LSTM-based stochastic model refinement for pseudolite/GPS PPP integrated navigation system
Abstract
An appropriate stochastic model can accurately reflect the statistical characteristics of the observations, serving as a prerequisite for obtaining high-precision positioning results. As the influencing factors in traditional pseudolite/precision point positioning (PL/PPP) stochastic models predominantly involve carrier-to-noise density ratio (CNR) and elevation angle, without considering satellite geometry configuration effects, and empirical fitting functions cannot accurately quantify the weighting of each influencing factor on observation errors, this paper proposes a stochastic model refinement method based on the long short-term memory (LSTM) neural networks. This LSTM-based model integrates multiple influencing factors: CNR, elevation angle, Horizontal Dilution of Precision contribution and measurement residual. These serve as input parameters to dynamically estimate observation noise. By fusing these signal quality indicators, the LSTM effectively captures the complex nonlinear relationship between the observation environment and ranging errors, thereby enabling real-time adaptive adjustment of the observation covariance matrix within the Kalman filter framework. Experiments were conducted using actual operational datasets collected from the Qinghai-Tibet Railway in 2019 and the land vehicle in 2025, covering dynamic and static experiments. The results indicate that, for the PL/PPP integrated navigation system, the performance of LSTM-based model significantly outperforms that of traditional stochastic models: in dynamic experiment, three-dimensional positioning accuracy improved by 60.26%, 54.50%, and 43.13% respectively over equal-weight models, elevation model, and CNR model; in static experiment, it improved by 54.69%, 54.33%, and 52.07%, respectively. The results confirm the LSTM-based model’s robustness and superiority in complex environments, offering a promising solution for high-precision vehicle positioning applications.