UDC 528.738:629.783(497.12) GPS - PSEUDOKINEMATIC SURVEYMETH MSc. Miran Kuhar, M.Se. Janez Oven, Simona Savšek-Saftc, MSc. Bojan Stopar FAGG-Oddelek za geodezijo, Ljubljana Received far publication: Feb. 25, 1993 Abstract The article describes the measurement and calculation of points' coordinates far photogrammetric control points gained by the GPS pseudokinematic survey method. Further, the pseudokinematic observation method and a 12 points measurement example on the Pivka territory is described. Calculated are coordinates of points in the GK system and the accuracy analysis. Keywm:ds: accuracy, control points, Globa! Positioning System, photogrammetry, GPS pseudokinematic survey method, Slovenia INTRODUCTION r a research in photogrammertry in December 1992 in the Pivka territory a network of 12 points was calculated by the GPS pseudokinematic survey method. The Pivka example was chosen due to the fact that in 1991 in this area CAS was carried out and connective network calculated. The coordinates of points were calculated at the Surveying Institute of the Republic Slovenia whereas topography is stored at the Surveying and Mapping Administration in Postojna. For the measurement ground control points were used. CONTROL POINTS COORDINATES DETERMINATION BY THE GPS determine photogrammetric control points 12 points were calculated by the GPS pseudokinematic survey method. (Tub le 1) The points were divided into two groups. The first group is formed by points of the given GK coordinates (5 points). In the group there are trigonometric points of the fourth order: 113z, 106z, and 175z; trigonometric point of the third supplementary order, point 104z and connective point 86. Eight control points (fl, f2, f3, f4, f5, f6, f7 and f8) form the second group of points. These were calculated by the GPS measurements. The f2 point is identical with the point 106. All points are approachable by car. The control points had to be determined coordinates in the GK coordinate system. PSEUDOKINEMATIC METHOD - OBSERVATION The required accuracy of control points determination was given as to the accuracy of photogrammetry, namely mx= my = ±0,05 m and mz = ±0,10 m. According to the required accuracy, relatively short distances (to 5 km) and good reachability of Geodetski vestnik 37 (1993) 1 points, the GPS pseudokinematic method, which is satisfactory as to the given requirements, was used to determine new points by GPS measurements (King 1987). The GPS pseudokinematic survey method resembles the kinematic method as to the observation method (data collection) and the statistical method in data processing. The method is known also as the method with intervals or statistic method with interruptions. To execute GPS pseudokinematic survey at least two receivers with antennas are needed. By a typical GPS pseudokinematic survey one of the receivers is located at a known point, with the other one we move from point to point and at each we register data for 5 to 10 minutes. After approximately one hour we retu:rn with the mobile receiver to each point once more and observe it again for 5 to 10 minutes. Thus for each point approximately one hour observation without data in the middle is made (Thble 2). The importance Hes in each receiver visiting the same point twice. The one hour time-lag between the first and the second visit of the point is needed for the arrangement of the satellites in the sky to be changed in such an extent as to allow integer ambiguity determination. The time-lag between observation of the same point is not to be shorter than 50 minu.tes and not longer than 120 minutes (Ewing 1990). Fig. 1: Points on which observations were carried out (section from a map 1:50 000) y planning the GPS pseudokinematic survey at least 3 (better 4 or more) satellites of the same kind have to be available to be in the sky for the wh9le observation period of one group of points (two visits of all points). When on road between the points there is no need to receive a satellite signal. In case we have more mobile eodetski vestnik 37 (1993) 1 receivers simultaneously collecting data, and the operators in radio connection, we can determine also vectors among them. The pseudokinematic method does not require one of the receivers to be ona permanent point but all the receivers may be mobile. This procedure is more productive especially in the case when there is a lesser number of receivers available. In this way we gain less independent vectors. Fig. 2: Pseudokinematic survey method (one permanent, one mobile receiver) In our case the measurements of points was executed by three two frequency GPS Ashtech XII receivers. The observations were made on December 16, 1992. According to