The Blind Tricyclist Problem and a Comparative Study of Nonlinear Filters

摘要

A blind tricyclist problem, an example nonlinear Kalman filtering problem, has been developed and used to compare several nonlinear estimation methods. This comparison illustrates potential weaknesses of algorithms that many practitioners had believed to be suitable for most nonlinearon-Gaussian problems. It also highlights the strength of a relatively new algorithm, the Backwards-Smoothing Extended Kalman Filter (BSEKF). The blind tricyclist problem has nonlinear dynamics and measurement models. The kinematic state of the tricyclist is comprised of the two-dimensional Cartesian position in the horizontal plane and the heading. The tricyclist navigates based on relative-bearing measurements to moving targets that have parametric location uncertainties. Thus, the full filter state includes the tricyclist's position and heading along with the unknown parameters of the moving reference points. The extended Kalman filter (EKF), the unscented sigma-points Kalman filter (UKF), the particle filter (PF), a batch least-squares filter (BLSF), and the BSEKF are all tested on this problem. For moderate levels of initial uncertainty, all of the filters show reasonable performance. For larger initial uncertainties,however, the EKF performs poorly, as does the UKF and the PF. The BLSF has degraded accuracy, but it does not diverge. The BSEKF performs the best. The BSEKF is expensive computationally, but the PF is even more expensive on this problem. Additional tests using two 1- dimensional problems counter-balance the results on the blind tricyclist problem. They show that the PF has advantages in certain situations.