## 2 Methodology
### Improved VI-CFAR
#### 2.2.1 Fosta-Cfar  
When the environmental type is misjudged, the detection performance of VI-CFAR significantly decreases due to the poor robustness of the detection algorithm used in a clutter edge environment. Therefore, the detection algorithm with strong robustness should be used in clutter edge environments. OSTA-CFAR is a threshold-adjustable OS-CFAR [1]. In OSTA-CFAR, the homogeneous clutter power level estimation \(a\) is calculated by the prior knowledge, the cells in the reference window are sorted in ascending order, and the \(l\)-th reference cell \(X_{lN}\) is determined as the clutter edge environment judgment sample. If \(X_{lN}\) is greater than \(a\), the environment is judged as the non-clutter edge environment, and the background clutter estimation is determined as the \(k\)th reference cell sample value. In contrast, if \(X_{lN}\) is less than or equal to \(a\), the environment is judged as the clutter edge environment, and the background clutter estimation is determined as the \(k+1\)-th reference cell sample value. OSTA-CFAR has better false alarm control ability than OS-CFAR. Furthermore, as a member of the order statistic class detection algorithms, OSTA-CFAR has stronger robustness to the environment. However, in the actual detection process, it is very difficult to obtain prior knowledge and calculate the value of \(a\) due to the variability of the environment. In addition, even if the prior knowledge can be obtained and the value of \(a\) can also be calculated, OSTA-CFAR only replaces the background clutter estimation from the \(k\)-th reference cell sample value to the \(k\)+1-th reference cell sample value in clutter edge environment, which constraints the performance improvement of this detection algorithm. In the process of target detection, background clutter often exhibits significant uncertainty and fuzziness. The OSTA detection algorithm, characterized by limited threshold variability, struggles to respond accurately to transitional environmental states, making it susceptible to local disturbances that can degrade detection performance. Fuzzy theory excels at handling such uncertainty and ambiguity. It enables the modeling of input variables as fuzzy sets and allows flexible reasoning through fuzzy rules to produce continuous, adaptive outputs. This capability addresses a deficiency in the OSTA-CFAR detector when operating in complex environments. Compared to tools such as neural networks, fuzzy theory offers a simpler mathematical structure, so it not only resolves the aforementioned issues but also maintains the real-time responsiveness of the detector. Therefore, to further enhance the adaptability of the OSTA-CFAR to compensate for the performance degradation of VI class CFAR detectors caused by environmental misjudgment, combining fuzzy theory, FOSTA-CFAR is proposed, and its calculation block diagram can be shown in Figure 2.  
In Figure 2, the homogeneous signal \(l\) and the orthogonal signal \(Q\) are processed by the envelope detector and input into FOSTA-CFAR. The samples \(X_{i}\) in the leading window A and the lagging window B are arranged in ascending order to calculate \(MR\). The difference between MR and the threshold is input into the fuzzy inference system to obtain the appropriate \(m\) value, and then the clutter estimation suitable for the current environment is obtained for target detection. From (4), it can be seen that the higher the value of \(MR\), the higher the mean ratio of the clutter power of the leading window and the lagging window, that is, the higher the amplitude of the clutter power jump, and the lower the probability of misjudgment in this case. Instead, it can be concluded that the lower the value of \(MR\), the higher the probability of misjudgment in this case. Therefore, the clutter power jump amplitude and misjudgment can be reflected by \(MR\)in the current environment. Also, the thresholds \(K_{MR}\) and \(K_{MR}^{-1}\) are determined before target detection.