Error detection and data smoothing based on local procedures

Abstract

This thesis presents an algorithm which is able to locate isolated bad points and correct them without contaminating the rest of the good data. This work has been greatly influenced and motivated by what is currently done in the manual loft. It is not within the scope of this work to handle small random errors characteristic of a noisy system, and it is therefore assumed that the bad points are isolated and relatively few when compared with the total number of points. Motivated by the desire to imitate the loftsman we conducted a visual experiment to determine what is considered smooth data by most people. This criterion is used to determine how much the data should be smoothed and to prove that our method produces such data. The method ultimately converges to a set of points that lies on the polynomial that interpolates the first and last points; however convergence to such a set is definitely not the purpose of our algorithm. The proof of convergence is necessary to demonstrate that oscillation does not take place and that in a finite number of steps the method produces a set as smooth as desired. The amount of work for the method described here is of order n. The one dimensional and two dimensional cases are treated in detail; the theory can be readily extended to higher dimensions