Orthonormal Equations for Surveying Adjustment

The usual set of simultaneous normal equations can be avoided and replaced by a set of orthonormal equations, in each of which only one unknown appears. Many independent computation controls based on conditions of orthogonality, in addition to the usual sum controls, are available at every stage of computation, and thus make the orthonormal method suitable for both manual and machine computation. Rounding-off errors in this method are not cumulative. All information provided by the traditional normal equations can be obtained from orthonormal equations. The technique of constructing orthonormal equations may also be used for matrix inversion, and will never fail in problems of surveying adjustment. Examples illustrate the detail in setting up orthonormal equations in the correlate and the direct method of adjustment, and determine the inverse matrixes associated with them.