A Constellation-Aware Transformer Architecture for Multi-GNSS Positioning: Learned Inter-System Bias Estimation and Attention-Based Satellite Selection

Multi-constellation Global Navigation Satellite Systems (GNSS) positioning — combining GPS, Galileo, BeiDou, and GLONASS — is the operational standard for modern navigation receivers. However, current machine learning approaches to GNSS positioning treat all satellite observations identically, ignoring the distinct signal characteristics of each constellation. Meanwhile, inter-system biases (ISBs) between constellations remain handled by rigid classical stochastic models, and satellite selection relies solely on geometric criteria. This paper proposes the Constellation-Aware Transformer (CxTF), a novel transformer-based architecture that addresses these three limitations simultaneously. CxTF introduces: (1) learnable constellation embeddings that encode system-specific signal characteristics, analogous to segment embeddings in natural language processing transformers; (2) a cross-constellation attention mechanism that implicitly learns inter-system biases without requiring predefined stochastic models; and (3) an attention-based satellite selection module that jointly optimizes geometric diversity, signal quality, and constellation balance. The architecture processes multi-GNSS observations as a variable-length token sequence, applies elevation-dependent positional encoding reflecting signal quality physics, and outputs position corrections relative to an initial single-point solution. The complete architecture is specified mathematically through 37 equations and a six-step forward pass algorithm, with a recommended configuration of approximately 800 thousand parameters. A comprehensive interpretability framework is developed to analyze the learned attention structure, including a novel K²-block decomposition that reveals how cross-constellation relationships map to inter-system biases. Computational analysis confirms real-time feasibility with sub-50-millisecond inference latency. A complete experimental protocol — including dataset specification, preprocessing pipeline, baseline definitions, and evaluation metrics — is provided to enable direct empirical validation. Empirical validation on the Google Smartphone Decimeter Challenge (GSDC) dataset using 12 driving traces (18,676 epochs) from a single receiver type demonstrates a 30% reduction in median 3D position error (5.15 m → 3.59 m) and a 20.6% reduction in 3D RMSE (6.68 m → 5.30 m) compared to classical weighted least-squares, with the learned satellite selection module exhibiting physically meaningful elevation-dependent behavior. CxTF establishes a new design paradigm for constellation-aware deep learning in GNSS positioning, with implications for smartphone navigation, autonomous driving, and precision surveying.