ION GNSS 2012
Session A6: GNSS and the Atmosphere 2

Title: New Correction Approaches for Mitigating Ionospheric Higher Order Effects in GNSS Applications
Author(s): M.M. Hoque and N. Jakowski, German Aerospace Center (DLR), Germany
Date/Time: Friday, September 21, 2012, 4:26 p.m.
Room: 103/104 (NCC)

By combining two or more Global Navigation Satellite Systems (GNSS) signals the major part (about 99%) of the ionospheric propagation delay can be corrected in real time precise positioning. However, higher order propagation effects such as the ray path bending error remains uncorrected in dual- or triple-frequency ionosphere-free combination. The range computation between a satellite and a ground receiver is affected up to several centimeters due to higher order ionospheric terms. Therefore, they cannot be neglected in precise point positioning applications, especially during times of high total electron content (TEC). Neglecting the ray path bending by assuming a straight Line of Sight (LOS) propagation introduces mainly two errors in the range computation. Firstly, the TEC along a curved path is slightly larger than that along the straight LOS. This causes differential TEC between two GNSS signal paths which results in uncorrected ray path bending error in the first-order ionosphere-free combination in addition to the higher order terms of the refractive index. Secondly, the total length of a curved path is slightly longer than the LOS one. Since, the ionosphere is dispersive in nature; the path length will not be the same for two GNSS signals. This indicates that the dual-frequency range equation must have additional terms for correcting differential bending. It has been found that in the range equation the excess TEC and excess path terms practically compensate each other. In other words, if we consider one term ignoring the other term would degrade the accuracy of the range computation. Our investigation shows that the access TEC in addition to the LOS TEC is proportional to the inverse square power of the signal frequency. The excess path in addition to the LOS path is proportional to the inverse quartic power of the frequency. To mitigate the LOS propagation assumption error, i.e., the ray path bending error, we have derived different correction formulas based on simulation studies. The correction formulas are functions of the signal frequency and the ionospheric parameters such as TEC, the maximum ionization NmF2 and its height hmF2, and the atmospheric scale height.

However, it is difficult to estimate ionospheric parameters NmF2, hmF2 and scale height in real time applications. Considering this we have modified the correction formulas keeping functional dependencies only on known ionospheric parameters such as the TEC and TEC derivative with respect to the elevation angle. The TEC and the TEC derivative are assumed to be known to the dual-frequency users. We have found that using the TEC derivative in addition to the TEC information we can improve the correction results. Validation studies based on multi- layered Chapman profiles have proved that about 70-80% of the ray path bending errors can be corrected if ionospheric parameters are known. In the present work, we have presented different approaches for ray path bending corrections. We have simulated a large number of ray paths using a 2D ray tracing tool and the three dimensional NeQuick model. The electron density distribution given by the NeQuick model is assumed to be as representative of the true ionosphere. The excess TEC and excess path have been computed at different location over the globe at different local time conditions. The elevation and azimuth angles of the ray paths are varied with in their ranges 1- 90ø and 0 - 360ø, respectively, at each user location. The simulations are done for high as well as low solar activity periods 2002 and 2008, respectively. Now for the same user location and ray path geometry, the computations are done using our correction formulas.

We have found that the TEC derivative with respect to the elevation angle is very sensitive to the electron density gradients or irregularities. Considering this, the correction formulas are simplified excluding the TEC derivative term and we have determined new coefficients for correction formulas. Our investigation shows that the maximum estimate of the excess TEC term is found to be about 35 mm for GPS L1-L2 combination at high solar activity time with slant TEC = 390 TEC units and the usage of correction formula can approximate this with in 4 mm level of accuracy. The corresponding maximum estimate of the excess path term is found to be about 20 mm whereas the correction formula can approximate this with in 2 mm level of accuracy. During the low solar activity year 2008, we have found that the maximum estimates of the excess TEC and excess path reduce to 10 and 5 mm, respectively, for a slant TEC of about 150 TEC units. The correction formulas can approximate these terms with in accuracy levels of 2 and 1 mm, respectively. Our study shows that in average about 70% and 75% of the excess TEC error can be corrected by our approach during low and high solar activity conditions, respectively. The corresponding numbers for the excess path length correction are 65% and 80%, respectively.

The consideration of higher order ionospheric terms in the range equation will enable more accurate range computation between a satellite and a receiver which in turn will enable more accurate point positioning results.

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