Theoretical Form and Numerical Calculation of Detection Threshold for DP-TBD in Processing Plot-List Data

Compared with the constant false alarm ratio (CFAR) detector, the dynamic programming algorithm for track-before-detect (DP-TBD) can utilize target motion information in large-scale interframe time to achieve better performance advantages in detecting targets with low signal-to-clutter ratio. To reduce computational complexity and minimize clutter interference, the DP-TBD algorithm directly processes the plot-list data, which is obtained by performing threshold preprocessing (or the CFAR detector) on the raw radar data. However, it is difficult to provide theoretical guidance on the detection threshold of the algorithm. Therefore, for the DP-TBD algorithm in processing the plot-list data, we theoretically derive and propose a numerical method to determine the detection threshold. First, we theoretically derive the probability density function of the clutter merit function, thereby providing a formula for calculating the probability of false alarm (PFA) of DP-TBD. Second, to mitigate the model error caused by the independent and identical distribution assumption, we propose a modified model with a coefficient to be determined from real data. Third, based on the theoretical formula, we propose a numerical calculation method implemented by fast Fourier transform to calculate the theoretical detection threshold. The experimental results demonstrate that the proposed method can effectively and accurately describe the PFA of DP-TBD for different simulation conditions in a uniform clutter environment.