Full State Estimation for Triangular Tethered Satellite Formations: Filter Design, Observability Analysis, and Performance Evaluation

This article aims to present a full state estimation scheme for the triangular tethered satellite formations (TSF), which have rarely been studied and face some challenges including coupled dynamics, strong nonlinearity, and high-dimensional motion. First, a minimalistic estimation scheme is proposed to obtain the angular velocity of satellites, tether lengths, and 3-D formation attitudes through filter design. Without using global information, this scheme can obtain drift-free 3-D formation attitudes because the coupled dynamics capture the gravity gradient force and bridge the angular velocity of satellites with the 3-D formation attitudes. Second, given the strong nonlinearity and high-dimensional motion of the system dynamics, a neural particle filter (NPF) is designed to obtain all system states for the triangular TSF. To overcome the particle impoverishment, the NPF integrates the particle filter with the radial basis function neural network to optimize the weight distribution and enhance the particle diversity before resampling. Third, a high-fidelity calculation method for the posterior Cramer-Rao bound (PCRB) is developed using NPF to evaluate the performance of the proposed estimation scheme. This calculation method can be used to approximate the PCRB for non-Gaussian and nonlinear filtering with unknown true states. Finally, rigorous observability analysis and sufficient simulation comparison are provided.