## 2 Related Works  
Among the statistical methods can be distinguished methods involving the deliberate selection of training bins [19; 20; 21]. In article [20], it was described as a method of training sample selection (training sample selection), which consists in accepting only those training cells for which the covariance matrices are similar in a certain way to the covariance matrix of the bin being tested for the presence of a target. Another method used to select training bins to determine the clutter covariance matrix is the Generalized Inner Product (GIP) method. STAP based on the GIP method may inaccurately estimate the clutter covariance matrix, leading to degradation of STAP performance [20; 22]. Most of the known basic statistical methods associated with the selection of appropriate training bins described above have modifications aimed at eliminating undoubted disadvantages that negatively affect the performance of a given STAP method. Over time, statistical methods based on the above have been developed, such as Prolate Spheroidal Wave Functions GIP (PSWF-GIP) or Cross-Spectral Metric Smoothing GIP (CSMS-GIP), which also select appropriate training bins based on certain statistics and a pre-transformed clutter covariance matrix of the entire set of training bins [23; 24]. It should be noted that these methods are highly effective for homogeneous clutter. This is due to the assumption that clutter bins have identical probability decompositions. However, statistical methods require access to a large number of training bins, which is mostly difficult to meet. Currently, researchers are focusing all their efforts on improving non-static methods, which are computationally less complex methods in terms of both time and memory [25; 26; 27]. Nonetheless, statistical methods are subject to computational errors, which reduces the probability of accurate object detection. When considering the development of non-statistical methods for determining the clutter covariance matrix, direct data domain STAP (D3-STAP) algorithms should also be mentioned. The idea behind this type of algorithm is to use a single cross-section of a radar data cube, that is, data collected for a single distance bin, to determine a vector of weights. Two typical D3 STAP algorithms are the direct data domain least square (D3 LS) algorithm and the direct data domain sparse recovery (D3 SR) algorithm, which uses the sparsity of the interference matrix [28; 29; 30; 31]. Currently, on the basis of the latest literature, it is necessary to cite a completely new D3-STAP method proposed in the works [32; 33], which is based on the knowledge of the Doppler frequency of the target and the speed of movement of the radar platform, as well as an optimization method that is used to determine the necessary distance bins required to reconstruct the clutter covariance matrix. The name of the proposed method is not given directly; however, for the purposes of this article, the acronym D3-STAP-ANM (D3-STAP based on atomic norm minimization) is adopted. In the past few years, a whole series of studies on non-statistical methods for the estimation of the clutter covariance matrix has mainly focused on the combination of direct data domain (D3) STAP methods, together with sparse recovery algorithms, as evidenced by publications [34; 35; 36; 37; 38; 39]. Thus, it has been shown that by using a small number of training bins or, in some cases, one, as well as by using sparsity of clutter in the spatial-temporal domain, it is possible to obtain a high resolution of the spatial-temporal clutter spectrum, which directly provides the estimation of the clutter covariance matrix. To improve the target detection performance of airborne radar in the presence of clutter, adaptive real-time processing (STAP) with a single-input-multiple-output (SIMO) array (i.e., phased array) has been proposed [40; 41; 42]. The key of STAP is the use of an adaptive multivariate filter to create a deep indentation on the clutter ridge and thus effectively suppress the clutter.