Effect of sampling time jitter on robust [formula omitted] filtering estimates

Abstract

In discrete-time processes, the sampling time jitter occurs naturally due to various unavoidable reasons, which make the model uncertain. Therefore, robust state estimators should be used. To find out if it is rational to design such estimators or if we can simply ignore the time jitter, in this paper we investigate its effect on the robust H2 optimal finite impulse response (OFIR) filter in a comparison with the OFIR filter. As benchmarks, we also use the maximum likelihood FIR, unbiased FIR, and Kalman filters. The robust batch H2-OFIR filter is developed for timing jitter under disturbances, initial errors, and measurement errors. For Gaussian errors, its iterative algorithm is designed using modified Kalman recursions. Numerical investigations and applications to blood sugar monitoring in diabetic patients with daily timing jitter have shown that the robust H2-OFIR filter improves the accuracy of the OFIR filter by the factor of less than the fractional time jitter. That is, for large fractional timing jitter of 10% the improvement would be less than 10% that is small. Otherwise, it is worth using robust estimators.