Ionospheric Estimation using Extended Kriging for a low latitude SBAS

The ionosphere causes the most difficult error to mitigate in Satellite Based Augmentation Systems (SBAS). The problem has been solved for the mid latitude regions using the thin shell approximation. There, it is very accurate on quiet days and allows the augmentation system so send the information in a two dimensional grid with a five by five degree resolution. However, even during quiet days, this approximation does not model correctly the ionosphere in the low latitudes: the decorrelation of the projected ionospheric vertical delays over the thin shell is very large. Several ionospheric estimation methods have been proposed to decrease the User Ionospheric Vertical Error (UIVE), among which are the ‘conical domain’ approach, tomography and extended kriging. The conical domain approach requires several measurements from the same satellite to work properly and in tomography the equation to solve is underdetermined, leading to artificial constraints and very large estimation errors at the edge of coverage. Extended kriging was developed to avoid these problems. The idea is to use kriging with several layers and an average vertical density profile to define the covariance between measurements (unlike in previous applications of kriging, where only one layer, the thin shell at 350 km, is used). Early results show that extended kriging gives estimation errors 30% to 50 % lower than the planar fit using the thin shell model. As a consequence this method has the potential to reduce the UIVEs by the same amount, thus increasing the availability of the augmentation system. In this paper we will first recall the basics of extended kriging and the assumptions needed. Then we will present a new error analysis more adapted to disturbed ionospheric conditions and apply it to real ionospheric delay measurements taken at reference stations over Brazil. Based on this error analysis, we will propose a new Vertical Position Level equation and evaluate it using an SBAS simulation tool. The results show that, even under severe ionospheric disturbances, the 95 percentile of the Vertical Protection Level is to not too far from 50 meters. INTRODUCTION Up to now, no ionospheric estimation method fitting in the current standards has proven to be good enough to provide an acceptable level of service in the Equatorial regions for single frequency SBAS users. In the best cases, the residual errors appear to be almost five times larger than in the mid latitudes [1], [2], [3]. Several factors are behind this. Above all of them is the ionospheric behavior, which is characterized by sharp Total Electron Content gradients both spatial and temporal and large TEC values which are difficult to predict and describe [4]. But we can also blame: the current ionospheric algorithms, the message standards, and an error analysis based on Gaussian statistics that is well suited for quiet ionospheric conditions but that predicts very large errors in disturbed conditions. With the coming new signals (L5, L2C and Galileo signals), ionosphere induced delay on the pseudoranges will no longer be an issue for Satellite Based Augmentation Systems (SBAS), as dual frequency will enable users to remove it. Therefore, it might seem that the best option for providing SBAS in the Equatorial regions – where the ionosphere is not well modeled by the thin shell model and the planar approximations used in the mid latitudes – is to wait until dual frequency is available. However, civil dual frequency will not be operational before 2015 and even this date is uncertain; so there is a risk involved in relying only on the new signals. Moreover, single frequency will still be a fall back mode for dual frequency users. As such, and taking into account that the new signals will require new standards, it is worthwhile finding: an ionospheric estimation algorithm adapted to disturbed conditions, a way to analyze the errors during these conditions that is not overly pessimistic, and the ideal way to send the ionospheric corrections to the user. In this paper, we explore the benefits of combining Extended Kriging [3] and a new error analysis which does not rely on Gaussian statistics. First the main ideas behind Extended Kriging will be presented; second, an error analysis departing from the usual vertical error residual [3] will be described; finally, based on this error analysis, the expected performance in the position domain of an SBAS in Brazil will be evaluated. (In this paper, we will not investigate the message structure allowing the application of Extended Kriging. Instead we will assume that all measurements are known by the user.)