Three-Dimensional Positioning—by Multilateration

by William E. Ball, Jr., (M.ASCE), Engrg. Analyst; U.S. Dept. of the Interior, Bureau of Land Mgmt., Sci. Systems Development Ofc., Denver, CO,

Serial Information: Journal of the Surveying and Mapping Division, 1974, Vol. 100, Issue 1, Pg. 63-78

Document Type: Journal Paper


Systems of equations are derived and computational routines are outlined that can be used to determine the geodetic coordinates and elevation of a point by three-dimensional multilateration using slope distances only. The geodetic coordinates and elevation of a point are computed using slope distances (only) that have been measured from three or more points having known geodetic coordinates and elevations to the point of unknown position. By an alternate method, the position of a point is also determined using as few as two slope distances if, in addition, the elevation of the point is known. Least squares methods are employed and precision evaluation estimators are computed.

Subject Headings: Geodetic surveys | Slopes | High-rise buildings | Least squares method | Distance measurement

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