Double Summation of Errors in Aerial Triangulation

by Gordon Gracie,

Serial Information: Journal of the Surveying and Mapping Division, 1965, Vol. 91, Issue 2, Pg. 13-26

Document Type: Journal Paper


Data from a 100-model grid triangulation are used to demonstrate certain features associated with the double summation of errors in the transfer of scale, azimuth, and longitudinal tilt in a strip of aerial triangulation. Errors in the x, y, and z machine coordinates of pass points on the center line of the strip, are first determined from the observed data. Plotted curves of these machine coordinate errors display their characteristic, systematic appearance. The second difference of these errors are then calculated and subjected to two statistical tests. These tests reveal that the systematic appearance of the machine coordinate errors can arise from the double summation of normally distributed random errors. Hence, there need not be any systematic component in the triangulation to produce a systematic appearance. This emphasizes that it is difficult to determine whether or not systematic errors are present in an aerial triangulation simply by observing the machine coordinate errors.

Subject Headings: Triangulation | Errors (statistics) | Equipment and machinery | High-rise buildings | Information management | Light rail transit | Grid systems | Azimuth

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