Optimum filtering and control of randomly sampled systems

Kalman´s concept of optimum filtering is interpreted in such a way that it can be applied to both nonlinear and linear systems with Gaussian or non-Gaussian statistics. The essential idea is to synthesize a generalized Kalman filter in two stages, a) propagation and b) measurement and correction. The analysis of each stage is independent of the other, and the generalized results are quite simple. In the present paper, the application of the above result is confined to linear systems: 1) Optimum filtering and interpolation of randomly sampled signals; for the interpolation problem it is assumed that the signals are measured exactly at the sampling instant. 2) Optimum filtering of related continuous and randomly sampled signals. 3) Optimum control of randomly sampled linear systems with quadratic cost criterion.