Approximations to unsupervised filters

The problem of recursive estimation of an additive noise-corrupted discrete stochastic process is considered for the case where there is a nonzero probability that the observation does not contain the process. Specifically, it is assumed that, independently, with unknown, constant probabilities, observations consist either of pure noise, or derive from a discrete linear process, and that the true source of any individual observation is never known. The optimal Bayesian solution to this unsupervised learning problem is unfortunately infeasible in practice, due to an ever increasing computer time and memory requirement, and computationally feasible approximations are necessary. In this correspondence a quasi-Bayes (QB) form of approximation is proposed and comparisons are made with the well-known decision-directed (DD) and probabilistic-teacher (PT) schemes.