Identification and estimation algorithms for a Markov chain plus AR process

Identification and recursive filtering problems related to a signal described by a Markov chain plus autoregressive(MCPAR) process are considered. These subjects are motivated by application to modelling of 1-D image data with multipeaks in their histgram of gray levels as well as by describing some real data such as ones measured from random nonlinear vibration etc.. Firstly both recursive and iterative identification algorithms are presented based upon the minimum prediction error method. Secondly a new suboptimal algorithm of the minimum mean square estimate of the MCPAR signal from noisy corrupted data is proposed. Finally computer simulation results for our proposed algorithms are contained.