Analysis of GNSS Baseline Solutions in Ghana

Accuracy is highly desired in all geodetic and mapping projects. Global Navigation Satellite Systems (GNSS) has many positioning capabilities which can produce the desired accuracies needed for establishing Ground Control Points (GCPs). However accuracy of positioning results from GNSS survey routines are influenced by session duration and baseline length. This study is targeted at determining optimum observation times for specific baseline lengths for GCP fixing and densification in Ghana. The study used four ground stations in Accra, Kumasi, Assin-Fosu and Sunyani. Each station was occupied for a total of four hours on three different days and the data were later split into various time segments to obtain different data sets. Using the Kumasi station as base, each of the baselines was processed three times for each of 3-day 4-hour observation sessions and the mean results accepted as the ‘true’ position values. Repeatability tests were carried out on the computed baselines and the ratios ranged between 1:1,141,100 and 1:4,918,000. All comparisons were based on the true position values. Root Mean Square Error (RMSE) and accuracies were computed from the differences. A plot of the RMSE against time showed that accuracy of positions continued to improve but after 50 minutes of observation there was no significant improvement in the accuracy of measured baselines. This study therefore set 50 minutes as the optimum duration for GNSS baselines up to 195km when using geodetic grade GNSS receivers in differential mode to establish GCPs.


Introduction
The level of accuracy achieved in Global Navigation Satellite System (GNSS) positioning depends on the method of measurements and techniques of processing field data (Rizos, 1999;Seeber, 2003).
As such, new innovations in GNSS measurements and data processing methods continue to emerge.
Network adjustment of baseline solutions is one of the most accurate GNSS data processing techniques which computes redundant baselines and performs least squares adjustment to fix rover positions (Schwieger et al.,2009).Burns et al. (2010) and Gopi (2005) in their studies have shown that accuracies of position solutions are influenced greatly by the session duration but the length of the baselines did not have a significant impact.In their report, Eckl et al. (2001) revealed that accuracies continue to improve with longer session durations leading to the recommendation that more time should be spent on rover positions in order to achieve better accuracies.The main challenge is to determine how much time (optimum duration) to be spent on rover positions in order to obtain the desired accuracy since different projects require different levels of accuracies.This study investigated optimum observation times for ground control points fixing using baselines of up to 195km tailored specifically for cadastral mapping.
None of the aforementioned studies has ever been carried out in our part of the world.Ghana is located near the equator, which presents interesting challenges with regards to the ionospheric and tropospheric situation.Conducting this study in Ghana therefore offers the opportunity to use data observed in Africa and for that matter results from this study stand to resonate well with many African researchers and surveyors.The Accra site was mounted with a Trimble NetR5 receiver and TRM29659 antenna.Assin Fosu and Kumasi sites were mounted with Sokkia GSR 2600 receivers and SOK600 antennas.The passive control point in Sunyani was mounted using a Trimble R4 receiver with TRMR4 antenna.Four hours of data were logged and downloaded for each of three days from the CORS sites and a passive control point in May 2007.The quality of these data was checked against multipath, data completeness and cycle slip using Leica GNSS QC v2.0 software (http://www.leica.com)and all the data passed.Precise ephemeris for these data was obtained from International GNSS service (IGS) via internet service (Kouba, 2009).The post processing criteria used included: epoch rate of 30 seconds; elevation cut-off angle of 10 degrees; L1/L2 fixed iono-free processing style and varying observation times.

Methodology and Data Processing
Each of the 4-hr data for each day was partitioned into non-overlapping sub-sessions of several data sets.Thus, for each baseline, the length was kept fixed whilst the observation duration was varied from 5-minutes to 4-hours.The data were post processed using Topcon Tools processing software version 8.25 based on international terrestrial reference frame of 2008 (ITRF2008).
Each baseline was individually processed three times and the mean of the three results was used as the 'true' position of the rover stations.Three sets of measurements for each baseline were obtained and used for repeatability analysis.The positions of the rover stations were similarly computed from the sub-session data and compared with the 'true' positional coordinates to obtain differences in X, Y and Z coordinate values in the WGS84 reference frame Snay et al. (2002).These residuals were used to compute root-mean-squared errors (RMSE) and accuracies for various sub-sessions (Wing et al., 2005) and Deakin & Kildea (1999).RMSE and accuracies were plotted against session lengths in turns for each of the three baselines; Accra, Assin Fosu and Sunyani.Interpreting these graphs, useful discussions and conclusions were drawn.However comparison of accuracies from these baselines would have been more rigorous if identical GNSS receivers were for all the selected stations.

