An approach to useful but nonoptimal nonlinear filters

Dynamical forms of the optimal nonlinear filter have been available for at least ten years and various types of "approximations" have been proposed. Even if valid for short periods of time, errors accumulate, and eventually the meaning of the approximation is (frequently) lost. This paper attempts to understand, conceptually, via a heuristic mathematical argument how the observational information is processed by one particular approximation and exploits these insights to develop a set of engineering principles which, in turn yields an improved filter. The interest is in how useful filters work, and not in which one is preferable in some particular case.