Home Articles Comparative evaluation and validation of single and dual frequency GPS observations

Comparative evaluation and validation of single and dual frequency GPS observations

R. Ghosh


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.
[email protected]

Introduction
Global positioning system (GPS) technology today have a solution of position accuracy on earth from

  • 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.
  • Design of the Experiment
    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
    Parameters Selected input
    Cut-off angle (deg.) 10
    Tropospheric model Hopfield
    Ionospheric model Computed
    Solution type Standard
    Ephemeris Broadcast

    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.