A Bayesian solution and its approximations to out-of-sequence measurement problems

Abstract Target tracking using delayed, out-of-sequence measurements is a problem of growing importance due to an increased reliance on networked sensors interconnected via complex communication network architectures. In such systems, it is often the case that measurements are received out-of-time-order at the fusion center. This paper presents a Bayesian solution to this problem and provides approximate, implementable algorithms for both cluttered and non-cluttered scenarios involving single and multiple time-delayed measurements. Such an approach leads to a solution involving the joint probability density of current and past target states. In contrast, existing solutions in the literature modify the sensor measurement equation to account for the time delay and explicitly deal with the resulting correlations that arise in the process noise and current target state. In the Bayesian solution proposed in this paper, such cross correlations are treated implicitly. Under linear Gaussian assumptions, the Bayesian solution reduces to an augmented state Kalman filter (AS-KF) for scenarios devoid of clutter and an augmented state probabilistic data association filter (AS-PDA) for scenarios involving clutter. Computationally efficient versions of AS-KF and AS-PDA are considered in this paper. Simulations are presented to evaluate the performance of these solutions.