Parameter estimation and outlier detection with different estimation methods

Abstract

The best suitable values of unknown parameters are determined by adjustment of observations done more than the number of unknown parameter in applied sciences. Adjustment methods should determine the out lier, that inevitably exists in the observations, while doing estimation of the best appropriate parameter for the unknown parameters. The adjustment is made on the basis of an objective functions with the best parameter estimation from the mathematical model, written for the observations done more than the number of unknown parameters. The most applied methods used for adjustment are Least Square (LS), Least Absolute Values (LAV) and Total Least Square (TLS) Methods. Although there are many advantages of these methods, the LS method also has some disadvantages, such as more affected from gross observation errors in the observation and spread of gross error in other observations. The solution of LAV method and the results obtained with trial and error method for the parameter estimation are less affected by gross observation error; and this method is used successfully in removing the outlier. Besides, with these methods in recent years, the TLS method is used for the adjustment. In this method, the design matrix used for the solution is also erroneous and the residuals of observation and design matrix are calculated together in the solution. In this study, after three adjustment methods have been explained, the parameter estimation and outlier detection are made with using the application data. The success of adjustment methods for parameter estimation and outlier detection had been determined as well by examining the results of these methods. ©2011 Academic Journals.