Performance of Single-frequency GPS Precise Point Positioning
Satirapod and Phakphong (2006) have recently developed simple PPP software that can provide an accuracy of better than 1 metre, over a 15-minute observation period using a dual-frequency GPS receiver. This developed PPP software opens the door for the use of a single-frequency GPS receiver to replace the traditional differential positioning technique for various applications in remote sensing especially in establishment of Ground Control Point (GCP) (Satirapod et al., 2003). However, the cost of dual-frequency GPS receiver is still far more expensive than the single frequency GPS receiver. Thus, this research aims to develop simple PPP software that can provide positional accuracy at the same level as the pseudorange-based differential GPS technique using a single-frequency GPS receiver. Therefore, our developed PPP software is a simplified version of the above-mentioned PPP technique. This paper will present the level of performance of the developed software using data retrieved from five IGS stations. In the following sections, the components of the developed PPP software are described. Next, tested data and data processing strategy are explained. An analysis of results is presented in the next section to assess the level of positioning accuracy obtained from the developed software. Some concluding remarks are given in the last section.
2. Components of Single-frequency GPS PPP software
The Matlab-based GPS Precise Point Positioning (PPP) software for single-frequency data was developed at Chulalongkorn University, Bangkok, Thailand. The main purpose of the software development is to support the use of a simple GPS technique in GCP establishment. In addition, the development of such software is intended for educational and further software development. Thus, the Matlab codes for the developed PPP software are freely available to the reader from www.eng.chula.ac.th/survey/staff/cst/chon.htm. Both carrier phase and pseudorange measurements are used and many error mitigation methods are implemented in the PPP software. An Extended Kalman Filtering technique was implemented in this software as a basis of estimation technique. With regard to the error sources, the PPP software can be considered as consisting of three principal error mitigation components.
2.1 Determination of satellite position and satellite clock correction
This component refers to the use of the precise orbit in the SP3 format from the IGS to compute the satellite position at any specific time. Since the precise orbit file contains the satellite positions and satellite clock corrections only at 15-minute intervals, polynomial fitting is required in order to enable computation of the satellite positions and clock corrections at the time of signal transmission. The main advantages of this procedure are the simplicity of computation and the rather modest requirements for computer-time and memory. The Lagrange polynomial fitting technique is considered the most convenient and effective method compared to other polynomial representations (Cheney and Kincaid, 1994) and is therefore implemented in the developed software.
2.2 Mitigation of Ionospheric bias
Since the ionospheric effect disrupts the code and phase differently (Hofmann-Wellenhof et al., 2001; Leick, 2004; Rizos, 1997; Teunissen and Kleusberg, 1998), it is possible to use an ionosphere-free code and carrier phase combination to eliminate common ionospheric bias. Equation 1 represents an ionosphere-free code and carrier phase combination (Witchayangkoon, 2000; Gao and Shen, 2002) and is used as a fundamental observation equation in the developed software.
where €p(L1) is the ionosphere-free code and carrier phase combination (m)
P(L1) is the measured pseudorange on L1 (m)
) is the measured carrier phase on L1 (m)
2.3 Mitigation of Tropospheric bias
Unlike the ionospheric delay, the tropospheric delay is not frequency-dependent. It cannot therefore be eliminated through linear combinations of L1 and L2 observations. The tropospheric delay is a function of elevation and altitude of the receiver, and is dependent on many factors such as the atmospheric pressure, temperature and water vapour content. For the sake of simplicity, standard troposphere model is commonly used to estimate the tropospheric delay. In this software, the Saastamoinen troposphere model (Saastamoinen, 1971) was introduced to calculate the total tropospheric zenith delay while the Neill mapping function (Neill, 1996) was used to map the tropospheric zenith delay to the line of sight delay.
3. Tested Data and Processing Strategy
3.1 Tested Data
Five IGS stations located in different countries, namely ASC1, CAS1, KERG, MAS1 and METS, were selected for the purpose of testing. The locations of the selected IGS stations are shown in Figure 1. In order to investigate an effect of season on positioning results, three different periods of GPS data in year 2003, January, May and September, were selected. Three consecutive days of data starting from the beginning of each period at each IGS station were downloaded from http://www.hartrao.ac.za/geodesy/data.html.
Figure 1. Locations of the five IGS stations