Grid ionospheric vertical error analysis in the context of WAAS


A. D. Sarma
Research and Training Unit for Navigational Electronics Osmania University
Hyderabad-500007
ad_sarma@yahoo.com


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
s_SE = square-root variance of the vertical delay estimate and depends on the quantity and spatial distribution of the data
where
Data_i = WRS delay measurement
N= Number of measurement samples

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