Adjustment Computations, 6th Edition

CHAPTER 20CONSTRAINT EQUATIONS

20.1 INTRODUCTION

When doing an adjustment, it is sometimes necessary to fix an observation to a specific value. For instance, in Chapter 14, it was shown that the coordinates of a control station can be fixed by setting its dx and dy corrections to zero, and thus the corrections and their corresponding coefficients in the J matrix were removed from the solution. This is called a constrained adjustment. Another constrained adjustment occurs when the direction or length of a line is held to a specific value or when an elevation difference between two stations is fixed in differential leveling. In this chapter methods available for developing observational constraints are discussed. However, before discussing constraints, the procedure for including control station coordinates in an adjustment is described.

20.2 ADJUSTMENT OF CONTROL STATION COORDINATES

In examples in preceding chapters when the coordinates of a control station were excluded from the adjustments, hence their values held fixed, constrained adjustments were being performed. That is, the observations were being forced to fit the control coordinates. However, control is not perfect, and not all control is of equal reliability. This fact is evidenced by the fact that different orders of accuracy are used to classify control.

When more than minimal control is held fixed in an adjustment, ...