Improvement of Klobuchar model for GNSS single-frequency ionospheric delay corrections

Broadcast ionospheric model is currently an effective approach to mitigate the ionospheric time delay for real-time Global Navigation Satellite System (GNSS) single-frequency users. Klobuchar coefficients transmitted in Global Positioning System (GPS) navigation message have been widely used in various GNSS positioning and navigation applications; however, this model can only reduce the ionospheric error by approximately 50% in mid-latitudes. With the emerging BeiDou and Galileo, as well as the modernization of GPS and GLONASS, more precise ionospheric correction models or algorithms are required by GNSS single-frequency users. Numerical analysis of the initial phase and nighttime term in Klobuchar algorithm demonstrates that more parameters should be introduced to better describe the variation of nighttime ionospheric total electron content (TEC). In view of this, several schemes are proposed for the improvement of Klobuchar algorithm. Performance of these improved Klobuchar-like models are validated over the continental and oceanic regions during high (2002) and low (2006) levels of solar activities, respectively. Over the continental region, GPS TEC generated from 35 International GNSS Service (IGS) and the Crust Movement Observation Network of China (CMONOC) stations are used as references. Over the oceanic region, TEC data from TOPEX/Poseidon and JASON-1 altimeters are used for comparison. A ten-parameter Klobuchar-like model, which describes the nighttime term as a linear function of geomagnetic latitude, is finally proposed for GNSS single-frequency ionospheric corrections. Compared to GPS TEC, while GPS broadcast model can correct for 55.0% and 49.5% of the ionospheric delay for the year 2002 and 2006, respectively, the proposed ten-parameter Klobuchar-like model can reduce the ionospheric error by 68.4% and 64.7% for the same period. Compared to TOPEX/Poseidon and JASON-1 TEC, the improved ten-parameter Klobuchar-like model can mitigate the ionospheric delay by 61.1% and 64.3% in 2002 and 2006, respectively.