# LEO-Based Satellite Constellation for Moving Target Detection
## 3 Results
### Multi-Source Fusion CFAR Detection Results  
The three-dimensional projection results from range-DFR domain \(R-f_{dr}\) to Cartesian-DFR domain \(X-Y-f_{dr}\) after multi-source fusion is demonstrated in Figure 9a. To evaluate the performance of the proposed method in detail, the slice of the fusion results along DFR bins is given in Figure 9b. Compared with Figure 9a, the noise power in Figure 9b will decrease. Assume there are \(K\) DFR bins in Figure 9a, and the noise power in Figure 9b is \(\frac{1}{K}\) that of Figure 9a due to the noise power accumulated along DFR bins with incoherent accumulation mode. One can see that the echoes with multiple satellites are focused on the same cell, which agrees with the theoretical analysis. Considering the target fluctuation characteristics caused by the diverse incident angles of multiple satellites, 3 dB amplitude fluctuation is added to the multi-source echoes in the simulation process, other simulation parameters are consistent with that in Section 3.1. Figure 8: The relationship between the target velocity and the optional cell interval in DFR domain. Figure 7: The distribution results of the target and the clutter. (**a**) The target echo in DFR domain; (**b**) The clutter echo in DFR domain. Assume that the sliding window is composed of 3 \(\times\) 3 cells, Figure 10a shows the weight distribution of the contrast ratio based on the sliding window, where the diffusion energy around the target cell is greatly decreased through introducing the contrast between the sliding window center and the edge region. Figure 10b reveals the exponential weighted likelihood ratio distribution corresponding to the fusion result. Compared with the likelihood ratio, the exponential weighted likelihood ratio increases the contrast between the target cell and the adjacent cells, which is conductive to improve the multi-source fusion CFAR detection algorithm. Suppose that the target fluctuation type follows Swerling I distribution [15], the performance corresponding to different likelihood ratio based (LRB) detection methods [4] is compared in Figure 11a, where the false alarm probability is set to 1 \(\times\) 10\({}^{-6}\), Monte Carlo simulation times is 500, and the SNR interval is set to 3-15 dB. One can see that the LRB detection method with multiple platforms could effectively enhance the detection probability, compared with LRB detection method with a single platform. Accordingly, the effectiveness of the multi-source fusion theory can be verified. While the proposed likelihood ratio weighting based (LRWB) detection method with multiple platforms could further improve the detection performance, especially for low target SNR interval. The  
Figure 10: The intermediate variables in the multi-source fusion process. (**a**) The weight distribution of the contrast ratio based on the sliding window; (**b**) The exponential weighted likelihood ratio distribution corresponding to the fusion result. Figure 9: The multi-source fusion results of the target echo. (**a**) The target fusion result in Cartesian-DFR domain; (**b**) The slice of the fusion result along DFR bins. fusion CFAR detection results with different methods are indicated in Figure 11b-d under the condition that the false alarm probability is \(1\times 10^{-6}\) and SNR is 7 dB, among which the target region can be extracted more precisely by means of the LRWB method. For multiple targets scenario, multi-source fusion results are demonstrated in Figure 12, where the two moving target coordinates are given by [\(-0.5\) km, \(1.5\) km] and [\(4\) km, \(2\) km] respectively, and other parameters are consistent with the former. Figure 12a shows the multi-source fusion result. From Figure 12b,c, both the weight distribution and the exponential weighted likelihood ratio distribution reveal that the diffusion energy around the two target cells is greatly decreased.