The second part was devoted to the rms-optimal filtration of the states of the Markov jump processes in continuous time which generalize the finite-state Markov processes. Equations for the conditional expectations and the probability density function were obtained. The Zakai equations for the corresponding unnormalized characteristics also were obtained. The proposed best nonlinear estimates were compared by way of a numerical example with the best linear estimates of the Kalman–Bucy filtration.
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Borisov, A.V., Analysis and Estimation of the States of Special Jump Markov Processes. I. Martingale Representation, Avtom. Telemekh., 2004, no. 1, pp. 50–65.
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Borisov, A.V. Analysis and Estimation of the States of Special Jump Markov Processes. II. Optimal Filtration in Wiener Noise. Automation and Remote Control 65, 741–754 (2004). https://doi.org/10.1023/B:AURC.0000028322.97957.ca
- Density Function
- Probability Density
- System Theory
- Probability Density Function