On Probabilistic Quantization and Mean-Value Fusion Design for Distributed Estimation in Sensor Networks

This paper considers the optimal probabilistic quantizer and fusion center (FC) design for the problem of quantization based parameter estimation in a distributed sensor networks. First, the mean square error (MSE) lower bound of quantization based parameter estimation is derived for sensors with binary quantization constrains. Based on the MSE lower bound, we propose a model-driven parameterized quantizer module, which solves the realization of arbitrary probabilistic quantization with any given probability, and derives the corresponding optimization problem to optimize the distribution of quantized data. Then, it is proved that using only the mean value of all quantized data from sensors has no performance degradation in terms of the MSE criterion. Thus, the parameterized mean-value fusion and estimation module is proposed for FC, along with the optimization problem of FC design parameters. Finally, based on the deep learning optimization methods, two loss function are derived to sequentially optimize the design parameters of quantizer and FC. Simulation results reveal that the proposed method outperforms the state-of-the-art techniques under certain scenarios.