Sheet-material measurement using a beta gauge

The paper considers the problem of designing an optimal filter for a beta gauge. The output from this kind of gauge is a doubly stochastic Poisson process, and, for the linear problem, the optimal filter is shown to have a particularly simple form. If the gauge output pulse train is not available directly, but only in a prefiltered form, then an optimal filter can still be developed, although it is difficult to implement. A simple approximation to the prefiltered observation process is shown to be adequate in cases where the Poisson pulse rate is high. In the linear case, this allows the well known Kalman-Bucy filter to be used. A numerical example demonstrates the usefulness of the approximate filter and confirms the conclusion that in practice the Kalman-Bucy filter is more than adequate.