Artificial Neural Network-Based Ionospheric Delay Correction Method for Satellite-Based Augmentation Systems

Abstract

Ionospheric delay is a critical error source in Global Navigation Satellite Systems (GNSSs) and a principal aspect of Satellite Based Augmentation System (SBAS) corrections. Grid Ionospheric Vertical Delays (GIVDs) are derived from the delays on Ionosphere Pierce Points (IPPs), which are observed by SBAS reference stations. SBAS master stations calculate ionospheric delay corrections by several methods, such as planar fit or Kriging. However, when there are not enough IPPs around an Ionosphere Grid Point (IGP) or the IPPs are unevenly distributed, the fitting accuracy of planar fit or Kriging is unsatisfactory. Moreover, the integrity bounds of Grid Ionospheric Vertical Errors (GIVEs) are overly conservative. Since Artificial Neural Networks (ANNs) are widely used in ionospheric research due to their self-adaptation, parallelism, non-linearity, robustness, and learnability, the ANN method for GIVD and GIVE derivation is proposed in this article. Networks are separately trained for IGPs, and five years of historical data are applied on network training. Principal Component Analysis (PCA) is applied for dimensionality reduction of geomagnetic and solar indices, which is employed as a network input feature. Furthermore, the GIVE algorithm of the ANN method is derived based on the distribution of the residual random variable. Finally, experiments are conducted on 12 IGPs over the East China region. Under normal ionospheric conditions, compared with the planar fit and Kriging methods, the residual reduction of the ANN method is approximately 15%. The ANN method fits the ionospheric delay residual error better. The percentage of GIVE availability under 2.7 m increases at least 25 points in comparison to Kriging. Under disturbed conditions, due to a lack of training samples, the ANN method is incompetent compared with planar fit or Kriging.