The blind tricyclist problem and a comparative study of nonlinear filters: A challenging benchmark for evaluating nonlinear estimation methods

Dynamic filters can provide powerful means to estimate hidden system states based on sensor data. For linear problems with Gaussian noise, the Kalman filter is the known optimal solution and has been available for a long time [1], [2]. Exact optimal solutions are rarely available for nonlinear problems, and the user typically selects from a variety of approximate techniques. These techniques include the traditional extended Kalman filter (EKF) [3]?[5], the iterated EKF (IEKF) [4], the unscented Kalman filter (UKF) [5]?[7], the particle filter (PF) [5], [8], [9], and the Gaussian mixture filter (GMF) [5], [10]?[12]. The EKF is widely used but is known to have degraded accuracy, or even to lose stability, for certain problems [5], [13], [14].