Interior point least squares estimation

Abstract

<p>Adaptive filters are used in linear estimation problems when no a priori knowledge of signal statistics is available or when systems are time varying. They have become a popular signal processing tool and have found application in many diverse areas. The work in recent years has led many to regard the recursive least-squares algorithm (RLS) and its variants as the state of the art. The principal advantage of RLS over the rivalling least mean square algorithm (LMS) is its fast rate of convergence, which in many applications justifies the higher computational complexity of RLS. Mathematically speaking, both RLS and LMS result from the application of particular iterative optimization algorithms to the minimization of the least-squares criterion. The purpose of this thesis is to investigate the applicability of a new class of optimization methods, interior point optimization algorithms, to the adaptive filtering problem. We develop a new recursive algorithm, called Interior Point Least Squares or IPLS, that can be efficiently implemented with a computational cost comparable to (but higher than) RLS. IPLS matches RLS in asymptotic performance, but has a faster transient convergence rate. This is significant because until now "...[RLS'] convergence speed [has been] considered to be optimal in practice, and [thus] a measure for comparison for other algorithms.", (Moustakides, in a paper in the IEEE Transactions on Signal Processing , October 1997). Additional properties of IPLS are its insensitivity to variations in initialization, numerical stability in the presence of limited precision arithmetic, and versatility in that it readily allows the inclusion of additional constraints on the weight vector. Some of the above mentioned properties are further investigated and exploited in applications to adaptive equalization and adaptive beamforming. Numerical simulations are used throughout the thesis to illustrate, confirm, and extend our analytical results.</p>