Grid ionospheric vertical error analysis in the context of WAAS

A. D. Sarma
Research and Training Unit for Navigational Electronics Osmania University
Hyderabad-500007
[email protected]

G. Sasi Bhushana Rao & K. Ramalingam
Airports Authority of India,
Hyderabad-500016

Abstract
A technique based on a recent paper is used for the estimation of GIVE. The GIVE produced here includes the three factors namely statistical error, spatial decorrelation and gradient error. The values of these parameters are taken from the literature. This method takes care of the distribution of WRS IPPs as well as the spread of delay measurements in the IGP estimation. Data from a dual frequency receiver located at Hyderabad is used for our calculations. As India comes under equatorial anomaly region, appropriate values for the parameters used in GIVE are to be assigned using Indian data.

Introduction
The GPS augmentation system will provide users with orbit, clock, and ionosphere corrections for single-frequency measurements of the GPS signal. For precision approach (PA) aircraft landings, ionospheric corrections take precedence over the other two factors. The ionospheric space above the earth is defined by 1809 grid points. Our ionosphere has been a subject of intensive investigation in the last several decades both for scientific and application potential. It is sufficient if we define 60 grid points to get accurate dynamic ionospheric delays over India (Sarma et.,al, 2000).The dual frequency GPS receivers at the wide area reference stations (WRSs) estimates delay imparted by the ionosphere along the line of sight from each receiver to each satellite. Interpolation of these measurements to a predefined set of grid nodes (Ionospheric Grid Points (IGPs)), at a designated height of 350 km, provides a series of ionospheric delay estimates. The intersection of line of sight from receiver to satellite and the shell defined by the IGPs is known as an Ionospheric Pierce Point (IPP). The user is then required to interpolate the grid node delays to the locations of his IPPs (RTCA/DO-229B, 1999). These estimates can then be used to correct user ionospheric delays. A bound on the residual error of the vertical ionospheric delay at each IGP is estimated along with the grid delays, which is known as Grid Ionospheric Vertical Error (GIVE). These GIVE values are used to compute the User Ionospheric Vertical Error (UIVE) which is corresponding bound on the user-computed vertical ionospheric delay error. Improvement in the GIVE accuracy directly increases the availability of precision navigation. WAAS of USA is designed to serve the requirements of USA, located in mid latitude region but is inaccurate for other parts of the world. As India comes under equatorial region where ionospheric behavior is dominated by intense irregularities and large horizontal gradients associated with F-region equatorial anomaly, extra precautions are necessary to compensate errors with wide day-to-day variability. The GIVE implementation presented here depends on the distribution of WRS pierce points as well as the spread of delay measurements (Harris, 1999). The inclusion of statistical error, spatial decorrelation and gradient in the delay estimation in GIVE calculation takes care of possible discrepancies between the ionospheric representation and its actual behavior for India . This method is expected to be better than the previous interpolation methods.

Ionospheric Calibration Errors
IGPs and GIVE values are broadcasted via geosynchronous satellite in ionospheric correction message format No.26. The aircraft uses theses values and corrects it’s position. GIVE calculation mainly depends on data availability around the IGPs. The IPP data reported in this paper is sufficient for the central part of India. IPP data are generally reduced near coasts and land boarders as WRS stations are very limited in those regions. It is therefore prudent to increase the uncertainty of the corrections where data are sparse. The GIVE implementation presented here is on the basis of the iononspheric calibration algorithm published by Harris et., al (1999). GIVE estimation includes calculation of three important factors and takes care of the distribution of WRS IPPs as well as the spread of delay measurements about the fit. The three factors statistical error, spatial decorrelation and gradient error describe the discrepancies between the ionospheric representation and its actual behavior. The formulas for the three factors are given below.

Statistical Error
Statistical errors of the vertical delay provides the measurement noise to the estimated parameters. It includes errors from the fitting procedure used to produce the vertical TEC maps. It does not reproduce errors incurred when users interpolate the gridded broadcast corrections and map them to slant ray paths.
a = scaling factor used to account for non-gaussian statistics
sSE = square-root variance of the vertical delay estimate and depends on the quantity and spatial distribution of the data
where
Datai = WRS delay measurement
N= Number of measurement samples

 
Table.1: Calculation of Statistical, Spatial decorrelation, and Gradient errors of GIVE

Fiti is the delay at the corresponding measurement pierce point computed by user. The factor 3.3 and si are introduced as the GIVE is designed to bound 99.9% of errors.

