Gauss process regression for real-time ionospheric delay estimation from GNSS observations

The number of devices equipped with global satellite positioning has exceeded seven billion recently. There are a wide variety of receivers regarding their accuracy and reliability. Low cost, multi-frequency units have been released on the market latterly; however, the number of single-frequency receivers is still significant. Since their measurements are influenced by ionospheric delay, accurate ionosphere models are of utmost importance to reduce the effect. This paper summarizes how Gauss process regression (GPR) can be applied to derive near real-time regional ionosphere models using raw Global Navigation Satellite System (GNSS) observations of permanent stations. While Gauss process is widely used in machine learning, GPR is a nonparametric, Bayesian approach to regression. GPR has several benefits for ionosphere monitoring since it is quite robust and efficient to derive a grid model from data available in irregular set of ionospheric pierce points. The corresponding instrumental delays are estimated by a parallel Kalman filter. The presented algorithm can be applied near real-time, however the results are offline calculated and are compared to two high quality TEC map products. Based on the analysis, the accuracy of the GPR modell is in 2 TECu range. The developed methods could be efficiently applied in the field of autonomous vehicle navigation with meeting both accuracy and integrity requirements.

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

Ground-Based Augmentation System (GBAS) is a GNSS augmentation system that meets International Civil Aviation Organization (ICAO) requirements to support precision approach and landing. GBAS is based on the local differential GNSS technique with reference stations located around the airport to provide necessary integrity and accuracy. The performance of the GBAS system can be affected by the gradient in the ionospheric delay between the aircraft and the reference stations. A nominal ionospheric gradient, which is bounded by a conservative error bound, is represented by a parameter σvig. σvig was commonly determined using station pair to GNSS Continuous Operating Reference Station (CORS) data. The station pair method is susceptible to doubling of receiver bias error and is not suitable with the CORS conditions in Indonesia. We propose a satellite pair method that is found to be more suitable for the CORS network over Indonesia which is centered in Java and Sumatra islands. The value of σvig (4.48 mm/km) is obtained using this method along with the preliminary results of a comparison of σvig from Java and Sumatra islands.

A satellite-based method for modeling ionospheric slant TEC from GNSS observations: algorithm and validation

Total Electron Content (TEC) modeling is critical for Global Navigation Satellite System (GNSS) users to mitigate ionospheric delay errors. The mapping function is usually used for Vertical TEC ionospheric correction models for slant and vertical TEC conversion. But the mapping function cannot characterize TEC variation in different azimuths between the user and satellites. The ionospheric modeling error resulting from the mapping function tends to be bigger in middle and low latitudes. Therefore, a new algorithm for ionospheric Slant TEC (STEC) modeling with Satellite-based Ionospheric Model (SIM) is proposed in this contribution. Validation tests are carried out with GNSS observation data from the Crustal Movement Observation Network of China during different solar activities and in different seasons. The performance of SIM is compared with that of several commonly-used Global Ionospheric Map (GIM) and Regional Ionospheric Map (RIM) products. The results show that the STEC bias and STD of SIM are within 1.0 TECU and about 2.0 TECU, respectively, and SIM can correct over 90% STEC RMS errors, outperforming the GIM and RIM products. Consequently, the SIM algorithm can be a new option for high-accuracy ionospheric delay correction in regional and local GNSS networks.

Accuracy Evaluation of Ionospheric Delay from Multi-Scale Reference Networks and Its Augmentation to PPP during Low Solar Activity

