A Probabilistic Model-adaptive Approach for Tracking of Motion with Heightened Uncertainty

This paper presents an approach for state tracking in scenarios where motion is highly uncertain. The proposed approach improves on traditional Kalman filters by integrating model parametric uncertainty in deriving state covariances for prediction at each time step. A model correction stage then continuously adjusts the mean and variance of state matrix elements based on the observation-corrected state, compensating for an initially inadequate system model. The symbiotic relationship between state tracking and motion model correction is leveraged to perform both tasks simultaneously in-the-loop. In a representative dynamic example, simulated experiments were performed and analyzed statistically for varying combinations of sensor and model uncertainty. For low model variance, traditional Kalman filters generally perform estimation better due to over-confidence with regards to model parameters. However, the proposed approach increasingly outperforms both traditional and adaptive Kalman filters in estimation when model and input uncertainty is appreciable. The motion model updating approach formulated here tends to improve parameter estimates over the course of state tracking, thus validating the symbiotic process. The robotics applications of this simultaneous estimation and modeling framework extend from target state tracking to self-state estimation, while broader signal processing applications can be readily extracted.