## 1 Introduction  
A radar system is an electronic device that employs electromagnetic waves for target detection, which is extensively used in various aspects of life, such as military early warning, wireless communication, navigation, meteorology, and so on. One of the principal roles of radar is to detect targets [1; 2; 3; 4]. Traditional radar target detection can be categorized into two steps: the first step is the filtering process, which involves suppressing clutter to enhance the signal-to-clutter ratio (SCR); the second step is to process the filtered data with a constant false alarm rate (CFAR). This method is complex and costly. In the past few years, adaptive detection has gradually come into people's sight. Its core idea is to jointly use the data to be detected and training samples to construct an adaptive detector, which integrates filtering and CFAR processing [5]. Compared with the step-by-step detection method, adaptive detection technology not only simplifies the process but also improves detection performance. It is important to mention that the clutter covariance matrix is typically unknown and requires estimation using training samples [6]. The traditional assumption model holds that the training samples and the data to be detected have the same statistical characteristics, following a complex Gaussian distribution [7], but this assumption often does not hold in complex electromagnetic environments. Due to factors such as clutter fluctuations in real scenarios, environments often show non-homogeneous characteristics, especially non-Gaussian environments. However, training samples should have some similarities to the data to be detected [8]; otherwise, they cannot provide useful information. In 1999, [PERSON] et al. put forward the generalized likelihood ratio test (GLRT) detector in a partially homogeneous environment, known as the adaptive coherence estimator [9]. In a partially homogeneous environment, the training samples share the same covariance matrix, but an unknown power mismatch exists between the training samples and the data to be detected. In a complicated and changeable real environment, this assumption is also too idealistic. As the resolution of radar enhances, the quantity of scatterers within each resolution cell diminishes, leading to different levels of local roughness of clutter within different range resolution cells and causing larger amplitude fluctuations. In such cases, clutters exhibit non-Gaussian characteristics [10; 11; 12]. The distribution of amplitudes for non-Gaussian clutter exhibits a heavier tail, rendering the Gaussian model insufficient in accurately describing such clutter. The compound-Gaussian model [13; 14; 15] is an extensively accepted model for modeling non-Gaussian clutter, which can be characterized as the product of mutually independent slow-changing texture components and fast-changing speckle components, where the former is a non-negative random variable and the latter is a complex Gaussian random vector. Non-Gaussian clutter can be expressed as various compound-Gaussian models, depending on the specific texture component models. When the texture component follows a gamma distribution, the compound-Gaussian clutter is K distribution clutter. It can describe non-homogeneous clutter well at high resolution and small grazing angles. When the texture component follows an inverse gamma distribution, compound-Gaussian clutter is Pareto distribution clutter. It is more suitable for describing clutter with heavy tails. When the texture component follows an inverse Gaussian distribution, compound-Gaussian clutter is CG-IG distribution clutter. It has a better fitting capability for high-resolution sea clutter. Among them, the most common clutter is K distribution clutter [16; 17; 18]. However, not all types of real clutter can be modeled as a compound-Gaussian model. Additionally, some models that fit real clutter well do not conform to the compound-Gaussian model, such as Weibull distribution [19] and Log-Normal distribution [20].