BLAC-Q4DIM: a bayesian optimization and LSTM driven adaptive clustering quasi-four-dimensional ionospheric model

Abstract

Accurate Slant Total Electron Content (STEC) modeling is essential for high-precision Global Navigation Satellite System (GNSS) positioning and space-weather monitoring. However, conventional Global Ionospheric Maps (GIMs) and fixed-parameter ionospheric models have limited capability in capturing rapid ionospheric variations associated with geomagnetic disturbances, low-latitude irregularities, and heterogeneous GNSS station distributions. Their performance is constrained by fixed spatial scales and insufficient adaptivity to the dynamic and spatially varying characteristics of the ionosphere. This study proposes BLAC-Q4DIM, an adaptive clustering quasi-four-dimensional ionospheric model driven by Bayesian Optimization (BO) and Long Short-Term Memory (LSTM). It directly clusters STEC in a Four-Dimensional (4D) latitude-longitude-elevation-azimuth domain and integrates four classical algorithms (GRID, KMEANS, DBSCAN, and AGGLO), four robust variants (TKMEANS, DPMEANS, HDBSCAN, and LEIDEN), 15 spatiotemporal features, and three optional geomagnetic drivers within a closed-loop adaptive framework consisting of LSTM prior prediction, BO-based posterior correction, and periodic retraining. Global experiments conducted over two representative 30-day periods, covering geomagnetically quiet and disturbed conditions, demonstrate that BLAC-Q4DIM consistently outperforms the Fixed-Parameter Q4DIM Framework (F-Q) and a GIM baseline. The best-performing variants, HDBSCAN and DPMEANS, achieve Root Mean Square (RMS) errors of 0.96–1.01 Total Electron Content Units (TECU) during the quiet period and 1.34–1.40 TECU during the disturbed period, representing RMS reductions of 80%-85% relative to the GIM baseline and more than 58% relative to the best F-Q baseline. BLAC-Q4DIM also demonstrates strong robustness under low-latitude, station-sparse, and disturbed conditions. The four robust variants maintain RMS errors below 2 TECU at low latitudes and below 1.44 TECU under the sparsest reference-station configuration, while limiting the performance degradation caused by geomagnetic disturbance to only 0.41 TECU. HDBSCAN and DPMEANS require only 3.5 s and 5.9 s, respectively, for single-window LSTM prediction and BO posterior correction, demonstrating the potential for near-real-time ionospheric modeling. These results indicate that BLAC-Q4DIM provides an adaptive, accurate, robust, and efficient framework for STEC modeling, offering a promising solution for next-generation GNSS positioning and space-weather applications.