Auxiliary Particle Filtering Over Sensor Networks Under Protocols of Amplify-and-Forward and Decode-and-Forward Relays

In this paper, the particle filtering problem is investigated for a class of stochastic systems with multiple sensors under signal relays. To improve the performance of signal transmissions, a relay is deployed between each sensor and the remote filter. Both amplify-and-forward (AF) and decode-and-forward (DF) relays are considered under certain transmission protocols. Stochastic series are employed to describe multiplicative channel gains and additive transmission noises. Novel likelihood functions are derived based on the AF/DF relay models under different protocols. With the measurements collected from all the sensor nodes, a new centralized auxiliary particle filter (APF) is designed by resorting to the statistical information of the channel gains and transmission noises. Next, a consensus-based distributed APF is further established at each node that requires only locally available information. Finally, the effectiveness of the proposed filtering approach is demonstrated through target tracking simulation examples in different situations.