Minimalist Estimation Under Prescribed Performance for Tethered Satellite Formations: A Unified Framework

The state estimation of tethered satellite formations (TSF) faces challenges due to complex soft constraints (e.g., the tether constraints) and limited payload capability. This paper proposes a unified estimation framework with minimalist sensor design and prescribed performance guarantees for TSF. This framework leverages soft constraints to minimize the number of sensors required while guaranteeing weak local observability and prescribed performance metrics. This is achieved using a learning-based constrained filter (LCF), nonlinear observability analyses, and posterior Cramér-Rao bound calculations. The uncertainties inherent in soft constraints are modeled as a Gauss- Markov process, and the colored noise is converted into Gaussian white noise using the measurement differencing method. The designed LCF integrates soft constraints into an extended Kalman filter as pseudo-observations, and the updated state is then compensated online by the filtering error using an adaptive RBF neural network. Moreover, the stability analysis confirms that the estimation error of designed LCF remains bounded. To validate the proposed framework and designed filter, a symmetrical -type TSF is investigated as an application case, revealing a surprising finding about the minimal sensor configuration.