## 1 Introduction  
With many large-scale low Earth orbit constellation projects launched, such as Iridium, SpaceX, OneWeb and Hongyan, LEO satellites have recently received a lot of attention for their prospects of augmenting the global navigation satellite system (GNSS). Traditional GNSS systems, which require users to receive signals from satellites in medium Earth orbit, have signal strengths of only \(-158.5\) dBW when they reach the Earth. This means that the user must directly receive these signals to perform localization. However, LOS signal-dependent localization has notable limitations. In urban environments and areas with complex obstacles, severe signal degradation often occurs, making it difficult for the user to receive signals directly. Such signal unreliability significantly impairs positioning performance [1] and prevents GNSS from offering safe and reliable positioning services. In applications requiring high reliability, such as autonomous driving and UAV mission, these large positioning errors are unacceptable. In the direction of NLOS virtual station constuction, [PERSON] [2] proposed a virtual station localization method for joint time of arrival (TOA) and DOA in NLOS environments. The method constructs a virtual station by utilizing multiple reflected signals from a single base station, and the user's location is obtained through a two-step least squares position estimation algorithm. [PERSON] [3] employed an array antenna to distinguish between multipath signals, selecting the angle of arrival and distance information of the two strongest signals. A virtual base station is then established to convert NLOS paths into LOS paths, allowing for the calculation of the initial user position based on the virtual base station's angle and distance information. [PERSON] [4] applied matrix beam and matrix augmentation processing to measurement data from a uniform line array receiver, generating a virtual base station based on the known plan. [PERSON] [5] ranked base stations based on signal arrival time variance, selecting those with smaller variance for initial position computation using positive definite equations. Simultaneously, the pedestrian heading projection technique was employed to compute user positions in the first three steps. Following this, virtual base stations were constructed based on user positions from the first three steps, allowing LOS and virtual base stations to jointly participate in the positioning process. [PERSON] [6] compared the performance of NLOS inversion algorithms by analyzing their mean square error and optimal Clamello lower bound. [PERSON] [7] utilized the multipath properties of commodity WiFi signals to enhance indoor localization. First, the positions of the target and scatterers (e.g., furniture) were jointly estimated. Then, the difference in propagation time between reflected and direct paths was used to select the direct path as a reference, combined with the angle of arrival. Finally, a particle swarm optimization-based algorithm was developed to search for target and scatterer positions. [PERSON] [8] first identified single reflected scattering signals from the same scatterer using angle of arrival and time of arrival measurements. The LOS positioning algorithm was then used to locate the scatterer, which was treated as a virtual station for user positioning. [PERSON] [9] addressed the challenge of NLOS paths by using angle of arrival and time of arrival estimations in a multi-reflectance NLOS environment, enabling time differences to be equivalently used in place of distance differences. Numerous studies have concentrated on the development of robust algorithms and innovative methods to accurately estimate these parameters [10; 11; 12; 13; 14]. [PERSON] [15] developed a dimensionality-reducing MUSIC (Multiple Signal Classification) algorithm that simplifies azimuth estimation in a MIMO radar system by performing two one-dimensional searches, thereby avoiding the high computational cost of the 2D-MUSIC algorithm.