From Wiener to Hidden Markov models

The authors investigate common properties of 3 types of filters obtained by considering various stochastic models; Wiener filters, Kalman filters and hidden Markov model (HMM) filters. Unifying features which particularly stand out are the forgetting of old data and of initial conditions, and protection from round-off error effects' overpowering the calculations. They differentiate the concept of fixed-lag smoothing from filtering, and expose the comparative advantages and disadvantages. Once again, there are common properties which allow a unified viewpoint. We focus especially on characterizations of a maximally effective smoothing lag, and identification of the SNR circumstances under which smoothing is especially beneficial. The motivation is the processing of data from an array of acoustic sensors towed by a submarine.