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# 2009-2 - (Gm-09v Sol Page 1 of 11 NTNU Geomatics Exam...

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(Gm-09v – Sol) Page 1 of 11 NTNU Geomatics Exam: TBA4230 GEOMATICS Date: 8.12.2009 Time: 0900 – 1300 Solution, version 28.11.2010 Question no. 1: GPS, adjustment by parameters, etc. Here method 1 is used: The calculations are carried out in the local coordinate system. NB: Only calculations in the ground plane (horizontal plane) are done (no estimations of heights). Results from the estimation in the ground plane ( x , y ): ( ) 2 3,84 mgon pvv = = T V PV Figure 1.1 Observations and points The normal equations: 2,145 0,354 1,910 0,450 719372 1,029 0,400 0,740 1450000 2,717 1,581 0 2,219 1450000 C C D D x y x y = = = T X A PF the Q matrix of the estimated coord. 1.1 (a) State the number of excess measurements (degree of freedom) for the determination of the new points C and D on figure 1.1. The number of excess measurements, 5 baselines, 2 unknown points (NB: No calculations of heights): n - e = 5 2 – 2 2 = 6 With 2 known points (A and B) we also can choose to have 2 additional unknowns in the adjustments: Unknown scale and rotation. Normally this is done when GPS baselines calculated in WGS84 are used as observations in an adjustment in another datum: n - e = 5 2 – 2 2 – 2 = 4 (b) The observation with the unit weight is a plane bearing (as GPS is used). Calculate the standard deviation of the unit weight for the adjustment of the network in figure 1.1. Standard deviation of the unit weight, where n - e = 6 is used here, a plus if you use n - e = 4: ( ) 0 3,84 0,80 mgon 6 pvv n e σ = = = (With n – e = 4 we obtain 0,96 mgon) (c) Calculate the standard deviation of the estimated x coordinates of C and D. Calculate the covariance between the x coordinates of C and D. Calculate the covariance between the y coordinates of C and D. Interpret the results. x y B A D C

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