Single-Frequency Time-Step Ionospheric Delay Gradient Estimation at Low-Latitude Stations

Abstract

The irregularity of the local-area ionospheric delay is a primary impediment for Ground-Based Augmentation System (GBAS) services. Excessive ionospheric delay gradients may degrade aircraft positioning for high precision landing systems. Therefore, the spatial gradients of the nominal background ionosphere must be studied as their statistics will be sent to the approaching aircraft. For the well-known stationpair method, ionospheric delay gradient estimation requires at least 2 Global Navigation Satellite System (GNSS) reference stations. This method can be applied to both single or dual-frequency GNSS receivers. However, when the GNSS stations are far apart, it is not suitable for estimating the ionospheric delay gradients at short baselines, and the time-step method is an attractive alternative. In this work, we propose a singlefrequency time-step method for ionospheric delay gradient estimation. Careful baseline length selection is needed, due to ionospheric piercing point movements. We applied our method to GNSS data in 2014, at the peak of the 24th solar cycle, and showed that the standard deviations of the vertical ionospheric delay gradients were comparable to those derived from the dual-frequency time-step method. The standard deviations of vertical ionospheric gradients, VIG, ranged between 4 and 6 mm/km. The VIG values around the equinoxes were ~1.5 mm/km greater than at other times.

Improved Time-Step Method for Bounding Nominal Spatial and Temporal Ionospheric Gradients for Ground-Based Augmentation Systems in Hong Kong

“…The results show that the direction of IPP separation primarily lies in the north-south direction, indicating that the estimated gradients are dominant in the north-south direction and result in a less accurate gradient estimation in the east-west direction. This result presents one of the drawbacks of the time-step method, which is unable to describe 2D ionospheric gradients (Budtho et al, 2020).…”

“…The spatial gradient estimated by smoothing the time-step gradient differs in magnitude from the spatial gradient estimated by the station-pair method. This difference is due to the different choice of IPP pairs between the time-step method and the station-pair method (Budtho et al, 2020). A simple way to separate the temporal gradient from the spatial gradients is to smooth the time-step ionospheric gradient.…”

“…Use of this method has also been proposed to detect threatening spatial gradients in real time (Marini-Pereira et al, 2022, 2023. In addition, a single-frequency time-step method was proposed with desired ionospheric gradients estimated by Kalman filtering and ambiguity fixed by the least-squares ambiguity decorrelation adjustment (LAMBDA) method (Budtho et al, 2020). However, ionospheric gradients estimated by either the single-frequency or dual-frequency time-step method are computed over a time interval instead of at a single epoch, thereby including both temporal and spatial gradients (Chang et al, 2021).…”

Assessment of corrected time-step method for nominal ionospheric gradient calculation: A comparative analysis with spatial approaches

“…The use of the time-step method on a single receiver in real time on a single-frequency GPS was carried out in the region of Thailand (Budtho et al, 2020). However, none of the studies mentioned have analyzed a time-step correction method to eliminate temporal variations.…”

Construction of Nominal Ionospheric Gradient Using Satellite Pair Method Based on GNSS CORS Observation in Indonesia

“…Another sigma value search was conducted in Bangkok, Thailand using the time-step method on singlefrequency GPS [9]. The method is appropriate for Thailand's condition which most reference station distances are more than 20 km.…”