# Adaptive Constant False Alarm Detector Based on Composite Fuzzy Fusion Rules
## 5 Simulation Experiment Results and Analysis
### CFKLQ-CFAR Detection Performance
#### 5.1.2 Statistical Test
Therefore, it is believed that there is a significanct difference in the detection performance of ASKLQ-CFAR and CFKLQ-CFAR in a homogeneous environment. In a multiple-target environment, when three interferences exist in the leading window. The results of the paired \(t\)-test on CFKLQ-CFAR and ASKLQ-CFAR are as follows: \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Sum of** & **Degree of** & **Mean** & **F** & **P** \\  & **Squares** & **Freedom** & **Square** & & \\ \hline Between groups & 0.003 & 1 & 0.003 & 148.5259 & 3.9252 \(\times\) 10\({}^{-10}\) \\ Within group & 0.00041 & 18 & 0.000023 & & \\ Total & 0.004 & 19 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: ANOVA in a homogeneous environment. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Pair** & **Average Value** & **Number of Cases** & **Standard Deviation** & **Standard Error Mean** \\ \hline ASKLQ & 57.424050 & 10 & 0.0039803 & 0.0012587 \\ CFKLQ & 57.450900 & 10 & 0.0044932 & 0.0014209 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Paired sample statistics in a homogeneous environment. As shown in Table 7, the average detection probability of ASKLQ-CFAR is 55.0254%, and that of CFKLQ-CFAR is 55.0429%. The average of CFKLQ-CFAR is 0.0175% higher than that of ASKLQ-CFAR. This shows that the detection performance of CFKLQ-CFAR with the composite fusion rule has been improved in a multiple-target environment. In order to further compare whether the detection performance of the two detectors has reached the level of statistical difference, paired \(t\)-tests are performed for ASKLQ-CFAR and CFKLQ-CFAR. The average value is \(-\)0.01749, the standard deviation is 0.0036413, the standard error mean is 0.0011515, the 95% confidence interval for the difference is \([-0.0200948,-0.0148852]\), t-value is \(-\)15.189, degree of freedom is 9 and \(p\)-value is \(1.0116\times 10^{-7}\). As can be seen from the above data, the T value of the paired \(t\)-test of the average detection probability of ASKLQ-CFAR and CFKLQ-CFAR is \(-\)15.189. \(p\) value is 1.0116 \(\times 10^{-7}\), which is less than 0.05 at the significance level of 0.05. Therefore, it is believed that there is a significant difference between the detection performance of ASKLQ-CFAR and CFKLQ-CFAR in a multiple-target environment. The same data are used for the following ANOVA. In the ten sets of ASKLQ-CFAR data, the mean is 55.02544, the standard deviation is 0.0039390, and the 95% confidence interval of the mean is [55.022622, 55.028258]. In the ten sets of CFKLQ-CFAR data, the mean is 55.02493, the standard deviation is 0.0036878, and the 95% confidence interval of the mean is [55.040292, 55.045568]. From these data, it can be seen that the average detection probability of CFKLQ-CFAR is 0.01749 higher than that of ASKLQ-CFAR. According to the confidence intervals of the two sets of data, it can be seen that the two sets of data are quite different. It can be considered that CFKLQ-CFAR improves detection performance.The ANOVA is shown in Table 8.  
As shown in Table 8, the sum of squares between groups is 0.002, and the sum of squares within groups is 0.000262. The F value of the sum of squares between groups is 105.062. The \(p\) value is 6.0995 \(\times\)\(10^{-9}\), which is less than the significance level of 0.05. Therefore, it is believed that there is a significant difference in the detection performance of ASKLQ-CFAR and CFKLQ-CFAR in a multiple-target environment.