Mitigating Quantization Effects on Distributed Sensor Fusion: A Least Squares Approach

In this paper, we consider the problem of sensor fusion over networks with asymmetric links, where the common goal is linear parameter estimation. For the scenario of bandwidth-constrained networks, existing literature shows that nonvanishing errors always occur, which depend on the quantization scheme. To tackle this challenging issue, we introduce the notion of virtual measurements and propose a distributed solution LS-DSFS, which is a combination of a quantized consensus algorithm and the least squares approach. We provide detailed analysis of the LS-DSFS on its performance in terms of unbiasedness and mean square property. Analytical results show that the LS-DSFS is effective in smearing out the quantization errors, and achieving the minimum mean square error (MSE) among the existing centralized and distributed algorithms. Moreover, we characterize its rate of convergence in the mean square sense and that of the mean sequence. More importantly, we find that the LS-DSFS outperforms the centralized approaches within a moderate number of iterations in terms of MSE, and will always consume less energy and achieve more balanced energy expenditure as the number of nodes in the network grows. Simulation results are presented to validate theoretical findings and highlight the improvements over existing algorithms.