Nonlinear event-based state estimation using particle filter under packet loss

In this research paper, we investigate the problem of remote state estimation for nonlinear discrete systems. Specifically, we focus on scenarios where event-triggered sensor schedules are utilized and where packet drops occur between the sensor and the estimator. In the sensor scheduler, the SOD mechanism is proposed to decrease the amount of data transmitted from the sensor to a remote estimator and the phenomena of packet drops modeled with random variables obeying the Bernoulli distribution. As a consequence of packet drops, the assumption of Gaussianity no longer holds at the estimator side. By fully considering the non-linearity and non-Gaussianity of the dynamic system, this paper develops an event-trigger particle filter algorithm to relieve the communication burden and achieve an appropriate estimation accuracy. First, we derive an explicit expression for the likelihood function when an event trigger occurs and the possible occurrence of packet dropout is taken into consideration. Then, using a special form of sequential Monte-Carlo algorithm, the posterior distribution is approximated and the corresponding minimum mean-squared error is derived. By contrasting the error covariance matrix with the posterior Cramér-Rao lower bound, the estimator's performance is assessed. An illustrative numerical example shows the effectiveness of the proposed design.