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Discrete-time piecewise linear filtering with small observation noise

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2 Author(s)
Milheiro de Oliveira, P. ; Fac. de Engenharia, Porto Univ., Portugal ; Roubaud, M.C.

A problem of discrete-time piecewise linear filtering with small observation noise is considered. The case in which the observation function is not one-to-one and has two intervals of linearity is studied, in particular when this function is symmetric. Under some detectability assumption, a procedure is presented to detect the intervals of linearity of the observation function. During such time intervals, one can then approximate the optimal filter by the corresponding Kalman-Bucy filter

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Automatic Control, IEEE Transactions on  (Volume:40 ,  Issue: 12 )