Discrete-time estimation in continuous-time communication systems

An alternative to continuous-time Kalman filtering is sampled digital processing. The purpose is to develop a good model for this situation and investigate the resulting performance. The error dependence on the sample rate is studied. It is found that a sample rate considerably higher than twice the half power-frequency is necessary to avoid loss of performance where zero-lag filtering is desired. Smoothing is discussed and in this context three results of major importance are found; (1) an optimal sample rate exists for each smoother (2) only a few steps of lag is necessary to approach the ideal unrealizable error (3) a considerable lower sample rate can be accepted for smoothing as compared with filtering. This finding is of interest as the corresponding ideal continuous-time smoother has been reported unstable. Finally a comparison is made with approximate models suggested in the relevant literature.

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