The Meir Hanin International Aerospace Prize Guest Seminar – The Challenges of Nonlinear Kalman Filtering

The challenges of nonlinear Kalman filtering are presented, and a number of proposed solutions are examined. A Kalman filter forms an a posteriori estimate of the state of a dynamic system, and it computes an estimation error covariance.  It provides the optimal solution to any problem that is linear and Gaussian.  Various approximate Kalman filters and related estimation algorithms have been developed for nonlinear problems.  Some of them work well for important applications, but none of them can provide a good solution to every conceivable nonlinear problem.  A given filter may diverge on certain problems.  Alternatively, it may converge, but yield much more estimation error than would an optimal filter.  Another filter may converge and achieve good accuracy, but at a prohibitive cost in terms of computational resources.  The set of nonlinear filters that are reviewed and compared include the Extended Kalman Filter (EKF), the Sigma-Points Filter — also known as the Unscented Kalman Filter (UKF), the Particle Filter (PF), the Backward-Smoothing Extended Kalman Filter (BSEKF) – a modification of the Moving Horizon Estimator (MHE), and the Gaussian Mixture Filter (GMF).  Nonlinear problems that are used to examine these filters’ performance include spacecraft attitude/rate/ moment-of-inertia estimation, angles-only spacecraft orbit determination, and the Blind Tricyclist nonlinear estimation benchmark problem.  The filters are compared in terms of convergence reliability, accuracy, and computational cost.  These comparisons demonstrate that no single nonlinear filtering algorithm is superior to all others in every respect.  Therefore, a good estimation practitioner must know about many or most of these filtering options and choose among them to develop the best solution to a given problem.