| GISdevelopment.net ---> Technology ---> Global Positioning System |
Comparative evaluation and validation of single and dual frequency GPS observations
R. Ghosh
P. Jayaprasad, B. Narender, Anjum Mahtab and Ajai
Land use Planning and Photogrammetry Division
Forestry, Land use and Photogrammetry Group
Remote Sensing Application area
Sunanda P Trivedi, Y. P. Rana and P. K. Srivastava
Satellite Photogrammetry and Digital Cartography Division
Signal Image Processing Group Space Applications Centre
(ISRO) Ahmedabad-380 015.
Gujarat.
ranendu@hotmail.com
R. Ghosh
P. Jayaprasad, B. Narender, Anjum Mahtab and Ajai
Land use Planning and Photogrammetry Division
Forestry, Land use and Photogrammetry Group
Remote Sensing Application area
Sunanda P Trivedi, Y. P. Rana and P. K. Srivastava
Satellite Photogrammetry and Digital Cartography Division
Signal Image Processing Group Space Applications Centre
(ISRO) Ahmedabad-380 015.
Gujarat.
ranendu@hotmail.com
Introduction
Global positioning system (GPS) technology today have a solution of position accuracy on earth from < 1m to 100 m depending upon the type of receiver and mode of observation one uses. The basic observable of GPS at least those that permit us to determine position, velocity and time are the pseudorange and the carrier phase. Combining the basic observables in various ways can generate additional observable that have certain advantage. But the accuracy of the measured observable is not totally error free. The error sources are due to ionosphere, satellite and receiver clock, multipath, dilution of precision, selective availability and anti-spoofing. Dual frequency receiver takes care of the error due to ionosphere to a large extent. Rest of the errors significantly reduces in differential mode of observation. In order to answer some of these hypothesis objectively, an experiment was planned to measure the co-ordinates of ten points in and around Ahmedabad using both single and dual frequency receivers. The scope of the experiment were set are :
The purpose of this exercise was to obtain coordinates of few points distributed in and around Ahmedabad, using single and dual frequency GPS receivers. A comparative study of the performance of single and dual frequency was also carried out. Validation of the coordinates obtained was done, by comparing baseline distances computed using GPS with that from actual ground measurements. The accuracy of measurements was verified using triangle error of closure.
Approach for GPS Observations
Ten points in the vicinity of 20 Km were selected for the GPS observation. Out of these points, one point was considered as reference point and rest all as rover points. One dual and one single frequency GPS receivers were placed at the reference point. Since both the receivers cannot be placed at the same position simultaneously, the single frequency receiver was placed at known fix distance and direction away from the reference point. The dual frequency receiver was placed with the choke ring antenna in order to take care of the multipath conditions. At all the rover points one after another, the GPS receivers were set and GPS observations were taken for one hour at each point. For each of the point the minimum elevation angle 10 degrees, observation recording rate 10 seconds and set data collection parameters - compacted were selected.
In the exercise two types of GPS receivers were used, three single frequency and two dual frequency Leica receivers. To process the GPS data SKI processing software version 2.3.1 was used.
Analysis of the Exercises Performed
The accuracy assessment of the experiment was done by the evaluation of the performance of various ionosheric models on the GPS measurements and the comparative performances of single and dual frequency observations.
Performance evaluation of various models on the accuracy of the dual frequency observations
The various types of ionoshperic models used in this study were No model, Standard, Computed, Global/ Regional and Klobuchar. For each of the model, baselines were computed between reference and rover points. The processed data file gives the standard deviation in geodetic coordinates (Table-1). Table-1 shows that no model and the global model gives the same standard deviation values. As per the SKI software, the computed ionospheric model can be selected if there are at least 45 minutes of observations at the reference receiver for each baseline otherwise for baseline below 20 Km, the standard ionospheric model is used. It comes out from the table that for one hour GPS observation, there is not much variation in any of the model values but in case of point no. 3 where three hours GPS observation data is available, the variation in the effect of the model is appearing. Concluding that the computed model is suitable for one hour observation data, all further exercises were performed with computed ionospheric model.
Table.1: The standard deviations obtained in X, Y & Z using different ionospheric models provided in SKI GPS observations processing software.
Accuracy evaluation of the measurement of the same points using single and dual frequency receivers
The GPS observation data with single frequency and dual frequency were processed using SKI processing software version 2.3.1. Baselines were computed between the reference and respective rovers for single and dual frequency observations and results are shown in the Table- 2. In processing following specification were selected.
