Out of Sequence Variational Filtering with Forward Tracklets

We consider the problem of variational Bayes Kalman filtering (VB-KF) with out-of-sequence measurements (OOSMs), and generalize a standard OOSM method for linear Kalman filtering to the VB-KF setting. We show that at the cost of introducing a memory buffer, the method produces near identical results to in-sequence processing, but removes the need for more computationally heavy re-processing of measurements. Furthermore, we demonstrate that the proposed method is implementable for various VB-KF algorithms, including free-form approximations of the posterior distributions with Gaussian, Inverse-Wishart, and Inverse-Gamma factors. The theoretical results are demonstrated with examples of non-homogeneous target tracking. Compared to re-ordering and reprocessing, we show significant improvements in computational time (approximately linear in the delays) at a modest increase in mean-square error (MSE), making VB-KFs viable for OOSM processing.