Home Articles Accuracy assessment in trilateration and surveying

Accuracy assessment in trilateration and surveying

B Narender


B Narender
[email protected]

P Jayaprasad


P Jayaprasad

and

Ajai


Ajai
Forestry, Landuse and Photogrammetry Group,
Remote Sensing Applications Area, Space Applications Centre (ISRO),
Ahmedabad – 380 015. India.

GPS has revolutionalised the field of navigation and surveying by solving the man’s longest and most troublesome problem “where on earth am I.” It also answers to the questions “what time, what position and what velocity is it? ” quickly, and accurately anywhere on the earth at any time. GPS owes its popularity to the dependable high accuracy with which position and time can be determined. Although GPS was already better than many other navigation system, the termination of selective availability from May 2000 has increased the accuracy of stand alone civil GPS. Surveying with GPS has become popular due to the advantage of speed, versatility and economy. GPS surveying is a differential method, where a baseline is observed and computed between two receivers. Surveying with GPS has been carried out by scientific and professional teams. Corbenu et. al, 2000 used two dual frequency GPS receivers for landslide monitoring. Abidin et.al, 1998 used dual frequency as well as single frequency receivers to establish second and third order networks. They obtained a relative accuracy of network as 2-3 cm. While establishing the precise coordinates or computing the baselines for surveying, the important questions to be addressed are i) what is the accuracy of the established position coordinates of the point and the baselines ii) what is the optimum time for GPS observation to achieve the desired accuracy. In the present paper, an attempt has been made to establish baseline distances by GPS observations in differential mode using single frequency receivers. The accuracy assessment has been carried by distance verification and vector closure analysis. An attempt has also been made to study the effect of observation time on closing error.

Methodology Single frequency GPS receivers have been used for taking observations in the present study. The survey was carried out in and around Ahmedabad City located in Gujarat state (the western part of India). Static Differential positioning survey was carried out in the present study. In this method, one receiver is kept at a fixed point (called reference) and the other receiver is moved (called rover) to take different observation. The baseline is computed by taking simultaneous observations in both the receivers. When two receivers observe the same set of satellites simultaneously, most of the atmospheric effects are canceled out. The shorter the baseline the truer the distance will be.

The carrier phases observed at rover stations are measured with respect to the carrier phase observed at reference station. The accuracy of single frequency GPS receiver observations, in differential mode, was evaluated by using both vector closure method as well as baseline distance validation.

Vector Closure Analysis
Three single frequency GPS receivers were installed at three non – collinear stations to collect the carriers phase data simultaneously. The vector closure analysis for the triangle was carried out, by calculating baseline vector components for each side of the triangle. The algebraic sum of dx, dy, dz for the three sides of triangle represents vector closure in x, y, z direction. The effect of observation time on closing error has also been studied by taking these measurements for different durations.

Baseline Distance Measurement
The baseline distance obtained from differential GPS measurements was compared with actual distance on the ground. Two single frequency GPS receivers were kept at two different stations, for which the actual ground distance between the two was known. The data were collected simultaneously for a period of two hours.

Data Collection and Analysis
The accuracy assessment of the single frequency GPS observations was carried out using vector closure analysis and baseline distance measurement method.

In vector closure analysis, three single frequency GPS receivers were simultaneously used to collect the data. Three triangles were selected for the vector closure analysis. The baseline distances between the pair of stations forming the sides of the triangle1 were 1044.2105 m, 1734.6913 m and 2775.3634 m and for the triangle 2 it is 2775.3634 m, 509.6323m and 2329.4722 m and for triangle 3 it is 10800.7970 m, 8290.4855 km and 2510.3571 m respectively. To study the effect of observation time on closing error, the common observations were taken for one hour, two hours, three hours and four hours respectively. For each time interval the data was processed and closing error in ppm was computed. For each triangle, closing error in ppm was calculated by ratio of resultant closure to total length of the triangle. The resultant closure is the square root of the sum of closing error in x, y, z direction and the total length of triangle is sum of the baseline distances of each side of the triangle. Sum of the by vector closure analysis was carried out. The post processing of GPS observations was carried out using SKI Software V 2.3. The closing error for different observation times for the three triangles is given in table 1,2,3.

In case of baseline computations, the data were processed in differential mode and the baseline distance between the points was computed and compared with the actual ground distance. The result of distance computed between stations 1-2 is given in table 4.The observation period was two hours.

Results and Discussion
The total loop length for the triangle1 is 5.54 km. From the table1 it is apparent that one hour observation gives closing error of 0.45 ppm. Two hours observation gives closing error of 0.16 ppm, three hours of observation gives closing error of 0.11 ppm and four hours of observation gives closing error of 0.08 ppm The closing error is more precise after two hours of observation. From the table 2 it can be observed that, one hour observation gives closing error of 0.29 ppm for a loop length of 5.61 km. The closing error is more precise with longer time of observation. From the table 3 it can be observed that, one hour observation gives closing error of 0.69 ppm for a total loop length of 21.60 km. Two hours observation gives closing error of 0.13 ppm and three hours observation gives closing error of 0.03 ppm. From the table 4, it can be observed that difference in baseline distances between actual and computed is around 5cm. This error may be attributed to the error involved in measurement of actual distance on ground.
Table 1: Closing error for different observation periods for triangle 1

Observation Time Closing Error (mm) in X,Y,Z directions Closing Error (ppm)
X (mm) Y (mm) Z (mm)
1 hour -0.6 -2.1 -1.2 0.45
2 hours -0.2 -0.8 -0.3 0.16
3 hours 0.4 0.4 0.3 0.11
4 hours -0.2 -0.4 -0.1 0.08

Table 2: Closing error for different observation periods for triangle 2

Observation Time Closing Error (mm) in X, Y, Z directions Closing Error (ppm)
X (mm) Y (mm) Z (mm)
1 hour 0.5 2.3 1.9 0.29
2 hours 0.2 1.2 0.7 0.14
3 hours 0.0 0.5 0.4 0.06
4 hours -0.7 -0.6 -0.1 0.09

Accuracy assessment in trilateration and surveying

Table 3: Closing error for different observation periods for triangle 2

Observation Time Closing Error (mm) in X,Y,Z directions Closing Error (ppm)
X (mm) Y (mm) Z ( mm)
1 hour -1.8 -5.1 -4.4 0.69
2 hours -0.3 -2.4 -1.6 0.13
3 hours 0.5 -0.6 0.1 0.03
4 hours 0.9 0.8 2.4 0.12

Table 4: Baseline distance comparison with actual ground distance

Stations Computed Distance (m) Actual ground Distance (m) Reiduals (m) (Actual-computed)
01 – 02 3505.145652 3505.2 0.0543480

Conclusions
From the present study, it can be concluded that, for static differential surveying using single frequency GPS receivers, one hour of observation is sufficient to obtain accuracy of 1 ppm or better for a network of length up to 20 km. The effect of observation time on closing error for dual frequency receivers has to be validated.

Acknowledgements
Authors express their sincere gratitude to Dr. A.K.S. Gopalan, Director, SAC for his initiative and interest in this study. We are thankful to Dr.P.K.Srivastava, head SPDD/SIPG, SAC, Ahmedabad for fruitful discussions.