A new algorithm for continuous-discrete filtering with randomly delayed measurements

Abstract

The filtering of nonlinear continuous-discrete systems is widely applicable in real-life and extensive literature is available to deal with such problems. However, all of these approaches are constrained with the assumption that the current measurement is available at every time step, although delay in measurement is natural in real-life applications. To deal with this problem, we re-derive the conventional Bayesian approximation framework for solving the continuous-discrete filtering problems. In practice, the delay is often smaller than one sampling time, which is the main case considered here. During the filtering of such systems, the actual time of correspondence should be known for a measurement received at the kth time instant. In this paper, a simple and intuitively justified cost function is used to decide the time to which the measurement at kth time instant actually corresponds. The performance of the proposed filter is compared with a conventional filter based on numerical integration which ignores random delays for a continuousdiscrete tracking problem. We show that the conventional filter fails to track the target while the modification proposed in this paper successfully deals with random delays. The proposed method may be seen as a valuable addition to the tools available for continuous-discrete filtering in nonlinear systems.