Filtering in Gaussian linear systems with fuzzy switches

Zied Bouyahia (1) , Stéphane Derrode (2) , Wojciech Pieczynski (3, 4, 5)

1 Dhofar University
2 imagine - Extraction de Caractéristiques et Identification
3 TSP - CITI - Communications, Images et Traitement de l'Information
4 IP Paris - Institut Polytechnique de Paris
5 TIPIC-SAMOVAR - Traitement de l'Information Pour Images et Communications

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.

Keywords: Triplet Markov models; Fuzzy switching linear model; Fast filtering

Domains: Signal and Image Processing

Zied Bouyahia, Stéphane Derrode, Wojciech Pieczynski. Filtering in Gaussian linear systems with fuzzy switches. IEEE Transactions on Fuzzy Systems, 2020, 28 (8), pp.1760-1770. ⟨10.1109/TFUZZ.2019.2921944⟩. ⟨hal-02912919⟩