Spatial sparse sampling-based iterative optimization framework for GNSS Direct Position Estimation

Abstract

Direct position estimation (DPE), a promising technique in Global Navigation Satellite Systems (GNSS) receivers, enables estimation of position, velocity, and time (PVT) solutions directly from correlator outputs. The conventional grid search (GS)-based DPE is computationally intensive, as it relies solely on locating the peak of the cross ambiguity function (CAF), and it does not fully leverage the PVT information present in the correlation values. This paper proposes an iterative optimization DPE framework that capitalizes on spatial coherence and spatial gradient via spatial sparse sampling (SS). In SS-DPE framework, the correlation outputs of spatial sampled PVT points all serve as measurements, where the spatial gradient and spatial coherence are derived to capture the information density and diversity of different correlation values. The analytical Cramér-Rao Bound (CRB) is derived and indicates that both spatial coherence and gradient determine the theoretical performance limit via the noise covariance and Jacobian matrices analysis. The proposed theoretical framework not only validates the feasibility of sparse sampling but also guides weight optimization to distinct correlation values, effectively integrating these insights with a general gradient-based optimization. Theoretical derivations are validated via Monte Carlo simulations. Field experiments further demonstrate the practical feasibility of the proposed SS-DPE optimization framework. Comparative analysis shows that the proposed SS-DPE achieves comparable PVT estimation accuracy to the conventional GS-DPE while consumes only sparsely sampled correlation values, improving the information utilization efficiency and reducing the computation load.