An Efficient Threshold Determination Algorithm for DP-TBD Based on Structural Analogy and Saddle-Point Approximation

Dynamic programming track before detect (DP-TBD) is widely applied in the radar detection for weak targets. The algorithm selects the most advantageous state in each stage to integrate the merit function and return the corresponding target status to the merit function that exceeds the detection threshold in the final stage. However, due to the recursive search strategy included in DP, the constant false alarm rate (CFAR) detection threshold is difficult to be quickly determined by numerical integration. Monte Carlo counting, extreme value theory, or its extended algorithm are commonly used to determine the detection threshold of DP. However, these methods require many times of the Monte Carlo simulation, which is time-consuming and difficult to apply to practical projects. In order to achieve fast and accurate acquisition of CFAR detection threshold, this article proposes an efficient approximation algorithm to determine the DP-TBD CFAR threshold. The algorithm approximates the computational structure of DP-TBD by structural analogy, and then uses the saddle-point approximation method and the numerical integration of the fitting formula to quickly determine the CFAR threshold. Numerical simulation experiments under various conditions and radar field experiments are carried out to verify the high accuracy of the approximate threshold determined by the proposed algorithm. In addition, the algorithm is further extended and can be applied in the noise background with varying power. The corresponding numerical simulation experiments prove the effectiveness of the extended algorithm.