The marginalized square-root Quadrature Kalman Filter

Bayesian filtering appears in many signal processing problems, reason which has attracted the attention of many researchers to develop efficient algorithms, yet computationally affordable. Ranging from Kalman Filter (KF) to particle filters, there is a plethora of alternatives depending on model assumptions. We focus our interest into a recently developed algorithm known as the square-root Quadrature Kalman Filter (SQKF). Under the Gaussian assumption, the SQKF is seen to optimally tackle arbitrary nonlinearities by resorting to the Gauss-Hermite quadrature rules. However, its complexity increases exponentially with the state-space dimension. In this paper we study a marginalization procedure to alleviate this problem which roughly consists in taking advantage of the linear substructures of the model. A target tracking application is used to validate the proposed algorithm. The results exhibit a reasonable performance of the proposed algorithm, while drastically reducing the computational complexity when compared to state-of-the-art algorithms.