Optimal and Robust State Estimation

9Robust FIR State Estimation for Uncertain Systems

A statistical analysis, properly conducted, is a delicate dissection of uncertainties, a surgery of suppositions.

Michael J. Moroney [132], p. 3.

In physical systems, various uncertainties occur naturally and are usually impossible to deal with. An example is the sampling time that is commonly set constant but changes due to frequency drifts in low‐accuracy oscillators of timing clocks. To mitigate the effect of uncertainties, more process states can be involved that, however, can cause computational errors and latency. Therefore, robust estimators are required [79,161]. Most of works developing estimators for uncertain systems follow the approach proposed in [51], where the system and observation uncertainties are represented via a single strictly bounded unknown matrix and known real constant matrices. For uncertainties considered as multiplicative errors, the approach was developed in [56], and for uncertainties coupled with model matrices with scalar factors, some results were obtained in [180]. In early works on robust FIR filtering for uncertain systems [98,99], the problem was solved using recursive forms that is generally not the case. In the convolution‐based batch form, several solutions were originally found in [151,152] for some special cases.

Like in the case of disturbances, robust FIR estimators can be designed using different approaches by minimizing estimation errors for maximized uncertainties. Moreover, ...