method, satenites arrangement, and number of receivers an observation planning was made which is crucial for effectiveness. The satellites arrangement (20 launched satelli.tes till now) enabled observations between 10.15 and 12.15 and from 12.45 on by local tirne. The needed observation tirne together with travels among points with 2 receivers would encompass 8 hours, and four hours with 3 receive:r:s. The observations were carried out in two sections. In both sections one of the receivers was on a permanent place and two mobile. The observations with the mobile receivers were executed simultaneously (radio connection) in such a manner, that a calculation of 18 vectors was possible. The course of measurements according to sections was as follows: 1st Section 10.15 10.23 104 f3 10.33 10.41 104 175 10.52 11.02 104 f6 11.12 11.20 104 f3 11.30 11.38 104 175 11.48 11.57 104 f6 Geodetski vestnik 37 (1993) fl 86 f2 fl 86 f2 ;td Section Begiri End Receiver .Receiver L 2 12.50 13.03 86 104 13.18 13.26 86 f8 13.45 13.55 86 f5 14.10 14.18 86 104 14.32 14.41 86 f8 14.53 15.05 86 f5 The real observation tirne is evident form tables of the section 1 and 2. PSEUDOKINEMATIC METHOD - CALCULATIONS . Receiver .3 113 f4 f7 113 f4 f7 By GPS observation processing programme 18 spatial vectors (Tuble 3) and their accuracy were calculated. Then by Columbus programme the vectors were adjusted in the net. The net was first adjusted as a free net on ellipsoid so that we adopted for the given coordinates of one point (ep, A, H). By the adjustment of a free net we can estimate the quality of observations. We found out there were no faults in the net. Then, the net was adjusted so that we adopted as a given point the point 113 with coordinates (ep, ;l., H) and four points with altitudes (113, 86, 175 and 104) the hypothesis beeing that locally the geoid is not changing (ellipsoid altitude differences correspond to altitude differences). By such net adjustment we acquire the coordinate;; .· ....... ··.y ....... · ..•.. · .. x••··•·•• .. ·• ···. ·.·•· z··•···.>< ··. dY d.x ·• ·•·· .·dZ ·.· ... ·· I·· 104 40527,854 59853 070 590250 -004 - 010 ,000 113 37239,027 59751,440 628 530 003 020 000 175 39758,049 61080 511 552100 011 009 000 86 36767 710 61658,828 589 740 -,010 - 018 ,000 15 ±,000 Tabk 3b Point• > >Y .. 1 ...... ·.·.• ··.·•.•··· ......... < .. x ..... · ........... I< • ./ z \ ..... < f1 36280,920 61385 209 582256 f2 37831,818 61393 072 563199 f3 39738 622 61077366 551608 f4 36071,325 59500200 588177 f5 37705 691 59503 454 575,612 f6 39729 547 59286379 586553 f7 36417 364 57752429 473 504 f8 39623 740 57571,894 553,846 ere are no residual errors at altitudes in the Tuble 3a since we connected the local net in altitude sense to points 104, 113, 175 and 86. ANALYSES From the observations at 12 points 18 spatia:l vectors were calculated. The observations ofvectors are good, when the mean error of double phase difference determination (rms) is 0.09 and when the relation between the most probable values for thewhole number ofwaves (ratio) is 3. At the Pivka observations it amounted to: rms: 0,003 < rms < 0,04, ratio: 25 < ratio < 284. he mean errors of measured coordinate differences of vectors according to individual axes were from 3 to 61 millimeters. Before net adjustment the errors of closure of shapes (triangulars and quandrangulars) were calculated. The errors were within range of precision of mean errors of vectors. By the net calculation f rom spatial vectors also the accuracy of each point in the net is given (Fig. 4). The errors in the Y-axis are between 11 and 32 mm, in the X-axis between 9 a~d 28 mm, and in the Z-axis between 27 and 61 mm, which shows that the heights of points are twice worse determined as the position. This may result from bad heights of given points or else is the ellipsoid a bad approximation for a geoid. An independent verification was executed at the point 106 (one ofthe photogrammetric points), which had the given GK coordinates. The errors at the point 106 are: /1 Y = /1X = 0,01 m and 11Z= 0,07m. eodetski vestnik 37 (1993) 1 CONCLUSION Pivka measurements stated that the uu,J,u.uv.,uu«'-' mensuration method in GPS system is appropriate and effective at measurements in nets with distances not longer than a few kilometers. It is longed for the points be easy reachable. The GPS pseudokinematic method would be vu.uu,,v for new local nets, connective nets or nets of photogrammetric control points. References: Ewing, B., 1990, Pseudokinematic GPS for the surveyor, GPS World, Chester, Sept.-Oct., p. 50-52. King, R. W, Masters, E. G., 1987, Surveyif'!gwith the GPS, Duemmlers Verlag, Bonn. Review: Dušan Miškovic Barbara Sušnik Geodetski vestnik 37 (1993)