## 6 Test and Analysis
Following the principles of target acoustic positioning for the multiple five-element acoustic arrays, we processed the acoustic information of the UAV target using the VMD and correlation function algorithms. The temporal information of each sensor in basic array A, as shown in Figure 7, is: \(t_{0}^{A}=52.96\) ms, \(t_{1}^{A}=51.32\) ms, \(t_{2}^{A}=40.03\) ms, \(t_{3}^{A}=45.08\) ms, \(t_{4}^{A}=57.11\) ms. The temporal information of each sensor in basic array B, as shown in Figure 8, is: \(t_{0}^{B}=293.25\) ms, \(t_{1}^{B}=292.46\) ms, \(t_{2}^{B}=301.78\) ms, \(t_{3}^{B}=293.96\) ms, \(t_{4}^{B}=284.83\) ms. The temporal information of each sensor in basic array C, as shown in Figure 9, is: \(t_{0}^{C}=216.32\) ms, \(t_{1}^{C}=224.87\) ms, \(t_{2}^{C}=214.78\) ms, \(t_{3}^{C}=211.21\) ms, \(t_{4}^{C}=212.98\) ms. According to Formulas (10) and (11), we calculate the time difference of each sensor in the basic array A as: \(\tau_{01}^{A}=1.64\) ms, \(\tau_{02}^{A}=12.93\) ms, \(\tau_{03}^{A}=7.88\) ms, \(\tau_{04}^{A}=-4.15\) ms. The time difference of each sensor in the basic array B is: \(\tau_{01}^{B}=0.79\) ms, \(\tau_{02}^{B}=-8.53\) ms, \(\tau_{03}^{B}=-0.71\) ms, \(\tau_{04}^{B}=8.42\) ms. The time difference of each sensor in the basic array C is: \(\tau_{01}^{C}=-8.55\) ms, \(\tau_{02}^{C}=1.54\) ms, \(\tau_{03}^{C}=5.11\) ms, \(\tau_{04}^{C}=3.34\) ms. Further, using the calculation functions for basic arrays A, B, and C in Formula (2), the UAV target positions for the signals in Figures 7-9 are calculated. \(P_{A}(x_{A}\ ^{\prime},y_{A}\ ^{\prime},z_{A}\ ^{\prime})=(-2.10,5.75,14.63)\), \(P_{B}(x_{B}\ ^{\prime},y_{B}\ ^{\prime},z_{B}\ ^{\prime})=(3.01,-33.92,014)\), \(P_{C}(x_{C}\ ^{\prime},y_{C}\ ^{\prime},z_{C}\ ^{\prime})=(-0.48,-0.06,0.11)\). Subsequently, applying the conversion relationships of basic arrays A, B, and C in the \(Oxyz\) coordinate system, we determined the relative positions for the UAV signals corresponding to Figures 7-9. \(P(x_{A},y_{A},z_{A})=(27.9,5.75,14.63)\), \(P(x_{B},y_{B},z_{B})=(-33.01,-33.92,0.14)\), \(P(x_{C},y_{C},z_{C})=(-0.48,29.94,0.11)\). To further validate the feasibility of the proposed algorithm in this paper, based on the selected hardware equipment and performance metrics, we conducted five experiments. Following the target signal processing algorithm using VMD and the time difference calculation algorithm based on the correlation function as proposed in this paper, we processed the collected acoustic information from the five UAV instances. Tables 1-3 present the corresponding temporal information \(t_{0}^{A}-t_{4}^{A}\), \(t_{0}^{B}-t_{4}^{A}\), \(t_{0}^{C}-t_{4}^{C}\), the processed positions \(P_{A}(x_{A}\ ^{\prime},y_{A}\ ^{\prime},z_{A}\ ^{\prime})\), \(P_{B}(x_{B}\ ^{\prime},y_{B}\ ^{\prime},z_{B}\ ^{\prime})\), \(P_{C}(x_{C}\ ^{\prime},y_{C}\ ^{\prime},z_{C}\ ^{\prime})\) of the unit acoustic arrays for the UAV target, and the positions \(P(x_{A},y_{A},z_{A})\), \(P(x_{B},y_{B},z_{B})\), \(P(x_{C},y_{C},z_{C})\) in the \(Oxyz\) coordinate system. Figure 9: The processing effect of five acoustic sensors in basic array C.  
According to the test results in Tables 1-3, it is verified that the signal processing method of low-altitude target acoustic positioning based on variational modal decomposition proposed in this paper aligns with the test requirements. The algorithm fully considers the characteristics of multiple frequency components of the target and uses the VMD to decompose different frequency signals to ascertain the optimal solution of the algorithm, thereby obtaining the actual signal frequency component of the target. In the calculation process, it is not difficult to find that the effectiveness of VMD mainly depends on the number of modes K and the quadratic penalty factor \(\sigma\). The modal number K is the K modal components obtained by the decomposition of the original signal. The number of components present by VMD reduces the occurrence of modal aliasing.