Incremental maximum likelihood estimation for efficient adaptive filtering

Adaptive filtering is a well-known problem with a wide range of applications, including echo cancellation. Extensive research during the past few decades has led to the invention of various algorithms. However, the known computationally-efficient solutions show a tradeoff between convergence speed and accuracy. Moreover, running these algorithms involves heuristically setting various parameters that considerably affect their performances. In this paper, we propose a new algorithm which we refer to as online block maximum likelihood (OBML). OBML is a computationally-efficient online learning algorithm that employs maximum likelihood (ML) estimation every $P$ samples. We fully characterize the expected performance of OBML and show that i) OBML is able to asymptotically recover the unknown coefficients and ii) its expected estimation error asymptotically converges to zero as $O({1\over t})$. We also derive an alternative version of OBML, which we refer to as incremental maximum likelihood (IML), which incrementally updates its ML estimate of the coefficients at every sample. Our simulation results verify the analytical conclusions for memoryless inputs, and also show excellent performance of both OBML and IML in an audio echo cancellation application with strongly correlated input signals.