Ionospheric Correction Using Tomography

The most demanding application of wide area di erential corrections to GPS is vertical positioning of aircraft on precision approach. Here the Wide Area Augmentation System (WAAS) combines accuracy requirements on the order of ones of meters with safety of life integrity requirements which specify that any vertical position errors greater than the Vertical Protection Limit be enunciated to the ight crew within six seconds. The ionosphere is the foremost impediment to satisfying these requirements. Stanford, as a member of the National Satellite Test Bed (NSTB), is developing techniques for estimating the ionosphere in real-time. Previous research has established a connection between ionospheric error and vertical positioning error within the framework of modal decomposition. Ionospheric tomography is a natural extension of modal decomposition to the estimation of the ionosphere's three-dimensional electron density. We present a tomographic estimation algorithm and its implementation over the NSTB network. This estimator supplies not only corrections to the user but also appropriate con dence information for predicting the accuracy of those corrections in the aircraft. The tomographic approach to ionospheric correction obviates the troublesome obliquity factor associated with typical gridded vertical delay algorithms. The capability of ionospheric tomography is demonstrated by a time series of 3D electron density reconstructions over the Coterminous United States (CONUS). The accuracy, integrity, and availability afforded the user by this approach is quanti ed through application on live NSTB observations. Supported by FAA Grant 95-6-005. INTRODUCTION The ionosphere induces a propagation delay over and above the free space delay on radiowaves propagating through the associated plasma. Although this is nuisance parameter for ranging applications, at L-band the additional delay is well modeled as a linear operator. In addition, since the ionosphere is a dispersive medium this delay can be observed using radiowaves at two di erent carrier frequencies. In the case of GPS dual frequency receivers a direct measure of the ionospheric delay along the line of sight to each GPS satellite in view can be made. The premise of the Wide Area Augmentation System (WAAS) ionospheric correction process is to form an estimate of the ionosphere using such measurements [1]. The resulting estimate may then be transmitted to single frequency receivers in order to correct the ionospheric range error. We have developed two distinct ionospheric estimators for use in the WAAS correction process. The rst is comprised of a two-dimensional grid over latitude and longitude which models the ionosphere as a thin shell xed at an altitude in the neighborhood of 350 (km) [2]. Vertical delay is estimated at each grid point from dual frequency reference station (TRS) measurements. The single frequency receiver then employs a xed function of elevation, the so-called obliquity factor, to map an interpolated vertical delay into a range delay prediction along the line-of-sight. The second estimator centers around the tomographic inversion of the linear phase delay operator which is simply the Radon transform. Using the known TRS and satellite locations the three-dimensional phase delay operator is an observation matrix formed via some basis. The ionospheric electron density estimate is the inner product of the \inverted" observation matrix and the TRS measurements. A single frequency receiver can then predict its ionospheric range error by dotting the electron density estimate into its own ionospheric observation matrix.