Modified Filter for Mean Elements Estimation with State Jumping

Abstract

To investigate the real-time mean orbital elements (MOEs) estimation problem under the influence of state jumping caused by non-fatal spacecraft collision or protective orbit transfer, a modified augmented square-root unscented Kalman filter (MASUKF) is proposed. The MASUKF is composed of sigma points calculation, time update, modified state jumping detection, and measurement update. Compared with the filters used in the existing literature on MOEs estimation, it has three main characteristics. Firstly, the state vector is augmented from six to nine by the added thrust acceleration terms, which makes the filter additionally give the state-jumping-thrust-acceleration estimation. Secondly, the normalized innovation is used for state jumping detection to set detection threshold concisely and make the filter detect various state jumping with low latency. Thirdly, when sate jumping is detected, the covariance matrix inflation will be done, and then an extra time update process will be conducted at this time instance before measurement update. In this way, the relatively large estimation error at the detection moment can significantly decrease. Finally, typical simulations are performed to illustrated the effectiveness of the method.