Minimalistic estimation with stochastic constraints for closed-type tethered satellite formations

This paper aims to propose a constrained estimation scheme with minimalistic sensor settings for a class of closed-type tethered satellite formation (TSF). The estimation scheme is built on the fusion of dynamic model, priori tether length constraints, and position observation through a learning-based constrained particle filtering (CPF) design. The CPF characterizes the tether lengths as stochastic constraints and integrates these constraints within Bayesian framework based on pseudo observation and radial basis function (RBF) neural network. The RBF neural network can learn the underlying relationship between the system states and uncertain tether oscillations to establish a probability distribution function (PDF) of stochastic constraints. Nonlinear observability analysis using observability rank criterion is performed to yield insight into the minimum number of positioning sensors needed for n-body (n≥3) closed-type TSF. Furthermore, it is found that the use of pseudo observation for filtering can reduce the number of needed positioning sensors. Interestingly, the minimum number of positioning sensors required for determining all position information of n-body (n≥3) closed-type TSF is 1. Finally, the effectiveness of proposed estimation scheme is verified by posterior Cramér-Rao lower bound (PCRLB) calculation and extensive simulations. The proposed estimation scheme can be readily extended to other types of TSF. For example, the chain-type TSF.