## 1 Introduction  
The constant false alarm rate (CFAR) detector determines the existence of a target by comparing the sample value of the cell under test (CUT) with the threshold. As an important component of radar, it is applied widely in advanced assisted driving, ship navigation, and electronic reconnaissance. A CFAR-enhanced ship detection method based on YOLOv5 is proposed in Ref. [1], which improves the detection performance of ship targets in SAR images by incorporating traditional features, especially enhancing robustness in complex sea conditions. Ref. [2] combines CFAR with dual-polarization data to propose a novel radar target detection framework, demonstrating excellent performance in large-scale SAR ship detection, particularly in the detection of small and near-shore vessels. Ref. [3] introduces an imaging technique based on Multi-Input Multi-Output Synthetic Aperture Radar (MIMO-SAR), which enhances target detection capabilities for radar in intelligent driving systems by improving side-view resolution. Ref. [4] presents a deep learning-based radar object detection network (RODNet) for millimeter-wave radar, achieving efficient real-time target detection by integrating camera and radar data, addressing the challenge of target recognition in complex environments. The performance of the CFAR detector will be directly impacted by the background environment in the reference window and the type of detector. It usually contains three different background environments: multiple target, clutter edge, and homogeneous. CFAR detectors can be categorized into mean-based, order-statistic-based, and adaptive types based on how background clutter is estimated. The mean-based category includes algorithms such as cell-averaging CFAR (CA-CFAR), smallest-of CFAR (SO-CFAR), and greatest-of CFAR (GO-CFAR). In CA-CFAR, the clutter level is estimated by taking the average of reference cells from both the leading and lagging windows [5]. CA-CFAR performs well in homogeneous environments, but its detection capability decreases in scenarios involving multiple targets or clutter edges [6]. Furthermore, the SO-CFAR and GO-CFAR detectors were proposed in Ref. [7]. In SO-CFAR, the background clutter is estimated by selecting the smaller total from the reference cells in the leading and lagging windows. In contrast, GO-CFAR estimates the background clutter using the larger total from these two windows. In both detectors, the thresholds are obtained by multiplying their background clutter estimations and the threshold coefficients. SO-CFAR demonstrates improved detection performance over CA-CFAR in multiple-target environments but performs poorly in homogeneous and clutter edge scenarios [8]. Likewise, GO-CFAR outperforms CA-CFAR in clutter edge environments, while its effectiveness diminishes in homogeneous and multiple-target environments [9]. To enhance detection capability under multiple-target conditions, an order statistic CFAR detector (OS-CFAR) was introduced in Ref. [10]. In OS-CFAR, the sample quartile (SQ) estimator is used to select the \(k\)-th reference cell in ascending order for background clutter estimation. OS-CFAR exhibits better detection performance than CA-CFAR in multiple-target environments; however, its performance degrades in homogeneous and clutter edge environments. Furthermore, Ref. [11] proposed an order statistic class CFAR detector based on the Kaigh-Lachenbruch quantile (KLQ) estimator, known as KLQ-CFAR. Compared to OS-CFAR, KLQ-CFAR offers better detection performance in both homogeneous and multiple-target environments by substituting the KLQ estimator for the SQ estimator. Overall, when the prior parameters in the quantile estimator are properly selected, order statistic class CFAR detectors can generally achieve favorable detection performance in multiple-target environments [12]. However, the environment changes in real-world applications, and the detectors mentioned above usually only adapt to one environment's detection requirements.