# Dynamic Programming Ring for Point Target Detection
## 5 Conclusions  
Aiming to improve the point target detection performance of DP, this paper proposes an MFF-DPR to improve the point target detection probability. First, a second-order DP named the MFF-DP is proposed to reduce noise influence on the pixel state estimation. The current states of pixels on the image plane are estimated by maximizing the addition of the merit functions of the previous two frames and observation data of the current frame. Second, a merit function diffusion suppression structure is proposed. The sequential and reverse observation data are connected head to tail to form a ring structure according to the time reversal symmetry of the DP-TBD. The MFF-DP is constructed to run on the ring structure, and the sequential and reverse merit functions of the MFF-DPs are averaged to obtain the merit function of the MFF-DPR. Finally, the target trajectory is obtained by correlating the extreme points of the merit functions of the MFF-DPR. The simulation and analysis results show that the point target detection algorithm based on the MFF-DPR can achieve a significantly higher performance in point target detection compared with the traditional DP-TBD algorithms. The results also indicate that by merely adding a ring structure, the detection probability of the traditional DP-TBD algorithms can be improved by up to 40% when detecting point targets under the SNR of 1.8.  
The MFF-DPR has the same drawback as the traditional second-order DP-TBD. Due to the large search space, calculating the merit function of the MFF-DPR is time-consuming. Fortunately, the processing of each pixel on the image plane based on the MFF-DPR is almost the same; thus, using parallel computing optimization and implementing the GPU programming, the computational speed can be significantly improved. The MFF-DPR is also a batching processing algorithm, which is not suitable for application scenarios with high requirements for real-time performance. Therefore, to enhance the state-of-the-art performance of the current radars and infrared point target detection systems, an improved  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **CFO-DP/DPR** & **CSO-DP/DPR** & **MFF-DP/DPR** \\ \hline Single-frame & Test case 1 & 34/65 & 118/236 & 161/315 \\ processing time (ms) & Test case 2 & 34/65 & 119/237 & 155/313 \\  & Test case 3 & 53/95 & 175/353 & 235/485 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison of the computational efficiencies of the DP/DPR algorithms in multi-target detection.  
Figure 10: False alarm rates of different DP and DPR algorithms in multi-target detection. (**a**) test case 1; (**b**) test case 2; (**c**) test case 3.  
version of the MFF-DPR is needed; thus, reducing the complexity of the MFF-DPR based on the GPU programming could be a future research direction.  
The authors' contributions are as follows. [PERSON] proposed the idea, programmed the method, and revised the manuscript. [PERSON] wrote the first version of the manuscript. [PERSON] and [PERSON] performed an in-depth discussion of the related literature. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Key Research and Development Program of China (Grant No.2019 YFA0706001).  
The authors would like to thank their colleagues working with them in the Institute of Optics and Electronics at the Chinese Academy of Sciences. The authors also would like to thank the anonymous reviewers for their very constructive comments and suggestions.  
The authors declare no conflict of interest.