Adjustment Computations, 6th Edition

CHAPTER 7ERROR PROPAGATION IN ANGLE AND DISTANCE OBSERVATIONS

7.1 INTRODUCTION

All surveying observations are subject to errors from varying sources. For example when observing an angle, the major sources of error include instrument placement and leveling, target placement, circle reading, and target pointing. Although great care may be taken in observing an angle, these error sources will nonetheless render inexact results. To fully appreciate the need for adjustments, surveyors must be able to identify the major observational error sources, know their effects on the observations, and understand how they can be modeled. In this chapter, emphasis is placed on analyzing the errors in observed horizontal angles and distances. Chapter 8 explains the manner in which these errors propagate to produce traverse misclosures. Chapter 9 covers the propagation of errors in elevation determination. Chapter 10 shows how these estimated errors can be used as the foundation for a valid stochastic (weighting) model in a least-squares adjustment.

7.2 ERROR SOURCES IN HORIZONTAL ANGLES

Whether a transit, theodolite, or total station instrument was used in the survey, errors are present in every horizontal angle observation. Whenever an instrument's circles are read, a small error is introduced into the final angular value. Also, in pointing to a target, a small amount of error always occurs. ...