Computational complexity reduction techniques for quadrature Kalman filters

Nonlinear filtering is a major problem in statistical signal processing applications and numerous techniques have been proposed in the literature. Since the seminal work that led to the Kalman filter to the more advanced particle filters, the goal has been twofold: to design algorithms that can provide accurate filtering solutions in general systems and, importantly, to reduce their complexity. If Gaussianity can be assumed, the family of sigma-point KFs is a powerful tool that provide competitive results. It is known that the quadrature KF provides the best performance among the family, although its complexity grows exponentially on the state dimension. This article details the asymptotic complexity of the legacy method and discusses strategies to alleviate this cost, thus making quadrature-based filtering a real alternative in high-dimensional Gaussian problems.