Algorithms and architectures for adaptive least squares signal processing, with applications in magnetoencephalography
Paul S. Lewis · University of Southern California Digital Library · 2015
Least squares techniques are widely used in adaptive signal processing. While algorithms based on least squares are robust and offer rapid convergence properties, they also tend to be complex and computationally intensive. To enable the use of least squares techniques in real-time applications, it is necessary to develop adaptive algorithms that are (1) efficient and numerically stable, and (2) can be readily implemented in hardware. The first part of this work presents a uniform development of general recursive least squares (RLS) algorithms, and multichannel least squares lattice (LSL) algorithms. RLS algorithms are developed for both direct estimators, in which a desired signal is present, and for mixed estimators, in which no desired signal is available, but the signal-to-data cross-correlation is known. In both the RLS and LSL cases, two types of algorithms are developed and compared. Algorithms of the first type are based on a traditional data correlation matrix approach, while those of the second type are based on the more numerically stable QR decomposition of the data matrix. In the second part of this work, new and more flexible techniques of mapping algorithms to array architectures are presented. These techinques, based on the synthesis and manipulation of locally recursive algorithms (LRAs), have evolved from existing data dependence graph-based approaches, but offer the increased flexibility needed to deal with the structural complexities of the RLS and LSL algorithms. Using these techniques, various array architectures are developed for each of the RLS and LSL algorithms and the associated space/time tradeoffs presented. In the final part of this work, the application of these algorithms is demonstrated by their employment in the enhancement of single-trial auditory evoked responses in magnetoencephalography. In addition to demonstrating the algorithms, this application offers an improved method of a posteriori estimation of these signals. (Copies available exclusively from Micrographics Department, Doheny Library, USC, Los Angeles, CA 90089-0182.)