Filtering in Gaussian Linear Systems With Fuzzy Switches

Abstract

This work extends recent results on Conditionally Gaussian Observed Markov Switching Models (CGOMSM) by incorporating fuzzy switches in the model, instead of hard ones. This kind of generalization is of interest for applications involving continuous switching regimes, such as tracking an object using cameras in intermittent sunlight and shadow conditions. The filter developed hereby is recursive, optimal and exact, up to an approximation of integrals according to some fuzzy measure. Experiences on simulated and on real data-dealing with outdoor air temperature and power consumption of a building-confirm the accuracy and effectiveness of the proposed filter compared to the hard filter with 'crisp' switches.

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“…A fuzzy extension of the CGOMSM has been proposed and studied in [59] in which the switch process S N 1 is no longer assumed discrete but takes its values in the interval [0, 1] instead. Hence, the distribution of each S n is defined by density h n : [0, 1] −→ R w.r.t.…”

“…This parametrization is defined by 5 parameters (m, α 0 , α 1 , β and η). It is an extension of the parametrization studied in [59] and used for the estimation of buildings power consumption from outdoor temperatures.…”