Graphical Kalman Filter

The Extended Kalman Filter is a proven method for efficient Markov Chain inference. It is ubiquitous in indoor localization applications, and typically applied to combine relative motion with absolute positioning. However, an unmodified Extended Kalman Filter struggles to handle common problems in indoor applications. For instance, the presence of large and hard to estimate noise terms, large correlated outliers, and other non-linear effects. Typically, these problems necessitates the introduction of large smoothing propagation errors to ensure stability and to avoid converging on false results. As a result, the memory of the filter rapidly decays so that estimates only are influenced by the last few observations. This work introduces the Graphic Model Kalman Filter. It combines an Adaptive Kalman Filter with a probabilistic Graphical Model. In the filter, the adaptive component uses historical data to dynamically estimate observation and propagation uncertainty. Earlier and later states around a target state are predicted by the filter, and the relations between predictions and each observation are used to form the graphical model. The Kalman update step is then replaced by an optimization of the graphical model, which improves trajectory smoothness as well as robustness to outliers. Extensive simulations are used to show that this design outperforms regular Extended or Adaptive Kalman Filters.