A New Approach to Adaptive Signal Processing

Abstract

A unified linear algebraic approach to adaptive signal processing (ASP) is presented. Starting from just Ax=b, key ASP algorithms are derived in a simple, systematic, and integrated manner without requiring any background knowledge to the field. Algorithms covered are Steepest Descent, LMS, Normalized LMS, Kaczmarz, Affine Projection, RLS, Kalman filter, and MMSE/Least Square Wiener filters. By following this approach, readers will discover a synthesis; they will learn that one and only one equation is involved in all these algorithms. They will also learn that this one equation forms the basis of more advanced algorithms like reduced rank adaptive filters, extended Kalman filter, particle filters, multigrid methods, preconditioning methods, Krylov subspace methods and conjugate gradients. This will enable them to enter many sophisticated realms of modern research and development. Eventually, this one equation will not only become their passport to ASP but also to many highly specialized areas of computational science and engineering.