A modified Klobuchar model for single-frequency GNSS users over the polar region

For single-frequency Global Navigation Satellite System (GNSS) users, it is necessary to select a simple and effective broadcast ionospheric model to mitigate the ionospheric delay, which is one of the most serious error sources in GNSS measurement. The widely used Global Positioning System (GPS) Klobuchar model can achieve better performance in mid-latitudes, however, this model is not applicable in high-latitudes due to the more complex ionospheric structure over the polar region. Under the premise of no additional coefficients, a modified Klobuchar model is established for single-frequency GNSS users over the polar region by improving the nighttime term and the amplitude of the cosine term. The performance of the new model is validated by different ionospheric models and their applications in single-frequency single-point positioning, during different seasons and different levels of solar activities. The new model can reduce the ionospheric error by 60% over the polar region, while the GPS-Klobuchar even increases the ionospheric error in many cases. Over the polar region, the single-frequency SPP error using the new model is approximately 3 m in vertical direction and 1 m in horizontal direction, which is superior to GPS-Klobuchar. This study suggests that the modified Klobuchar model is more accurate to depict the polar ionosphere and could be used to achieve better positioning accuracy for single-frequency GNSS users over the polar region.