Remote State Estimation for Complex Networks Under Probabilistic Bit Flips: A Transmission Power Allocation Scheme

In this article, the problem of remote state estimation is investigated for a class of complex networks with noisy wireless communication channels. The employment of the binary encoding scheme allows for the description of the influence of channel noises as probabilistic bit flips, where the probability of these bit flips is influenced by several factors with the signal-to-noise ratio (SNR) being a crucial one. In engineering practice, the method of adjusting the transmission power for each node in a complex network is commonly applied to modify the SNR so as to reduce the data distortion caused by bit flips. Furthermore, due to restricted communication resources, the total available transmission power is often limited particularly in large-scale systems, such as complex networks. Consequently, the allocation of transmission power for all nodes under a total transmission power constraint becomes a concern. Utilizing the ultimately bounded filtering method, we devise a transmission-power-dependent state estimator, by which the combined effect of probabilistic bit flips and transmission power allocation on estimation performance is analyzed. Moreover, the task of co-designing the transmission power allocation scheme and estimator gains is modeled as an optimization problem, which is then addressed through a two-step optimization strategy. The existence of a unique optimal transmission power allocation scheme is also proven. Finally, numerical simulation examples are provided to demonstrate the effectiveness of the proposed co-design approach.