  A variety of filters with track-before-detect (TBD) strategies have been
developed and applied to low signal-to-noise ratio (SNR) scenarios, including
the probability hypothesis density (PHD) filter. Assumptions of the standard
point measurement model based on detect-before-track (DBT) strategies are not
suitable for the amplitude echo model based on TBD strategies. However, based
on different models and unmatched assumptions, the measurement update formulas
for DBT-PHD filter are just mechanically applied to existing TBD-PHD filters.
In this paper, based on the Kullback-Leibler divergence minimization criterion,
finite set statistics theory and rigorous Bayes rule, a principled closed-form
solution of TBD-PHD filter is derived. Furthermore, we emphasize that PHD
filter is conjugated to the Poisson prior based on TBD strategies. Next, a
capping operation is devised to handle the divergence of target number
estimation as SNR increases. Moreover, the sequential Monte Carlo
implementations of dynamic and amplitude echo models are proposed for the radar
system. Finally, Monte Carlo experiments exhibit good performance in Rayleigh
noise and low SNR scenarios.
