Uncertainty-Constrained Belief Propagation for Cooperative Target Tracking

Cooperative localization is essential for many Internet of Things (IoT)-related applications in harsh environments. Generally, the inertial navigation system is self-contained and adopted as the basis of a cooperative tracking system, but it still faces the problem of accumulated errors and cannot provide long-term, high-precision positioning. The particle filter (PF) is widely used to fuse multiple information to inhibit accumulative errors. However, particle degradation and impoverishment remain unsolved. This article proposed an IMU/time-of-arrival (TOA) fusion-based tracking method, namely, uncertainty-constrained belief propagation (UCBP). We address particle degradation and impoverishment by introducing uncertainty-constrained optimization into belief propagation (BP). An uncertainty-constrained resampling (UCR) method is applied to quantify the uncertainty in cooperative systems. Hierarchical resampling is realized to solve the particle impoverishment issue. Meanwhile, particle degradation is resolved through constrained resampling while ensuring the diversity of particles. Furthermore, we illustrated the factor graph (FG) structure of UCBP to mitigate the accumulation of errors through message fusion over the graph. Compared with the state-of-the-art methods, our proposed UCBP algorithm has better precision and robustness without introducing much time overhead.