Particle Filter for Randomly Delayed Measurements with Unknown Latency Probability

This paper focuses on designing a particle filter for randomly delayed measurements with an unknown latency probability. A generalized measurement model is adopted which includes measurements that are delayed randomly by an arbitrary but fixed maximum number of the steps, along with random packet drops. Recursion equation for importance weights is derived under 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 which ensure the convergence of the proposed particle filter. Finally, two numerical examples concerning problems of non-stationary growth model and the bearing-only tracking are simulated to show the effectiveness and superiority of the proposed filter.