A Two-Step Kriging Method to Construct Ionospheric Grid Integrating GPS and LEO Observations

Onboard global positioning system (GPS) observations and downlink navigation signals from low-Earth orbit (LEO) navigation constellations are expected to enhance the ionospheric grid model of the BeiDou Satellite-Based Augmentation System (BDSBAS). However, the LEO ionospheric observations traverse only a limited portion of the ionosphere, rendering them unsuitable for direct integration with GPS observations. To address this limitation, this study proposes a two-step Kriging method to construct the ionospheric grid by integrating GPS and LEO data. In the first step, onboard LEO observations are utilized to develop a top-side ionospheric grid model by leveraging Kriging, compensating for the lack of top-side ionospheric information in the LEO downlink data. In the second step, the entire ionospheric grid is constructed using Kriging, integrating both GPS observations and the compensated LEO data. In addition, a spatial threat model is developed for integrity monitoring based on a data deprivation scheme. A simulation environment covering GPS/LEO constellations and the ionosphere was established using data from 2014 to 2016, spanning periods of high, moderate, and low solar activity for parameter development and performance evaluation. Experimental results indicate that an increase in the orbital altitude of LEO satellites contributes to the enhancement of ionospheric grid performance. At the 1000-km setting, LEO observations reduce the root mean square (rms) of estimation errors by approximately 20% compared with GPS-only data at both system and user levels. Moreover, LEO observations also stabilize grid ionospheric vertical error (GIVE) with solar activity, reducing extreme values and preventing integrity events.