Performance analysis of stochastic event-triggered estimator with compressed measurements

This paper aims to investigate event -triggered (ET) state estimation problems under measurement compression. A stochastic ET mechanism is developed by using the normalized innovation as a basis for triggering. In particular, when fixing the compression matrix, the closed form of the minimum mean squared error estimator is derived from Bayesian theory. Moreover, the ET decision process is proven to be independent and identically distributed, which allows to derive the communication rate using an explicit formula. We also develop a method for performance analysis without computing the expected mean squared error explicitly. We find that larger communication rates and compression ratios lead to smaller expected mean squared errors. These analysis results also serve as a tool for the design of the compression matrix, which is discussed under two scenarios. When the compression ratio is greater than or equal to the ratio of the rank of the observation matrix to the dimension of measurement, an analytic optimal compression matrix is derived via singular value decomposition. In the other scenario where the compression ratio is larger than the ratio of the rank of the observation matrix to the dimension of measurement, it is no longer feasible to achieve optimal compression using singular value decomposition. Instead, we compute the compression matrix by minimizing an upper bound of the steady-state mean squared error. In fact, this problem involves a rank constraint which is computationally demanding. For this reason, we provide a reformulation which produces the same optimal objective value. Finally, the effectiveness and advantages of the proposed methods are verified by a target tracking system. (c) 2024 Elsevier Ltd. All rights reserved.