Risk-sensitive filtering and smoothing for hidden Markov models
Systems & Control Letters
Estimation with Applications to Tracking and Navigation
Estimation with Applications to Tracking and Navigation
Filtration of a random process in a statistically uncertain linear stochastic differential system
Automation and Remote Control
Numerical methods for nonlinear stochastic differential equations with jumps
Numerische Mathematik
SIAM Journal on Control and Optimization
Minimax a posteriori estimation of the Markov processes with finite state spaces
Automation and Remote Control
Estimating with partial statistics the parameters of ergodic finite Markov sources
IEEE Transactions on Information Theory
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The paper is devoted to a state filtering problem of Markov jump processes given the continuous and/or counting observations. All the transition intensity matrix, observation plan and counting intensity are parameterized by a random vector with uncertain distribution on a known support set. The estimation problem is formulated in minimax settings with a conditional optimality criterion. We reduce the initial minimax problem to a dual problem of constrained quadratic optimization. The corresponding numerical algorithm of minimax filtering is presented as well as its illustrative implementation in the monitoring of a TCP link status under uncertainty.