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Nonlinear and non-Gaussian state estimation: A quasi-optimal estimator. (English) Zbl 1016.93068

The author considers a nonlinear and non-Gaussian state space model which is described by the following two equations: \[ y_t= h_t(\alpha_t, \varepsilon_t),\quad \alpha_t= f_t(\alpha_{t-1}, \eta_t), \] where \(y_t\) represents the observed data at time \(t\) while \(\alpha_t\) denotes the state vector, \(\varepsilon_t\) and \(\eta_t\) are mutually independently distributed. The problem is to estimate \(\alpha_t\) given \(Y_s= \{y_1,y_2,\dots, y_s\}\). The author proposes a quasi-optimal filtering and smoothing procedure which shows a good performance in the sense of the root mean square error criterion and improves computational disadvantages of some known procedures.

MSC:

93E11 Filtering in stochastic control theory
93C10 Nonlinear systems in control theory
93C55 Discrete-time control/observation systems
65C05 Monte Carlo methods
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