Radix-Partition-Based Over-the-Air Aggregation and Low-Complexity State Estimation for IoT Systems Over Wireless Fading Channels

We consider remote state estimation for an internet-of-things (IoT) system, where a number of distributed IoT sensors monitor a dynamic plant and deliver the state measurements to a remote state estimator over an unreliable wireless network. We propose novel radix-partition-based over-the-air aggregation to coordinate the transmissions of the IoT sensors, which strongly enhances the spectral efficiency of radio resources and enables a smaller state estimation mean square error (MSE) at the remote state estimator, taking into consideration the quantization effect and radio resource allocation for the IoT sensors. We consider a fixed-filtering design at the remote state estimator, which significantly reduces the signal processing overhead at the remote state estimator compared to using the conventional Kalman-filtering-based state estimation approach. We show that the proposed low-complexity state estimation scheme enables state estimation stability via the linear matrix inequality (LMI) technique for on-off fading channels and via Lyapunov stability analysis for random fading channels. Based on this, we further propose efficient algorithms for the offline design of the filtering gain, connection topology and radix representation for IoT systems. Numerical results show that the proposed scheme has superior scalability performance and can achieve a smaller state estimation MSE compared to various state-of-the-art baselines.