Linearisation without calculus—a network adjustment example

Abstract There are many instances in the application of mathematics where linearisation, or differentiation, of complex equations is required. One such example is with survey network adjustments, where observation equations for survey measurements are linearised for a least squares solution of coordinates. The usual method of evaluating these derivatives is to linearise the observation equations using traditional calculus “rules”. The linearisation problem may be approached alternatively by approximating the differentiation numerically, avoiding any calculus derivatives. This paper shows how the principle of numerical evaluation of derivatives can be applied to network adjustment, in this case variation of coordinates on the Australian Map Grid (AMG). An investigation into the efficiencies of numerical evaluation of derivatives compared to calculus is also provided.