Particle Filter Track-before-detect Algorithm with Discontinuous Signals in Passive Sensor Systems

This paper considers the tracking problem of a moving emitter, which discontinuously emits certain signals, using a passive sensor system. There are two main difficulties, i.e., the detection uncertainty by classic thresholding process and the uncertainty of signal existence due to the discontinuous emission. The aim is to estimate both the kinematic state of the emitter and the unknown discontinuous property of the signal emission. This problem becomes more challenging when the signal-to-noise ratio (SNR) of the emitter is low. To this end, we first formulate it in the Bayesian framework and construct a joint posterior probability density function (pdf) incorporating the kinematic state with the discontinuous property. To calculate the goal pdf with signal emission uncertainty, we propose a varying period estimation (VPE) approach. First, a likelihood ratio test (LRT) is designed to estimate the discontinuous property, and determine the update time for Bayesian filtering. Then, the varying period Bayesian filtering for the kinematic state is derived based on the updated time. Furthermore, to avoid the performance degradation by detection uncertainty, a particle filter based track-before-detect (VPE-PF-TBD) with unthresholded measurements is designed. Simulation results demonstrate the effectiveness of the proposed algorithm.