A Method for Resolving the Merit Function Expansion of Dynamic Programming TBD

Existing dynamic programming based track-before-detect (DP-TBD) strategies suffer from merit function expansion phenomenon (MFEP), which aggravated the burden of designing the detection threshold. The traditional constant false alarm rate (CFAR) detection is ineffective because the noise energy can not be exactly estimated from the area of merit function expansion. the threshold setting of existing DP-TBD strategies usually resort to the traditional Monte-Carlo counting, the extreme-value theory or its generalized version. For the nonhomogeneous clutter background and the fluctuating target, all of these constant threshold setting strategies inevitably exist the target losing or higher false alarm rate. In addition, for the multi-target scenes, in order to avoid solving high-dimensional optimization problems, existing the most effective DP-TBD methods all use the additional heuristic procedures to extract target trajectories one-by-one from the merit function expansion area by assuming target tracks are always independent. To overcome the aforementioned challenges, a novel one-step greedy optimization TBD algorithm (OSP-TBD) is proposed in this paper. By constraining the physically admissible trajectories, such that the different targets do not occupy the same resolution cell during the same stage and the trajectory with higher merit function (MF) is estimated ahead of others, OSP-TBD can eliminate the MFEP intrinsically and traditional CFAR procedure can be used to detect target adaptively. Besides, the proposed OSP-TBD algorithm can be used to process multi-target situation directly and declare all of the target trajectories corresponding to the states whose MF at the final frame exceed the given detection threshold without any additional heuristic procedure. Numerical simulations are used to assess the performance of the proposed strategies.