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Nonlinear Filtering Under Stochastic Communication Protocol with Unknown Scheduling Probability

Dan Liu, Derui Ding*, Ying Sun, and Guoliang Wei
International Journal of Control, Automation, and Systems, vol. 19, no. 10, pp.3343-3353, 2021

Abstract : In this paper, the UKF-type nonlinear filtering problem is investigated for general nonlinear systems under stochastic communication protocols (SCPs) with unknown scheduling probabilities. In order to avoid the data collision and alleviate the network communication burden, SCPs, allowed only one sensor node to send data via the shared network, are exploited to orchestrate the scheduling order of sensor nodes. Different from traditional assumptions with accurate statistics, the scheduling probability of the selected node is unknown, but lies in a reliable interval with known upper and lower bounds. Due to the unknown probabilities, the exact estimation error covariance is not available and hence its upper bound is derived with the help of adding zero terms and eigenvalues of positive definite matrices. Such an upper bound is dependent on known upper and lower bounds of the scheduling probabilities and further utilized to reasonably design the filter gain at each time instant. In light of the obtained covariance and the filter gain, an improved unscented transformation is developed to carry out the designed UKFtype nonlinear filter by improving traditional approximate mean and covariance. Furthermore, the impact of the uncertain size of unknown scheduling probabilities is thoroughly discussed. Finally, a numerical example is given to confirm the effectiveness of the proposed nonlinear filter.

Keyword : Nonlinear systems, stochastic communication protocol, unknown scheduling probability, unscented Kalman filtering.

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