Cyclic estimation in primary processing of sensor signals (Q1112001)

Kalman estimation of a scalar quantity is considered which is measured together with additive practically white noise. The true value of the estimated quantity is assumed to be deterministic in each short estimation cycle, and it is approximated either by a finite Fourier sum, or by a polynomial. In the case of a cyclic Kalman-Bucy filter (KBF) with continuous time in a cycle, simple expressions are obtained for the variances of the estimation errors at the end of each cycle. In the case of a discrete-time cyclic KBF, the required computing capacity can be determined. Such a processing is advantageous in practice, because it can be realized in a built-in microprocessor, and also used for predicting changes in the quantity that is being estimated and for detecting failures of the sensor and of the monitored process.