Table. 2: Difference between Dual & Single Frequency observations
It is found that considering the offset of placing the single frequency receiver away from the dual frequency and comparing the baseline distance in terms of geodetic coordinates, it gives difference less than one metre in all the three latitude, longitude and height values.
The difference between the reference and the rover point coordinates are computed without considering the offset part in setting the GPS receivers. The differences in the distances are shown in the Table 3.1, 3.2 and 3.3.
Validation of results
Validation of results was carried out by baseline distance verification and computing the triangle closing error methods.
Baseline distance verification
Baseline distances were calculated from positional coordinates obtained using both single and dual frequency observations. These baseline distances were compared with that from actual ground measurements. Details of the comparisons is given in tables 3.1
Vector Closure Analysis
For determining the error of closure, simultaneous observations were carried out for three or four points. Out of these observations, triangles were formed by joining three points. Baseline vector has to be computed independently for each side of triangles by taking one station as the reference and others as rovers. Two different studies were carried out to evaluate the effect of duration of observation on vector closing error and geometry on vector closing error.
Effect of duration of observation on closing error
In order to analyse the effect of observation time on closing error; an experiment was carried out on two different triangles by using observations for 6 hrs. The common observation between the reference and rover points were divided into one hr, 2 hrs, 3 hrs and 4 hrs respectively. For each time interval, the baseline vector for all sides of the triangles were computed independently and closing error were computed. The results for two triangles were tabulated in tables 3.3 and 3.4. For tringle1, slope distances between the stations were 1.7 km, 0.5 km and 1.3 km respectively and for triangle 2; slope distances were 10.8 km, 8.3 km and 2.5 km.
Effect of observation point geometry on closing error
Error of closure for the present study was carried out for three triangles formed from simultaneous observations and the results are given in table 3.4. Three triangles were formed (T3, T4 and T5) and the slope distances between the base stations were as follows.
Results and Discussion
In order to evaluate the performance of various ionospheric models on the accuracy of dual frequency observations, GPS data was processed for five different ionospheric models. The analysis shows that there is not much variation in the results of the various ionospheric models for smaller observation time say 1/1.5 hrs. For longer hours of observation computed model gives better accuracy.
Tables 2 gives the comparison of baseline differences, between reference and rover points, computed using single and dual frequency receivers. It has been observed that residual error in latitude, longitude and height is around 0.50m, 0.25m and 1.0m respectively. The difference of observations with in 1 m between single and dual frequency receivers suggests that the baseline of 10 15 km hardly makes any difference in positional accuracy (~ 1m), only observation time matters.
Table 3.1 gives the comparison of baseline distances calculated from the positional coordinates obtained using single and dual frequency receivers with the actual ground distances. Table 3.1 shows that variation is around ± 0.15 m.
Table. 3.1: Comparison of baseline distances with actual ground distances
Table 3.2 shows that one hour observation is sufficient for baselines upto two kms to achieve an accuracy of 1 ppm or better.
Table 3.2
Table. 3.3
Table. 3.4: Effect of geometry on closing error
Table 3.3 shows that to achieve the above accuracy for a baseline of 10-15kms, two hours of observation is required.
Table 3.4 indicates that triangle T3 shows maximum closing error in all the three dimensions, which could be attributed to the poor geometry (very small base in comparison to other two sides) of the triangle. Moderate closure errors are seen in the case of T4 and T5 triangles. This could be because of small observation time and up to some extent geometry too.
Conclusions
The present experiment has given significant insight in the overall understanding of the various elements related to GPS measurements towards establishing the precise coordinates of the ground control points. The comparative evaluation of the performance of single frequency receivers vis-a vis dual frequency have been carried out. Also the impact of different ionospheric models on the accuracy of measurements have been studied. The baseline distances computed using single and dual frequency receivers show difference of less than a metre. The baseline distances as computed with differential GPS measurements showed a deviation of ± 0.15 m from the actual ground distance. Validation results also indicates that one hour observation is sufficient for baselines up to two km to achieve an accuracy of 1 ppm or better. However to achieve the same accuracy for a baseline of 10 to 15 km, two hours of observation is required.
