2009-1 - (Gm-09v) Page 1 of 6 Norges...

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(Gm-09v) Page 1 of 6 Norges teknisk-naturvitenskapelige universitet Institutt for bygg, anlegg og transport Faggruppe Geomatikk EXAM: TBA4230 GEOMATICS Language: English. (A Norwegian version is also available.) Contact information: Terje Skogseth mobile 952 88 301 (question 1 and 3) Knut Ragnar Holm mobile 992 51 188 (question 2) Date: December 8 th 2009 Time: 0900 – 1300 Credits: 7.5 Allowed aids: Code C: Specified printed and handwritten aids: Certain plain calculator (HP30S or Citizen SR-270X) Either: ”Matematisk statistikk (feilteori) og Estimering (MKM), elementmetoden”, Holsen og Skogseth Or: ”Mathematical statistics and estimation (least squares method); adjustment by parameters” Holsen and Skogseth The number of pages: 6 The 3 questions have the same weight. All the sub questions (x.1, x.2, …) within each question have the same weight. For the questions containing calculations, the progress of the calculations must be clearly shown in the answer. For relevant formulas it is assumed that the student has the allowed aids.
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(Gm-09v) Page 2 of 6 Question no. 1: GPS, adjustment by parameters, etc. Page 2 gives values and conditions to be used in both question 1 and 3, as it is the same project in these two questions. See figure 1.1. The length of the axis of a bridge between the new points C and D is measured-in by “classical” GPS, baseline measurements. Figure 1.1 shows which baselines that are measured. The control points A and B are known points. The axis of the bridge is horizontal, and the local coordinate system has the x axis in the same direction as the axis of the bridge, D-C. See figure 1.1. Coordinates in the local coordinate system in figure 1.1: Point x y Status A 1650.030 500.050 Known values B -1000.003 149.050 Known values C 719.372 1450.000 Estimated values D 0.000 1450.000 Estimated values Table 1.1 Local coordinates Figure 1.1 Observations and points Coordinates and heights in EUREF89-UTM-zone 32 and NN1954, and geoidal heights (undulations): Punkt N(orth) E(ast) H Geiodal height, N Status A 6577823.385 598268.505 10.471 38.733 Known values B 6575154.484 598405.440 20.963 38.702 Known values C 6577081.292 599371.617 15.011 38.667 Estimated values D 6576374.123 599502.456 15.011 38.653 Estimated values Table 1.2 UTM coordinates The method Adjustment by parameters is used to calculate the adjusted/estimated coordinates of the points C and D. To obtain estimated heights and coordinates in the map projection plane from the GPS measurements, the following two methods can be used: Method 1: Transform the GPS baselines to observables in the map projection
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2009-1 - (Gm-09v) Page 1 of 6 Norges...

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