Adjustment Computations, 6th Edition

CHAPTER 15ADJUSTMENT OF HORIZONTAL SURVEYS: TRIANGULATION

15.1 INTRODUCTION

Prior to the development of electronic distance measuring equipment and the global navigation satellite systems, triangulation was the preferred method for extending horizontal control over long distances. The positions of widely spaced stations were computed from observed angles and a minimal number of observed distances called baselines. This method was used extensively by the National Geodetic Survey in extending much of the national network. Triangulation is still used by many surveyors in establishing horizontal control, although surveys that combine trilateration (distance observations) with triangulation (angle observations) are more common. In this chapter, methods are described for adjusting triangulation networks using least squares method.

A least squares triangulation adjustment can use condition equations or observation equations written either in terms of azimuths or angles. In this chapter the observation equation method is presented. The procedure involves a parametric adjustment where the parameters are coordinates in a plane rectangular system such as state plane coordinates. In the examples, the specific types of triangulations known as intersections, resections, and quadrilaterals will be adjusted.

15.2 AZIMUTH OBSERVATION EQUATION

The azimuth equation in parametric form is

(15.1) ...