Constrained Estimation Analysis and Physical Parameters Study for Chain Tethered Formation Systems

Accurate state estimation of the tethered formation systems (TFS) is challenging due to complex dynamic coupling and elastic tether constraints. In this article, we develop a new fundamental tool to reveal the influence of tether physical parameters on the estimation performance for a class of chain-type TFS. First, we model the elastic tether as a Kelvin–Voigt material to evaluate the influence of tether stiffness and damping on estimation performance. To facilitate analysis, equilibrium configurations are used to characterize the dynamic behavior of chain TFS. Then, we extend the posterior Cramér–Rao lower bound (PCRB) to constrained subspace and derive a recursive form to calculate the constrained PCRB (C-PCRB) for discrete-time filtering with additive Gaussian noises and state equality constraints. Besides, a numerical approach using the particle filter is also developed to approximate the C-PCRB without directly calculating the complex mathematical expectations. Finally, we systematically investigate the influence of the tether stiffness and damping on estimation performance for a chain TFS by extensive simulations.