Risk-sensitive filtering and smoothing for hidden Markov models
Systems & Control Letters
Kalman filtering for linear systems with coefficients driven by a hidden Markov jump process
Systems & Control Letters
Estimation with Applications to Tracking and Navigation
Estimation with Applications to Tracking and Navigation
Inference in Hidden Markov Models (Springer Series in Statistics)
Inference in Hidden Markov Models (Springer Series in Statistics)
Minimax a posteriori estimation in the hidden Markov models
Automation and Remote Control
SIAM Journal on Control and Optimization
Minimax a posteriori estimation of the Markov processes with finite state spaces
Automation and Remote Control
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A problem of estimation of states and parameters in stochastic dynamic systems of observation with discrete time containing a Markovian chain is studied. Matrices of transient probabilities and observation plans are random with unknown distribution with a given compact carrier. Observations, on the basis of which the estimation is made, are available at a fixed interval of time [0, T]. As a loss function, we have a conditional mathematical expectation with respect to the available observations of 驴 2-norm of the estimation error of a signal process on [0, T]. The problem is in constructing an estimate minimizing losses correspondent to the worst distribution of the pair "a matrix of transient probabilities--a matrix of observation plan" form a set of allowable distributions. For a correspondent minimax problem is demonstrated the existence of a saddle point and is obtained a form of the wanted minimax estimation. The applicability of the obtained results is illustrated by a numerical example of the estimation of a state of TCP under the conditions of uncertainty of communication channel parameters.