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Extended and unscented filtering algorithms using one-step randomly delayed observations. (English) Zbl 1117.93070

Summary: The least squares filtering problem is investigated for a class of nonlinear discrete-time stochastic systems using observations with stochastic delays contaminated by additive white noise. The delay is considered to be random and modelled by a binary white noise with values of zero or one; these values indicate that the measurement arrives on time or that it is delayed by one sampling time. Using two different approximations of the first and second-order statistics of a nonlinear transformation of a random vector, we propose two filtering algorithms; the first is based on linear approximations of the system equations and the second on approximations using the scaled unscented transformation. These algorithms generalize the extended and unscented Kalman filters to the case in which the arrival of measurements can be one-step delayed and, hence, the measurement available to estimate the state may not be up-to-date. The accuracy of the different approximations is also analyzed and the performance of the proposed algorithms is compared in a numerical simulation example.

MSC:

93E11 Filtering in stochastic control theory
93E25 Computational methods in stochastic control (MSC2010)
93E24 Least squares and related methods for stochastic control systems
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