Delay-estimation-based asynchronous particle filtering for passive target tracking in underwater wireless sensor networks

Passive target tracking based on bearings-only or Doppler-bearing measurements is difficult because there is no way to determine the propagation time from source to receiver. This paper deals with the variable propagation delay problem in 3-dimensional passive tracking with the underwater wireless sensor networks (UWSNs). We propose an asynchronous particle filtering algorithm based on delay estimation to overcome the difficulty that asynchronous data can't be fused directly. Firstly, according to the 3-d geometry structure among the snapshot state, truly measured state, and node position, we deduce the particle delay from measured position to node position based on prior particle state. Then the measured state can be expressed as a function of snapshot state and the likelihood of the measurements with prior snapshot states is derived. Thus we build the relationship between snapshot state and asynchronous time-unclear measurements based on a reverse-transitivity particle filtering algorithm. Simulation results show that the proposed algorithm is effective in complex 3-d scenes, and further experiments illustrate that the fusion performance is related to both the target velocity and node number in UWSNs.