14 September 2004

A network-based approach to instantaneous (single-epoch) long-range real-time kinematic (RTK) GPS positioning has been implemented and tested in the Multi Purpose GPS Processing Software (MPGPS™), developed at The Ohio State University in corporation with the Technion — Israel Institute of Technology and the University of Warmia and Mazury in Olsztyn, Poland. The implemented approach is based on atmospheric corrections derived from reference station GPS observations that support the rover positioning. The use of this approach, in GPS kinematic positioning, significantly increases the distance, over which carrier-phase ambiguities can be recovered to their integer values. The positioning algorithm is based on a single baseline solution aided by network derived atmospheric corrections to support the ambiguity resolution. The motivation behind this research, supported by NOAA/NGS and the Survey of Israel (SOI), is to develop and evaluate the state-of-the-art methodology and algorithms for centimeter-level long-range instantaneous RTK GPS, suitable for geodetic, surveying and navigation applications. Instantaneous ambiguity resolution (AR) has several advantages over the on-the-fly (OTF) method; it is resistant to negative effects of cycle slips and can provide centimeter-level positioning accuracy immediately, without any delay needed for initialization for short distances, as required by the OTF technique (Bock, 2003; Kashani et al., 2003; Wielgosz et al., 2003). Since every epoch is virtually independent, loss of lock, a cycle slip, or a change in the tracked satellite constellation does not introduce additional complications to the data processing. 
 

NETWORK-DERIVED RTK CORRECTIONS 

The atmospheric RTK corrections provided by the network to the roving users include tropospheric delay (non dispersive) and ionospheric delay (dispersive). The tropospheric delay is parameterized as a Total Zenith Delay (TZD) - an undifferenced delay in the zenith direction for individual stations. The Zero Difference (ZD) ionospheric delays are estimated in two steps; in the first step the delays are parameterized as double-differences (DD), and then in the second step they are decomposed to the ZD delays for specific station-satellite pair. The network algorithm uses the pseudorange and phase observations while all the reference station coordinates are considered known (Kashani et al., 2004). A generalized least squares solution (GLS) was applied to solve the underlying mathematical model (Felus, 2004). The flexibility of this model allows an easy implementation of different stochastic constraints, weighted parameters or fixed constraints, in instantaneous as well as in batch or sequential solutions. The Least-squares AMBiguity Decorrelation Adjustment (LAMBDA) is used in order to fix the ambiguities to their integer values. The validation procedure used is the AR success rate, which is the probability of estimating the correct integers (Teunissen, 2000; de Jong and Tiberius, 1996). 
 

RTK ROVER POSITIONING

The RTK rover positioning can operate in both single-baseline and multi-baseline modes in a two-step procedure. In the first step, DD ionospheric delays and TZD are provided by the network to initiate the rover positioning solution. The OTF technique with accumulation of a few epochs is applied to start the system and to validate the initial AR. Once the ambiguities were resolved in the first step (fixed and validated), the instantaneous solution is applied afterwards (the second step). To enable the instantaneous ambiguity resolution, the DD ionospheric delays from the previous correctly resolved epoch are provided to the rover solution instead of the interpolated ones. The latency of 30–60 seconds of the DD ionospheric delays is acceptable, depending on the ionospheric conditions, the reference network scope and the baseline length. The RTK algorithm uses the double-frequency pseudorange and phase observations. The LAMBDA method is used as the AR method as in the network solution. However, the F-ratio test and the W-ratio were applied in the rover solution in order to validate the AR. 
 

EXPERIMENTAL RESULTS 

GPS observations from the Ohio CORS collected on August 31, 2003, with a 30-second sampling rate were used in the tests. The data were collected in two sessions: 08:00–09:00 UT (3–4 am local time), which demonstrate the lowest TEC, and 17:00–18:00 UT (1–2 pm local time), during the highest TEC values. The map of the reference network and an example of the COLB-MCON baseline solution is presented in Figure 1. It should be noted that COLB station served as a rover and did not contribute to the atmospheric corrections. The instantaneous solution starts after 3-epoch initialization, and is carried through to the end of the session. Table 1 refers to the baseline solution illustrated in Figure 1, and contains the estimate statistics. The ambiguities were fixed to their integer values with a 100 percent success rate. The analysis was performed in the post processing mode, while the algorithm is suitable for real-time application. Naturally, for the real RTK implementation, the issue of communication and the computing power at the rover station must be addressed properly.
 

Fig. 1: Map of the test area: network (red) and COLB-MCON baseline (green).
 

Table 1. Statistics for baseline COLB-MCON (110 km). Solution with 30-second latency of the atmospheric corrections. The AR success rate was 100 % for both sessions.
 

	Night Session mean [m]	Night Session std [m]	Day Session mean [m]	Day Session std [m]
dn	-0.004	0.007	0.005	0.008
de	0.008	0.008	-0.005	0.008
du	0.025	0.025	-0.032	0.028

SUMMARY

The feasibility of centimeter-level instantaneous RTK GPS over 100 km distance was demonstrated when atmospheric corrections are provided to the rover by the local reference network stations, followed by the use of previous-epoch ionospheric delay. Based on the results presented here and in Kashani et al. (2004), it can be concluded that the methodology and the algorithms developed for the long-range instantaneous RTK module in the MPGPS™ software can provide millimeter to centimeter-level horizontal rover position and centimeter-level vertical one, for baselines over 100 km. However, more tests are planned including longer data spans and different ionospheric conditions to fully assess the performance of this method.
 

Bock Y., de Jonge, P., Honcik, D. and Fayman, J. (2003): Wireless Instantaneous Network RTK: Positioning and Navigation, Proc. ION GPS/GNSS, September 9–12, Portland, OR, pp. 1397–1405

Felus, Y.A., (2004): Application of Total Least Squares for Spatial Point Process Analysis, Journal of Surveying Engineering, Vol. 130, No. 3, pp. 126–133

de Jonge, P.J. and Tiberius, C.C.J.M. (1996): The Lambda Method for Integer Ambiguity Estimation: Implementation Aspects, LGR Publication No. 12, August, pp. 1-49, (PDF file, 376 kB)

Kashani, I., Wielgosz, P., and Grejner-Brzezinska, D.A. (2003): Datum Definition in the Long Range Instantaneous RTK GPS Network Solution, Journal of Global Positioning Systems, Vol. 2, issue 2, 2003, (PDF file, 436 kB)

Kashani, I., Grejner-Brzezinska, D.A., and Wielgosz, P. (2004): Towards instantaneous RTK GPS over 100 km distances, Proc. ION 60th Annual Meeting, June 7–9, 2004, Dayton, Ohio, pp. 679-685,

Teunissen, P.J.G. (2000): On the GNSS Integer Ambiguity Success Rate, Lustrumboek Snellius, The 5th Element, pp. 103-108, (PDF file, 522 kB)

Wielgosz, P., Grejner-Brzezinska, D., and Kashani, I. (2003): Network Approach to Precise GPS Navigation, Proc.  ION Annual Meeting, June 23–25, CD ROM, pp. 397–403