Free adjustment of a triangulation net - Jackson, Jonathan (School of Architecture, Planning and Geomatics, 2016)
It is often useful to determine the measures of precision of the directly observed quantities in a triangulation net. Provided the net is not strained these measures are unique to a particular set of observations and weights. Unique measures for the precision of the indirectly observed quantities cannot be found by classical means although several ad hoc approaches can be used to approximate to this measure of the 'inherent strength' of a net. Bjerhammar's theory of generalised matrix inverses can be used to derive measures of precision for the indirectly observed quantities, which may be interpreted as reflecting the inherent strength of the net. The theory of adjustment of a triangulation net by the method of variation of co-ordinates is described, followed by an explanation of the theory bf generalised inverses. Methods for the practical derivation of particular inverses are described, following Mittermayer. The characteristics of Normal, Transnormal and Stochastic Ring inverses in solution of Normal equations BX = R, are described.