Application of Recursive Least Squares to Efficient Blunder Detection in Linear Models

In many geodetic applications a large number of observations are being measured to estimate the unknown parameters. The unbiasedness property of the estimated parameters is only ensured if there is no bias (e.g. systematic effect) or falsifying observations, which are also known as outliers. One of the most important steps towards obtaining a coherent analysis for the parameter estimation is the detection and elimination of outliers, which may appear to be inconsistent with the remainder of the observations or the model. Outlier detection is thus a primary step in many geodetic applications. There are various methods in handling the outlying observations among which a sequential data snooping procedure, known as Detection, Identification and Adaptation (DIA) algorithm, is employed in the present contribution. An efficient data snooping procedure is based on the Baarda’s theory in which blunders are detected element-wise and the model is adopted in an iterative manner. This method may become computationally expensive when there exists a large number of blunders in the observations. An attempt is made to optimize this commonly used method for outlier detection. The optimization is performed to improve the computational time and complexity of the conventional method. An equivalent formulation is thus presented in order to simplify the elimination of outliers from an estimation set-up in a linear model. The method becomes more efficient when there is a large number of model parameters involved in the inversion. In the conventional method this leads to a large normal matrix to be inverted in a consecutive manner. Based on the recursive least squares method, the normal matrix inversion is avoided in the presented algorithm. The accuracy and performance of the proposed formulation is validated based on the results of two real data sets. The application of this formulation has no numerical impact on the final result and it is identical to the conventional outlier elimination. The method is also tested in a simulation case to investigate the accuracy of the outlier detection method in critical cases when large amount of the data is contaminated. In the application considered, it is shown that the proposed algorithm is faster than the conventional method by at least a factor of 3. The method becomes faster when the number of observations and parameters increases.