Distributed Bayesian Filtering using Logarithmic Opinion Pool for Dynamic Sensor Networks
For multi-sensor networks, this work provides a theoretically grounded distributed filtering method with guaranteed convergence, addressing robustness and time-step constraints.
The paper presents a distributed Bayesian filtering algorithm for target tracking in dynamic sensor networks, achieving global exponential convergence of each agent's likelihood to the centralized joint likelihood. Theoretical bounds on convergence and robustness are provided.
The discrete-time Distributed Bayesian Filtering (DBF) algorithm is presented for the problem of tracking a target dynamic model using a time-varying network of heterogeneous sensing agents. In the DBF algorithm, the sensing agents combine their normalized likelihood functions in a distributed manner using the logarithmic opinion pool and the dynamic average consensus algorithm. We show that each agent's estimated likelihood function globally exponentially converges to an error ball centered on the joint likelihood function of the centralized multi-sensor Bayesian filtering algorithm. We rigorously characterize the convergence, stability, and robustness properties of the DBF algorithm. Moreover, we provide an explicit bound on the time step size of the DBF algorithm that depends on the time-scale of the target dynamics, the desired convergence error bound, and the modeling and communication error bounds. Furthermore, the DBF algorithm for linear-Gaussian models is cast into a modified form of the Kalman information filter. The performance and robust properties of the DBF algorithm are validated using numerical simulations.