ABSTRACT High‐precision state perception is essential for the Industrial Internet of Things (IIoT) to ensure reliable monitoring in complex networked environments. This letter addresses the recursive filtering problem for networked time‐varying systems subject to simultaneous stochastic nonlinearities, measurement degradations, and channel noises over an amplify‐and‐forward (AF) relay framework. To handle the complex statistical coupling induced by the AF amplification of nonlinear disturbances, we construct an augmented measurement model that integrates information from both relay and sensor nodes. By employing stochastic analysis and the completing‐the‐square technique, recursive update formulas for the prior and posterior error covariances are derived. The optimal filter gain is then analytically obtained by minimizing the trace of the posterior error covariance matrix. Numerical simulations based on an RLC circuit demonstrate that the proposed algorithm effectively suppresses estimation errors and achieves superior tracking precision, providing a robust state estimation solution for advanced IIoT applications.
Huo et al. (Fri,) studied this question.