Abstract
This paper focuses on developing a particle filter based solution for randomly delayed measurements with an unknown latency probability. A generalized measurement model that includes measurements randomly delayed by an arbitrary but fixed maximum number of time steps along with random packet drops is proposed. Owing to random delays and packet drops in receiving the measurements, the measurement noise sequence becomes correlated. A model for the modified noise is formulated and subsequently its probability density function (pdf) is derived. The recursion equation for the importance weights is developed using pdf of the modified measurement noise in the presence of random delays. Offline and online algorithms for identification of the unknown latency parameter using the maximum likelihood criterion are proposed. Further, this work explores the conditions that ensure the convergence of the proposed particle filter. Finally, three numerical examples, one with a non-stationary growth model and two others with target tracking, are simulated to show the effectiveness and the superiority of the proposed filter over the state-of-the-art.
Highlights
State estimation for nonlinear discrete-time stochastic systems has received considerable attention from researchers because of its application in various fields of science, including navigation and localization [1,2], surveillance [3], agriculture [4], econometrics [5], and meteorology [6], for example.The Bayesian approach [7] gives a recursive relationship for the computation of the posterior probability density functions of the unobserved states
Are as follows: (i) We propose a new particle filter (PF) with an explicit expression for the importance weight for randomly delayed measurements of any number of time steps with an unknown latency probability and in the presence of packet drops
Attributing to the random delays and packet drops in measurements, we investigate the impact of the modified likelihood density on the simple convergence of the particle filter that is otherwise converging with non-delayed measurements
Summary
State estimation for nonlinear discrete-time stochastic systems has received considerable attention from researchers because of its application in various fields of science, including navigation and localization [1,2], surveillance [3], agriculture [4], econometrics [5], and meteorology [6], for example. In Reference [27], a methodology to solve nonlinear estimation problems with multi-step randomly delayed measurements is proposed All these non-linear filters are restricted to Gaussian approximations. In References [30,31], the estimation of the unknown latency parameter with one-step randomly delayed measurements is addressed using data log-likelihood function within the Expectation-Maximization (EM) framework None of these works considered the presence of random packet drops. In References [25,35], randomly delayed measurements with the correlated measurement noise for a nonlinear system is addressed They have considered a maximum delay of one time step and used the Gaussian approximation to develop the filtering algorithm.
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