The Precise Point Positioning (PPP) with fast integer ambiguity resolution (PPP-RTK) is feasible only if the solution is augmented with precise ionospheric parameters. The vertical ionospheric delays together with the receiver hardware biases, are estimated simultaneously based on the uncombined PPP model. The performance of the ionospheric delays was evaluated and applied in the PPP-RTK demonstration during the low solar activity period. The processing was supported by precise products provided by Deutsches GeoForschungsZentrum Potsdam (GFZ) and also by real-time products provided by the National Centre for Space Studies (CNES). Since GFZ provides only precise orbits and clocks, other products needed for ambiguity resolution, such as phase biases, were estimated at the Geodetic Observatory Pecny (GOP). When ambiguity parameters were resolved as integer values in the GPS-only solution, the initial convergence period was reduced from 30 and 20 min to 24 and 13 min when using CNES and GFZ/GOP products, respectively. The accuracy of ionospheric delays derived from the ambiguity fixed PPP, and the CODE global ionosphere map were then assessed. Comparison of ambiguity fixed ionospheric delay obtained at two collocated stations indicated the accuracy of 0.15 TECU for different scenarios with more than 60% improvement compared to the ambiguity float PPP. However, a daily periodic variation can be observed from the multi-day short-baseline ionospheric residuals. The accuracy of the interpolated ionospheric delay from global maps revealed a dependency on the location of the stations, ranging from 1 to 3 TECU. Precise ionospheric delays derived from the EUREF permanent network with an inter-station distance larger than 73 km were selected for ionospheric modeling at the user location. Results indicated that the PPP ambiguity resolution could be achieved within three minutes. After enlarging the inter-station distance to 209 km, ambiguity resolution could also be achieved within several minutes.

Role of eddy diffusion in the delayed ionospheric response to solar flux changes

Simulations of the ionospheric response to solar flux changes driven by the 27 d solar rotation have been performed using the global 3-D Coupled Thermosphere Ionosphere Plasmasphere electrodynamics (CTIPe) physics-based numerical model. Using the F10.7 index as a proxy for solar extreme ultraviolet (EUV) variations in the model, the ionospheric delay at the solar rotation period is well reproduced and amounts to about 1 d, which is consistent with satellite and in situ measurements. From mechanistic CTIPe studies with reduced and increased eddy diffusion, we conclude that the eddy diffusion is an important factor that influences the delay of the ionospheric total electron content (TEC). We observed that the peak response time of the atomic oxygen to molecular nitrogen ratio to the solar EUV flux changes quickly during the increased eddy diffusion compared with weaker eddy diffusion. These results suggest that an increase in the eddy diffusion leads to faster transport processes and an increased loss rate, resulting in a decrease in the ionospheric time delay. Furthermore, we found that an increase in solar activity leads to an enhanced ionospheric delay. At low latitudes, the influence of solar activity is stronger because EUV radiation drives ionization processes that lead to compositional changes. Therefore, the combined effect of eddy diffusion and solar activity leads to a longer delay in the low-latitude and midlatitude region.

Improving the Stochastic Model of Ionospheric Delays for BDS Long-Range Real-Time Kinematic Positioning

Although ionosphere-free (IF) combination is usually employed in long-range precise positioning, in order to employ the knowledge of the spatiotemporal ionospheric delays variations and avoid the difficulty in choosing the IF combinations in case of triple-frequency data processing, using uncombined observations with proper ionospheric constraints is more beneficial. Yet, determining the appropriate power spectral density (PSD) of ionospheric delays is one of the most important issues in the uncombined processing, as the empirical methods cannot consider the actual ionosphere activities. The ionospheric delays derived from actual dual-frequency phase observations contain not only the real-time ionospheric delays variations, but also the observation noise which could be much larger than ionospheric delays changes over a very short time interval, so that the statistics of the ionospheric delays cannot be retrieved properly. Fortunately, the ionospheric delays variations and the observation noise behave in different ways, i.e., can be represented by random-walk and white noise process, respectively, so that they can be separated statistically. In this paper, we proposed an approach to determine the PSD of ionospheric delays for each satellite in real-time by denoising the ionospheric delay observations. Based on the relationship between the PSD, observation noise and the ionospheric observations, several aspects impacting the PSD calculation are investigated numerically and the optimal values are suggested. The proposed approach with the suggested optimal parameters is applied to the processing of three long-range baselines of 103 km, 175 km and 200 km with triple-frequency BDS data in both static and kinematic mode. The improvement in the first ambiguity fixing time (FAFT), the positioning accuracy and the estimated ionospheric delays are analysed and compared with that using empirical PSD. The results show that the FAFT can be shortened by at least 8% compared with using a unique empirical PSD for all satellites although it is even fine-tuned according to the actual observations and improved by 34% compared with that using PSD derived from ionospheric delay observations without denoising. Finally, the positioning performance of BDS three-frequency observations shows that the averaged FAFT is 226 s and 270 s, and the positioning accuracies after ambiguity fixing are 1 cm, 1 cm and 3 cm in the East, North and Up directions for static and 3 cm, 3 cm and 6 cm for kinematic mode, respectively.