Abstract
The on-line expectation-maximization (EM) algorithm along with stochastic approximations are employed in this paper to estimate unknown time-invariant/variant parameters recursively in an adaptive manner based on the maximum likelihood (ML) criterion. The impulse response of a linear transmission channel is modeled in different ways; as an unknown deterministic vector/process and as an Gaussian vector/process with unknown stochastic characteristics. In association with these channel impulse response (CIR) models, different types of recursive least squares (RLS) and Kalman filtering and smoothing algorithms are derived directly from the on-line EM algorithm. The EM algorithm as a powerful tool unifies the derivations of some adaptive estimation methods (which include RLS and Kalman) whose original criterion is minimum mean square error (MMSE), but under linear and Gaussian conditions can achieve ML or maximum a posterior (MAP) criterion.
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