Robust Distributed Cooperative Localization in Wireless Sensor Networks with a Mismatched Measurement Model

Distributed cooperative localization (CL) possesses the merits of high accuracy, robustness, and availability, and has garnered extensive attention in recent years. Due to the complex signal propagation environment, measurements often include errors from various unknown factors, leading to a mismatch between the nominal and actual measurement models, which reduces estimation accuracy. To tackle this problem, this paper proposes a robust distributed CL algorithm. First, we establish a unified measurement model incorporating latent variables capable of characterizing nonideal errors in the absence of additional prior environmental information. The latent variables are modeled using Gaussian-Wishart conjugate prior distribution with hyperparameters. Next, we decompose the robust CL problem into the alternate estimation of the variational posterior for agent positions and latent variables. By constructing the probabilistic graphical model, the estimation can be implemented in a distributed manner via the message passing framework. Closed-form solutions are derived for updating the variational posteriors of agent positions and latent variables, ensuring all parameters can be computed algebraically. Additionally, we analyze the algorithm's performance, computational complexity, and communication overhead. Simulation and experimental results show that the proposed algorithm exhibits superior estimation accuracy and robustness compared to existing methods.