Uncertain disturbed systems: Robust H2‐OUFIR filtering under measurement errors

Abstract

SummaryThis article considers uncertain disturbed systems represented under initial and measurement errors in linear discrete‐time state‐space. A novel bias‐constrained a posteriori optimal unbiased finite impulse response (OUFIR) state observer is derived, in which the requirements of the initial state is removed by embedding the unbiasedness constraint. A suboptimal bias‐constrained ‐FIR filtering algorithms using linear matrix inequality is also obtained. Based on an example of uncertain system and error matrices, it is shown that the ‐OUFIR state observer offers a better tradeoff between the accuracy and robustness than the OFIR filter, maximum likelihood FIR filter, and Kalman filter. It loses in robustness to the unbiased FIR filter, but provides a better accuracy. The performance of the proposed filter is verified experimentally based on daily glucose measurements in diabetic persons with timing jitter.