7.1 INTRODUCTION

The control methods described in the last chapter are limited to specific figures such as intersection, resection and traverse. Only in the case of the traverse is more than the minimum number of observations taken and even then the computational method is arbitrary as far as finding the coordinates of the points from the observations is concerned. A much better, but more complex, process is to use least squares estimation; that is what this chapter is about.

'Least squares' is a powerful statistical technique that may be used for 'adjusting' or estimating the coordinates in survey control networks. The term adjustment is one in popular usage but it does not have any proper statistical meaning. A better term is 'least squares estimation' since nothing, especially observations, are actually adjusted. Rather, coordinates are estimated from the evidence provided by the observations.

The great advantage of least squares over all the methods of estimation, such as traverse adjustments, is that least squares is mathematically and statistically justifiable and, as such, is a fully rigorous method. It can be applied to any overdetermined network, but has the further advantage that it can be used on one-, two- and three-dimensional networks. A by-product of the least squares solution is a set of statistical statements about the quality of the solution. These statistical statements may take the form of standard errors of the computed coordinates, error ellipses or ellipsoids describing the uncertainty of a position in two or three dimensions, standard errors of...