Minimal Constraints in Two-Dimensional Networks

by Alfred Leick, (A.M.ASCE), Asst. Prof.; Dept. of Civ. Engrg., Univ. of Maine, Surveying Engrg. Program, Orono, Me. 04469,

Serial Information: Journal of the Surveying and Mapping Division, 1982, Vol. 108, Issue 2, Pg. 53-68

Document Type: Journal Paper


The use of coordinates in the adjustment of two-dimensional networks leads to inherently singular solutions. Various minimal constraints are applied to eliminate the singularity. The variant and invariant quantities, with respect to a choice of minimal constraints, are identified. Inner constraints, which constitute a subset of all sets of minimal constraints, are useful in displaying the internal network geometry through error ellipses whose size, shape and orientation are independent of the definition of the coordinate system. Inner constraint solutions are helpful in simulation studies where the optimum station locations and observing program are investigated. Any minimal constraint solution can be used for checking the quality of observations and the detection of blunders.

Subject Headings: Geometrics | Errors (statistics) | Terminology and definition

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