Efficient orbit determination using measurement-directional state transition tensor

The high computational cost of current state transition tensor (STT)-based high-order extended Kalman filter (HEKF) algorithms limits in-orbit orbit determination (OD) applications. This paper proposes an efficient filter algorithm to reduce the computational cost in solving OD problems. First, a measurement-directional STT (MDSTT) is developed, in which the state space is decomposed into large-uncertainty and small-uncertainty directions according to the measurement model. The developed MDSTT ignores the high-order terms along the small-uncertainty directions; in this way, the number of high-order variables required to be calculated is significantly reduced. Then, a reduced version of HEKF is proposed by implementing the MDSTT in a HEKF framework. The expressions for the time and measurement update steps are derived by approximating the STT with the MDSTT. The algorithm is applied to resolve OD problems in highly nonlinear cases: cislunar space. Numerical results show that the algorithm outperforms the linear algorithm regarding estimated accuracy and uncertainty quantification capacity. In addition, the algorithm presents the same accuracy level as the HEKF, but it is about 67% faster than the HEKF.