Global positioning system (GPS) technology today have a solution of position accuracy on earth from < 1m to 100 m depending upon the type of receiver and mode of observation one uses. The basic observable of GPS at least those that permit us to determine position, velocity and time are the pseudorange and the carrier phase. Combining the basic observables in various ways can generate additional observable that have certain advantage. But the accuracy of the measured observable is not totally error free. The error sources are due to ionosphere, satellite and receiver clock, multipath, dilution of precision, selective availability and anti-spoofing. Dual frequency receiver takes care of the error due to ionosphere to a large extent. Rest of the errors significantly reduces in differential mode of observation. In order to answer some of these hypothesis objectively, an experiment was planned to measure the co-ordinates of ten points in and around Ahmedabad using both single and dual frequency receivers. The scope of the experiment were set are :
- To evaluate the performance of various in built ionospheric models on the accuracy of the measurement
- To evaluate the accuracy of the measurement of the same points using single and dual frequency receivers.
- Precision of base line measurement using single and dual receivers.
- To evaluate the effect of duration of measurement on the accuracy of the Co-ordinates.
The purpose of this exercise was to obtain coordinates of few points distributed in and around Ahmedabad, using single and dual frequency GPS receivers. A comparative study of the performance of single and dual frequency was also carried out. Validation of the coordinates obtained was done, by comparing baseline distances computed using GPS with that from actual ground measurements. The accuracy of measurements was verified using triangle error of closure.
Approach for GPS Observations
Ten points in the vicinity of 20 Km were selected for the GPS observation. Out of these points, one point was considered as reference point and rest all as rover points. One dual and one single frequency GPS receivers were placed at the reference point. Since both the receivers cannot be placed at the same position simultaneously, the single frequency receiver was placed at known fix distance and direction away from the reference point. The dual frequency receiver was placed with the choke ring antenna in order to take care of the multipath conditions. At all the rover points one after another, the GPS receivers were set and GPS observations were taken for one hour at each point. For each of the point the minimum elevation angle 10 degrees, observation recording rate 10 seconds and set data collection parameters - compacted were selected.
In the exercise two types of GPS receivers were used, three single frequency and two dual frequency Leica receivers. To process the GPS data SKI processing software version 2.3.1 was used.
Analysis of the Exercises Performed
The accuracy assessment of the experiment was done by the evaluation of the performance of various ionosheric models on the GPS measurements and the comparative performances of single and dual frequency observations.
Performance evaluation of various models on the accuracy of the dual frequency observations
The various types of ionoshperic models used in this study were No model, Standard, Computed, Global/ Regional and Klobuchar. For each of the model, baselines were computed between reference and rover points. The processed data file gives the standard deviation in geodetic coordinates (Table-1). Table-1 shows that no model and the global model gives the same standard deviation values. As per the SKI software, the computed ionospheric model can be selected if there are at least 45 minutes of observations at the reference receiver for each baseline otherwise for baseline below 20 Km, the standard ionospheric model is used. It comes out from the table that for one hour GPS observation, there is not much variation in any of the model values but in case of point no. 3 where three hours GPS observation data is available, the variation in the effect of the model is appearing. Concluding that the computed model is suitable for one hour observation data, all further exercises were performed with computed ionospheric model.
Table.1: The standard deviations obtained in X, Y & Z using different ionospheric models provided in SKI GPS observations processing software.
