CHAPTER 22THE GENERAL LEAST SQUARES METHOD AND ITS APPLICATION TO CURVE FITTING AND COORDINATE TRANSFORMATIONS
22.1 INTRODUCTION TO GENERAL LEAST SQUARES
When fitting points to a straight line it must be recognized that both the x and y coordinates contain errors. Yet in the mathematical model presented in Section 11.11.1, the residuals, as illustrated in Figure 11.2 are only applied to the y coordinate. Because both coordinates contain errors, this mathematical model fails to account for the x coordinate being an observation. In this chapter, the general least squares method is presented, and its use in performing adjustments where the observation equations involve more than a single observation is demonstrated.
22.2 GENERAL LEAST SQUARES EQUATIONS FOR FITTING A STRAIGHT LINE
Consider the data illustrated in Figure 11.2. To account properly for both the x and y coordinates being observations, the observation equation must contain residuals for all observations. That is, Equation (11.40) must be rewritten as
In Equation (22.1), x and y are a point's coordinate pair with residuals vx and vy, respectively, m is the slope of the line, and b is the y intercept. Equation (22.1) contains vx, vy, m, and b as unknowns and is nonlinear. Thus, its solution is obtained by using ...
Get Adjustment Computations, 6th Edition now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.
