SUMMARYModel-based adaptive algorithms are usually derived with the help of the Wiener-Hopf equation based on empirical statistics. They are often interpreted as an extension to their model-independent counterparts, i.e. the stochastic-gradient based adaptive ÿlters. As a consequence, it is generally not considered worthwhile to show the analogy between Kalman ÿlters and adaptive ÿlters. This article pursues just these two goals. First, it tries to remove the notion that the Kalman ÿlter is a complicated and unnecessary detour from the subject of adaptive ÿltering. Second, the advantage of a deeper insight into adaptive algorithms from Kalman's viewpoint emerges from our treatment. Based on a time-varying FIR ÿlter model, the Kalman ÿlter is completely derived and serves as a general framework for the special case of model-based adaptive ÿlters.
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