| Sr. No. | Baseline Identification | Ionospheric Model Used | Standard Deviation (geodetic coordinates) in m | ||
| SX | SY | SZ | |||
| 1 | Ref._10 | No model | 0.0108 | 0.0474 | 0.0644 |
| Standard | 0.0108 | 0.0474 | 0.0645 | ||
| Computed | 0.0107 | 0.0471 | 0.0641 | ||
| Global/Regional | 0.0108 | 0.0474 | 0.0644 | ||
| Klobuchar | 0.0108 | 0.0474 | 0.0644 | ||
| 2 | Ref._01 | No model | 0.0030 | 0.0124 | 0.0031 |
| Standard | 0.0030 | 0.0123 | 0.0032 | ||
| Computed | 0.0031 | 0.0122 | 0.0032 | ||
| Global/Regional | 0.0030 | 0.0124 | 0.0031 | ||
| Klobuchar | 0.0030 | 0.0124 | 0.0031 | ||
| 3 | Ref._07 | No model | 0.0011 | 0.0040 | 0.0029 |
| Standard | 0.0011 | 0.0042 | 0.0030 | ||
| Computed | 0.0011 | 0.0041 | 0.0029 | ||
| Global/Regional | 0.0011 | 0.0040 | 0.0029 | ||
| Klobuchar | 0.0011 | 0.0040 | 0.0029 | ||
| 4 | Ref._08 | No model | 0.0035 | 0.0105 | 0.0062 |
| Standard | 0.0035 | 0.0105 | 0.0062 | ||
| Computed | 0.0035 | 0.0105 | 0.0062 | ||
| Global/Regional | 0.0035 | 0.0105 | 0.0062 | ||
| Klobuchar | 0.0035 | 0.0105 | 0.0062 | ||
| 5 | Ref._09 | No model | 0.0032 | 0.0087 | 0.0053 |
| Standard | 0.0031 | 0.0084 | 0.0051 | ||
| Computed | 0.0032 | 0.0086 | 0.0053 | ||
| Global/Regional | 0.0032 | 0.0087 | 0.0053 | ||
| Klobuchar | 0.0032 | 0.0087 | 0.0053 | ||
| 6 | Ref._02 | No model | 0.0028 | 0.0075 | 0.0078 |
| Standard | 0.0028 | 0.0074 | 0.0077 | ||
| Computed | 0.0026 | 0.0071 | 0.0074 | ||
| Global/Regional | 0.0028 | 0.0075 | 0.0078 | ||
| Klobuchar | 0.0028 | 0.0074 | 0.0077 | ||
| 7 | Ref._03 | No model | 0.0005 | 0.0006 | 0.0014 |
| Standard | 0.0013 | 0.0016 | 0.0043 | ||
| Computed | 0.0013 | 0.0045 | 0.0019 | ||
| Global/Regional | 0.0005 | 0.0006 | 0.0014 | ||
| Klobuchar | 0.0039 | 0.0051 | 0.0126 | ||
| 8 | Ref._04 | No model | 0.0026 | 0.0066 | 0.0051 |
| Standard | 0.0025 | 0.0066 | 0.0050 | ||
| Computed | 0.0026 | 0.0067 | 0.0051 | ||
| Global/Regional | 0.0026 | 0.0066 | 0.0051 | ||
| Klobuchar | 0.0026 | 0.0067 | 0.0050 | ||
|
Accuracy evaluation of the measurement of the same points using single and dual frequency receivers
The GPS observation data with single frequency and dual frequency were processed using SKI processing software version 2.3.1. Baselines were computed between the reference and respective rovers for single and dual frequency observations and results are shown in the Table- 2. In processing following specification were selected.
Table. 2: Difference between Dual & Single Frequency observations
| Baseline Station | Residuals (Difference between Dual & Single Frequency observations ) | ||
| lat (cm) | long (cm) | height(cm) | |
| Ref. 01 | -46.83 | 9.78 | -68.44 |
| Ref. 02 | -44.13 | -22.47 | -68.08 |
| Ref. 03 | -42.69 | -24.57 | -76.84 |
| Ref. 04 | -42.42 | -13.14 | -72.26 |
| Ref. 07 | -34.59 | -15.96 | -92.97 |
| Ref. 08 | -15.96 | -15.93 | -83.1 |
It is found that considering the offset of placing the single frequency receiver away from the dual frequency and comparing the baseline distance in terms of geodetic coordinates, it gives difference less than one metre in all the three latitude, longitude and height values.
The difference between the reference and the rover point coordinates are computed without considering the offset part in setting the GPS receivers. The differences in the distances are shown in the Table 3.1, 3.2 and 3.3.
Validation of results
Validation of results was carried out by baseline distance verification and computing the triangle closing error methods.
Baseline distance verification
Baseline distances were calculated from positional coordinates obtained using both single and dual frequency observations. These baseline distances were compared with that from actual ground measurements. Details of the comparisons is given in tables 3.1
Vector Closure Analysis
For determining the error of closure, simultaneous observations were carried out for three or four points. Out of these observations, triangles were formed by joining three points. Baseline vector has to be computed independently for each side of triangles by taking one station as the reference and others as rovers. Two different studies were carried out to evaluate the effect of duration of observation on vector closing error and geometry on vector closing error.
