EM-based recursive estimation of channel parameters

Recursive (online) expectation-maximization (EM) algorithm along with stoch astic approximation is employed in this paper to estimate unknown time-inva riant/variant parameters. The impulse response of a linear system (channel) is modeled as an unknown deterministic vector/process and as a Gaussian ve ctor/process with unknown stochastic characteristics. Using these models wh ich are embedded in white or colored Gaussian noise, different tapes of rec ursive least squares (RLS), Kalman filtering and smoothing and combined RLS and Kalman-type algorithms are derived directly from the recursive EM algo rithm. The estimation of unknown parameters also generates new recursive al gorithms for situations, such as additive colored noise modeled by an autor egressive process. The recursive EM algorithm is shown as a powerful tool w hich unifies the derivations of many adaptive estimation methods.