A Comparison Study of State Estimators for Dynamics on the Sphere

The problem of state estimation for a spherical pendulum is studied by comparing the performance of a set-bounded estimation scheme designed for dynamics evolving on the sphere with that of an extended Kalman filter. The set-bounded estimator uses a global, coordinate-free description of the dynamics of a spherical pendulum, while the extended Kalman filter uses a local description of the motion using spherical coordinates. The dynamics model of the pendulum is assumed to be known; however, measurements of the pendulum state have unknown errors. The extended Kalman filter is known to be optimal for the case of zero-mean white Gaussian noise, while the set-bounded filter assumes that the measurement noise is bounded by known ellipsoidal set. Results are presented for numerical simulations in which the pendulum system has measurement errors with various statistical distributions, allowing for a direct comparison between the performances of the two state estimation strategies.