Over-the-Air Aggregation With Multiple Shared Channels and Graph-Based State Estimation for Industrial IoT Systems

We consider remote state estimation for an industrial Internet-of-Things (IoT) system, where the plant dynamics are monitored by a number of distributed industrial IoT sensors. We propose an “estimation friendly” remote state estimation framework, which not only maintains low computational complexity but also provides better estimation stability performance. Specifically, we propose a novel over-the-air-aggregation-based multiple access, which enhances the observability performance of the state estimation system and hence, provides better estimation stability. Additionally, exploiting the sparsity in the observation matrix induced by the over-the-air-aggregation-based multiple access, we propose a low-complexity 2-D message passing state estimation algorithm, where the cyclic loops in the 2-D factor graphs are removed based on the quasi-diagonal transformation of the aggregated channel matrix of the IoT sensors. As a result, the proposed state estimation scheme is of low complexity and can achieve exact maximum a posterior estimation. Using the Lyapunov drift analysis, we derive the closed-form necessary and sufficient conditions for stability of the mission-critical remote state estimation system. The numerical results demonstrate that the proposed scheme has a low computational complexity. Furthermore, it is scalable with the number of sensors and has a low power consumption.