Results and Analysis
Using the methodology described above the mean coordinates of the selected stations, the repeatability ratios, positions from partitioned data, residuals and root mean square errors were computed and presented in this section.Graphs of RMSE against session durations have also been presented in this section.The original coordinates of the Kumasi site which was used as base station are presented in table 1.  2 presents the mean positions after each baseline was processed three times for each of the 3days.For purposes of meaningful analysis of horizontal and vertical positioning the coordinates were rotated to eastings, northings and up directions (ENU) via a simple rotation matrix.In order to compute the accuracy of the positions for each sub-session the true position coordinates were compared with positions from the sub-sessions as presented in table 4. RMSE values were computed from the differences as shown in column-8 of table 4 (a), (b) and (c).

Discussion
In their research papers Creager and Maggio (1998); Eckl et al. (2001);Shen et al. (2009) and Wieser (2004) worked on longer baselines up to 300km or more and selected data with observation duration of (4-24)-hours in their analyses.They showed that longer observation durations produced better positional accuracies and concluded that accuracy is slightly affected by length of baseline but greatly affected by observation durations.Thus, GNSS is capable of producing different accuracies for different observation durations.However, accuracy requirements depend on project and purpose.
It is therefore cost effective and time-saving if the observation duration required (optimum time) to produce the desired accuracy in a given GNSS project is known.
In order to determine the optimum time for fixing positions by GNSS, accuracy (in the form of Accuracy often improved sharply between 5 and 20 minutes time span in all the three figures.The accuracy then continued to improve steadily between 20 and 50 minutes sessions.After 50 minutes of logging, no significant improvement of accuracy is recorded.This means that after 50 minutes of observation, any additional time spent on a point will not necessarily refine position results.Since the baseline was up to 195 km, the results pointed to the fact that 50 minutes could serve as the optimum observation duration. In   According to Hoehn and Niven (1985) RMSE values measure the scatter among a set of positions from several sub-session data for the same rover stations.Thus, RMSE values indicate the precision of the position coordinates for each of the sub-session data.Thus, precision improved with time.The graphs also fit perfectly on an exponential curve indicating that RMSE values could be predicted for given session duration between 5 minutes and 4 hours in this study.This information will help the surveyor to select observation duration to be spent on each point if the positional accuracy is specified.
The predictive curve is expressed in a mathematical equation below: [1] Where T is the duration in hours and c is a quantity in units of km root hour.

Conclusions
The study was set to determine how much time (optimum duration) to be spent on rover positions in order to obtain the desired accuracy using GNSS data observed locally from Ghana for baseline length up to 195km.This goal was achieved by analysing accuracies for observation durations spanning from 5 minutes to 4-hrs.After 50 minutes of observation, coordinate differences became insignificant yielding values of 0.003m, 0.002m and 0.026m in the ENU directions respectively.These coordinate differences were within the accuracy threshold for baselines up to 200km as published by the USACE in 2003.The study therefore set 50 minutes as the optimum observation duration when fixing ground control points at baseline length up to 195km.
Currently the interstation distances between the existing CORS stations in Ghana span within 200km.Therefore 200km has been set as the maximum baseline for this study.Three CORS sites in Kumasi, Accra and Assin-Fosu were selected together with a passive control point in Sunyani to form three baselines keeping the Kumasi station as base, refer to Figure1.

Figure 1 .
Figure 1.Study diagram showing stations and processed baselines in kilometres.

Figure 3
Figure 3 relates RMSE to observation duration such that RMSE values continued to decline as session duration increased thereby confirming the reports of earlier studies: Creager and Maggio (1998) and Eckl et al. (2001).

Table 1 .
Base Station Coordinates Published by Geodetic Reference Network Office of Ghana

Table 2 .
Mean Positions of Rover Stations from 4-hr Data

Table 3 .
Computation of Baseline Repeatability for Three Different Days

Table 4 .
Mean Coordinate Differences and Root Mean Squared Errors from Partitioned Data

table 2
could be confirmed that all positions were fixed within the acceptable accuracy limit of the USACE.This trend was seen in table 2(b) and (c) as well.