Distributed Optimization for Estimation and Communication Co-Design Under Bandwidth Constraints

In the Industrial Internet of Things (IIoT), multiple sensors are deployed in production sites to perform state estimation of large-scale physical systems, which is important to ensure the stable operation of the production process. Sensors can only transmit quantized local information composed of a finite number of bits, where more quantization bits improve estimation accuracy. However, ensuring the necessary data rate for such data transmission under bandwidth limitations requires larger transmission power, increasing the energy consumption of sensors. To address this trade-off, this paper considers the co-design of estimation and communication, where the data rate and transmission power are jointly allocated to minimize a weighted estimation-communication cost while satisfying the minimum data rate constraint. An $\ell _{p}$-box alternating direction method of multipliers (ADMM) based distributed optimization method is designed to solve this mixed-integer nonlinear programming (MINLP) problem, and the global convergence of the proposed method is proved. Moreover, a distributed estimation algorithm is proposed to ensure the convergence of estimation errors with minimum data rates, and the balance of the ultimate bound and convergence rate of estimation errors can be achieved by tuning the estimation gain. A numerical case study in the hot rolling process shows the superiority of the proposed distributed optimization and estimation methods.