Uncertainty Exchange through Multiple Quadrature Kalman Filtering

One of the major challenges in Bayesian filtering is the curse of dimensionality. The quadrature Kalman filter (QKF) is the method of choice in many real-life Gaussian problems, but its computational complexity increases exponentially with the dimension of the state. As a promising solution to overcome the filter limitations in such scenarios, we further explore the multiple state-partitioning approach, which considers the partition of the original space into several subspaces, with the goal to apply a low-dimensional filter at each partition. In this contribution, the key idea is to take advantage of the estimation uncertainty provided by the QKF to improve the interaction among filters and avoid the point estimate approximation performed in the original Multiple QKF (MQKF). The new filter formulation, named Improved MQKF, considers Gauss-Hermite quadrature rules to propagate the subspaces of interest, together with cubature rules for marginalization purposes. The nested quadrature-cubature approximation provides robustness and improves the filter performance. Simulation results for a multiple target tracking scenario are provided to support the discussion.