Spatial Decorrelation Error
Since WRS measured IPPs and user IPPs are widely separated, the spatial variability, or decorrelation, of the ionosphere becomes important. Therefore, an additional interpolation-based on GIVE term that depends on the distance between the user IPP and the WRS measured IPP is necessary. Since the locations of user IPPs are unknown during GIVE generation, a “worst case” distance DMAX for a user in the region surrounding an IGP is to be calculated.
Spatial Decorrelation Error term is GIVEDEC = bVMAX DMAX Where
VMAX = largest vertical ionosperic delay in the four quadrants surrounding the IGP
b = Scaling factor based on estimates of decorrelation derived from previous experiences of Jet Propulsion Laboratories (JPL, USA).

Gradient
WRS measurements are mapped to vertical, and IGP calibration delays to slant paths, using the obliquity function, which is based on the thin shell ionosphere model. Obliquity factor depends on elevation of a slant line of sight, but independent of azimuth. Therefore, calibration errors for users will arise that depend, on the local horizontal electron density gradients found in the real ionosphere that cause azimuthal delay variation. Such effects are accounted for by a mapping-based GIVE term GIVEGRAD = gÑMAX
Where
ÑMAX = Estimate of the maximum delay gradient surrounding the IGP
b = Scaling factor based on studies of obliquity function errors made at JPL. a, b and g values are taken from the JPL studies which are applicable for mid latitude region. Due to lack of relevant Indian values the same values are used.

Results and Discussion
The GPS data required for calculation of IPPs is collected from a dual frequency receiver located at NGRI, Hyderabad, India. The data corresponds to 18 th April, 1998. Latitude and longitude of some of the IPPs monitored in the four surrounding square grids (10° -20° latitude and 70° -80° longitude band) cover some of the IGPs. The IPP latitude, longitude, vertical ionospheric delay, slant factor, elevation angles and IGP delays are calculated using standard formulas (Conker, 1995) and also IRI-90 model is used in the prediction delays at various IPPs for comparison. The distances between IGP and the monitored IPPs are calculated using an algorithm known as Radar Operation Analysis Tool (ROAT, Westing House Corporation, USA). The GIVESE, GIVEGRAD and GIVEDEC terms and GIVETOT value are presented in Table1.

GIVE increases by 0.5m when gradient is 0.5cm/km and g is 1.6 x 106 meters . GIVE increases by 5% at 500km when b = 1.6 x 10-7 meters. The combined GIVE is mainly dependent on the statistical error. For example, at 10° latitude and 75° longitude the GIVESE and GIVETOT are 6.6177 and 7.3643 m respectively. The values of the a, b and g may not be applicable to Indian subcontinent. These results give only broad view of the influence of these parameters on GIVE.

Conclusions
To define the ionosphere above the Indian subcontinent, delays at 60 IGPs are to be deined. As India comes under equatorial region where ionospheric behavior is dominated by intense irregularities and large horizontal gradients associated with F-region equatorial anomaly, more care is to be taken in the calculation of GIVE. In the calculation of GIVE, the a, b and g are taken from the literature. Using Indian ionospheric data, better values for these parameters are to be found. These values may not be appropriate for Indian conditions. However, the GIVE calculations presented here give an insight on the influence of these parameters on GIVE.

Acknowledgements
The above work has been carried out under the project entitled “WAAS for India–A Test-Bed Approach” sponsored by the Ministry of Information Technology, Govt. of India, New Delhi, vide sanction order letter No. DE/SED/TDP–152 dated 31-03-1999.

References

• Sarma, A. D., G. Sasi Bhushana Rao and V. Venkata Rao, “Ionospheric Reference Station Placement for INWAAS – A Preliminary Study” J. of Ind. Geophys. Union, Vol. 4, No. 1, pp. 41-49, 2000.
• Minimum Operational Performance Standards for GPS/ WAAS Airborne Equipment”, RTCA/DO-229B, October6, 1999.
• Harris Ian, Manucci A, Iijima B, Lindqwister U, Muna D, Pi X and Wilson B C. and Dennis, L. Shaver, “Ionospheric Effects Symposium”,. Pp 221-229,1999.
• Conker R., El-Arini, B., Albertson, T. and Klobuchar, J., “Development of Real-time algorithms to estimate the ionospheric error bounds for WAAS” ION GPS, 1995.
• “Radar Operation and Analysis Tool”, Westing House Corporation, USA, 1995.