## 1 Introduction
explored the influence of satellite spatial distribution on GNSS position estimation, and analyzed the GNSS positioning error estimation performance of four Kalman filters in detail [23]. Although estimating the overall error in the positioning process has been proven to be able to effectively mitigate the impact of error factors on positioning results, the method of estimating the overall error has the defect of relying on the assumptions of GNSS observation noise and motion model. The application of GNSS positioning has introduced many complex and highly dynamic situations. How to solve the problems of error handling in complex environments and reliable positioning in highly dynamic environments urgently needs to be considered. Research on positioning error estimation methods can reduce or eliminate positioning deviations caused by additional positioning error factors. Traditional positioning error estimation methods for single error terms have the problems of low estimation accuracy and the need to make assumptions about GNSS observation noise. Although traditional methods for estimating the overall error can achieve higher estimation accuracy, they also require assumptions about GNSS observation noise. Therefore, a new GNSS positioning error estimation method is urgently needed. In recent years, the GNSS positioning error estimation field has been further developed. Scholars have applied artificial intelligence methods to address the GNSS positioning error estimation problem and obtained good results. The GNSS positioning error estimation method based on artificial intelligence does not rely on prior assumptions, and can exploit GNSS observation data to model complex positioning error factors, providing a new idea for improving the positioning accuracy and robustness of GNSS [24; 25]. [PERSON] et al. utilized an iterative approach to deal with multivariate optimization problems, and obtained the maximum likelihood estimator of the position under GNSS [26]. [PERSON] et al. explored a GNSS positioning error estimation method based on the random forest algorithm, and obtained excellent error estimation results [27]. Considering that the least squares method ignores the fact that velocity information is time-dependent, [PERSON] et al. investigated and implemented a GNSS position estimation method based on graph optimization, using historical states and measured values to estimate the current state [28]. By aiming at the problem that the accuracy and stability of multisource fusion navigation still cannot meet the needs of current practical applications, [PERSON] et al. studied a GNSS position error estimation algorithm based on multitask learning [29]. To obtain more accurate GPS positioning accuracy than existing statistical and linear machine learning methods, [PERSON] et al. utilized the long short-term memory network (LSTM) to dynamically model the factors affecting GPS positioning accuracy within a certain coherent time window and then predict the positioning error in the next second to a few seconds. The effectiveness of the presented method was verified through experiments. Implementing the presented LSTM model on hardware requires further considerations [30]. [PERSON] et al. studied an LSTM model with infinite impulse response (IIR) filtering by constructing a dynamic adaptive filter to remove outliers and interference. This innovative solution enhances the robustness of the LSTM network when processing noisy data and achieves better experimental results [31]. [PERSON] et al. studied the unmodeled error using historical GNSS observation data and proposed a positioning error estimation method based on convolutional neural network (CNN). The effectiveness of the presented method was verified through experiments, especially in the low-frequency component [32]. The research is of great significance to error elimination and reliability estimation in the GNSS positioning process.