## 1 Introduction  
Global navigation satellite system (GNSS) positioning technology has a wide range of applications in aviation, navigation, vehicle navigation, and other fields. GNSS positioning technology is necessary for achieving precise flight trajectory control and target navigation in aviation and navigation [1]. Real-time positioning is required to support autonomous driving and intelligent transportation systems in vehicle navigation [2]. Accurate positioning data are needed to study crustal movement and atmospheric changes in seismic monitoring and climate research [3]. The demand for high-precision and high-reliability positioning is increasing with the continuous development and transformation of GNSS technology. Previously, scholars focused on the research of GNSS high-precision positioning, and less exploration was undertaken on the problem of GNSS positioning error estimation. However, GNSS positioning and GNSS positioning error estimation are equally important [4]. Positioning errors may lead to the inaccuracy and unreliability of GNSS positioning, which has a serious impact on practical applications. Therefore, accurately estimating and controlling the positioning error are the keys to ensuring the accuracy and reliability of GNSS positioning. GNSS positioning is affected by errors that directly lead to inaccurate positioning results. The error sources in the GNSS positioning process mainly include satellite clock errors, ionospheric delay, tropospheric delay, multipath effect, receiver error, etc. [5]. Early research on GNSS positioning error estimation mainly focused on the estimation of a certain positioning error [6]. To minimize the impact of various factors on positioning results through modeling and analysis, many scholars have explored the problem of single error term estimation [7; 8; 9]. [PERSON] et al. designed a scheme to achieve high-precision positioning by estimating satellite clock errors [10]. This method has achieved excellent positioning results in both static and dynamic positioning. To address the problem that the dual-frequency ionospheric correction method ignores the high-order ionospheric error, [PERSON] et al. investigated a different approximation formula to estimate and correct the error caused by the excess path length [11]. Due to the lack of joint estimation of other error terms, the positioning error estimation method for a single error term has the problems of low accuracy and poor robustness. Subsequently, scholars have begun to focus on more refined positioning error modeling methods, and GNSS positioning accuracy has been improved to a certain extent [12]. The focus of related research is gradually shifting to error handling and precision improvement in complex environments [13; 14; 15]. [PERSON] et al. studied the GNSS positioning problem in a restricted environment, and applied the sparse estimation theory to estimate the GNSS positioning error caused by different environments [16]. [PERSON] et al. explored the GNSS positioning problem in an environment with severe occlusion and interference, and presented an assisted joint positioning algorithm that exploits near-Earth Doppler and other measurement data to track the target position [17]. Although the research has promoted the advancement of GNSS positioning error estimation methods in complex environments, it has not solved the problem of limited estimation accuracy caused by estimating only a single error term. Nowadays, multisystem fusion has become a popular research topic [18]. Researchers have begun to study how to apply multisystem satellite observation data for error estimation and correction to improve the accuracy and reliability of positioning. Researchers have gradually shifted from estimating individual errors to estimating the overall error in the GNSS positioning process [19; 20; 21]. [PERSON] et al. expatiated a GNSS positioning algorithm based on pseudorange error modeling and adaptive filtering [22]. [PERSON] et al.