Effect of duration of observation on closing error
In order to analyse the effect of observation time on closing error; an experiment was carried out on two different triangles by using observations for 6 hrs. The common observation between the reference and rover points were divided into one hr, 2 hrs, 3 hrs and 4 hrs respectively. For each time interval, the baseline vector for all sides of the triangles were computed independently and closing error were computed. The results for two triangles were tabulated in tables 3.3 and 3.4. For tringle1, slope distances between the stations were 1.7 km, 0.5 km and 1.3 km respectively and for triangle 2; slope distances were 10.8 km, 8.3 km and 2.5 km.
| Triangle | Base Station Slope Distance |
| T3 | 11.6 km, 0.007 km, 11.6 km |
| T4 | 1.6 km, 0.022 km, 11.6 km |
| T5 | 11.6 km, 0.18 km, 11.8 km |
Effect of observation point geometry on closing error
Error of closure for the present study was carried out for three triangles formed from simultaneous observations and the results are given in table 3.4. Three triangles were formed (T3, T4 and T5) and the slope distances between the base stations were as follows.
Results and Discussion
In order to evaluate the performance of various ionospheric models on the accuracy of dual frequency observations, GPS data was processed for five different ionospheric models. The analysis shows that there is not much variation in the results of the various ionospheric models for smaller observation time say 1/1.5 hrs. For longer hours of observation computed model gives better accuracy.
Tables 2 gives the comparison of baseline differences, between reference and rover points, computed using single and dual frequency receivers. It has been observed that residual error in latitude, longitude and height is around 0.50m, 0.25m and 1.0m respectively. The difference of observations with in 1 m between single and dual frequency receivers suggests that the baseline of 10 15 km hardly makes any difference in positional accuracy (~ 1m), only observation time matters.
Table 3.1 gives the comparison of baseline distances calculated from the positional coordinates obtained using single and dual frequency receivers with the actual ground distances. Table 3.1 shows that variation is around ± 0.15 m.
Table. 3.1: Comparison of baseline distances with actual ground distances
| Stations | Distance Computation | Actual GroundDistance (m) | Residuals w.r.t. Actual Ground Distance | ||
| Single (m) | Dual (m) | Single (m) | Dual (m) | ||
| 01 02 | 768.067373 | 768.264363 | 768.2 | 0.132627 | -0.064363 |
| 01 03 | 3505.145652 | 3505.341638 | 3505.2 | 0.0543480 | -0.141638 |
Table 3.2 shows that one hour observation is sufficient for baselines upto two kms to achieve an accuracy of 1 ppm or better.
Table 3.2
| Time of observation | Closing error (cm) | ||
| dx | dy | dz | |
| 1hour | - 0.03 | -0.07 | 0.00 |
| 2hours | -0.01 | -0.02 | 0.02 |
| 3hours | 0.00 | -0.02 | 0.01 |
| 4hours | 0.01 | -0.01 | 0.02 |
Table. 3.3
| Time of observation | Closing error (cm) | ||
| dx | dy | dz | |
| 1 Hour | -0.18 | -0.51 | -0.44 |
| 2 Hours | -0.03 | -0.24 | -0.16 |
| 3 Hours | 0.05 | -0.06 | 0.01 |
| 3.83 Hours | 0.09 | 0.08 | 0.24 |
Table. 3.4: Effect of geometry on closing error
| Triangle | Closing error (cm) | ||
| dx | dy | dz | |
| T3 | - 33.26 | - 15.52 | - 11.59 |
| T4 | 4.8 | - 10.63 | 3.09 |
| T5 | - 8.98 | - 12.56 | - 6.69 |
Table 3.3 shows that to achieve the above accuracy for a baseline of 10-15kms, two hours of observation is required.
Table 3.4 indicates that triangle T3 shows maximum closing error in all the three dimensions, which could be attributed to the poor geometry (very small base in comparison to other two sides) of the triangle. Moderate closure errors are seen in the case of T4 and T5 triangles. This could be because of small observation time and up to some extent geometry too.
Conclusions
The present experiment has given significant insight in the overall understanding of the various elements related to GPS measurements towards establishing the precise coordinates of the ground control points. The comparative evaluation of the performance of single frequency receivers vis-a vis dual frequency have been carried out. Also the impact of different ionospheric models on the accuracy of measurements have been studied. The baseline distances computed using single and dual frequency receivers show difference of less than a metre. The baseline distances as computed with differential GPS measurements showed a deviation of ± 0.15 m from the actual ground distance. Validation results also indicates that one hour observation is sufficient for baselines up to two km to achieve an accuracy of 1 ppm or better. However to achieve the same accuracy for a baseline of 10 to 15 km, two hours of observation is required.