I3

A retro-reector is embedded in the roof of the British Museum's curved ceiling to monitor defamation of the structure on a regular basis. It is designated target TRGl 1.1 Three total stations are used to measure ranges from xed points of known coordinates. The xed-point locations (in units of metres) are: Station Easting Northing Height [8100 1002.624 2028.911 42.744 13101 1022.472 2029.076 43.022 [8102 1021.010 2054.861 42.914 The measured ranges (metres) from the xed points to the target, and the associated uncertainties (10 standard deviation, metres) of each measurement are: Station range std. dev. IS100 18.270 0.003 13101 18.755 0.005 IS102 16.908 0.002 The nominal coordinates of the target are (E, N, h): 1011.900 2042.700 50.300 A) Use a non-linear least squares method with one iteration to update the coordinates of the target. - ....] B) Show the derivations of the various mathematical functions required for the solution (that is, the partial derivatives in the A-matrix, and the formulation of the observed- computed b-vector)