  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.
