University, Hamilton, Ontario L8S 4LB, Canada, in: Prentice-Hall Information and System Sciences Series, published by Prentice-Hall, Englewood Cliffs, NJ 07632, U.S.A., 1986, xvii+590 pp., ISBN 0-13-004052-5 025 , 1987 .