Least absolute deviation regression and stack filter phase lock loops

Robert Warren Hawley, Purdue University

Abstract

This thesis covers two topics in robust signal processing: algorithms for least absolute deviation regression and stack filter phase lock loops. The iterative algorithms for minimizing absolute error in regression problems are known to suffer from convergence problems when the data contains degeneracies. In this thesis, it is shown that the problem of degeneracy may be easily avoided with only minor modifications to these algorithms. Proof of convergence is based on establishing an equivalence between the use of the modified algorithm and perturbing the original data in such a way that no degeneracies exist. Both linear regression and polynomial regression cases are discussed. For linear regression on uniformly sampled data, it is shown that the data set size may be selected so that the minimum error fit is always unique. The linear regression algorithm is then applied to the problem of robust synchronization. Stack filter phase lock loops are an alternative to the iterative methods for accomplishing robust synchronization. A second order stack filter phase lock loop can closely approximate a minimum absolute error regression scheme. Other stack filter loops which are generalization of standard digital phase lock loops are also considered. These loops resist unlocking due to high energy noise bursts and can reach steady state faster than a standard digital phase lock loop of comparable steady state RMS error performance. The particular case of the median filter based loop is examined in detail.

Degree

Ph.D.

Advisors

Gallagher, Purdue University.

Subject Area

Electrical engineering|Statistics|Mathematics

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