An Adaptive Fuzzy State Noise Driven Extended Kalman filter for Real-time Orbit Determination

Abstract: The orbit determination of the satellite, just after injection into the orbit, is crucial for the satellite tracking and planning of various immediate maneuvers required. Generally, Extended Kalman Filter (EKF), which is a suboptimal nonlinear implementation of linear Kalman filter, is employed for the real time orbit determination. However, the divergence of the EKF can not be ruled out, or at least a poor convergence may creep in even after employing various methods to make it adaptive by injecting noise. The divergence may occur due to errors in modeling the system, finite precision arithmetic and associated truncation/round-off errors and large errors can be attributed to a priori estimate and covariance. The artificial noise injection method, generally used for making the state covariance matrix positive definite, may not lead to proper convergence due to the problems mentioned above. In this paper a fuzzy state noise driven adaptive EKF which is based on spring- mass-damper analogy, has been proposed for orbit determination. The formulation makes the filter faster in convergence in the real time orbit determination application. A comprehensive simulation on PSLV-C1 data has been carried out to show the better convergence with the proposed fuzzy model.