The Robust Statistics Method Applied to the Kalman Filter: Theory and Application

Alessandro Carosio, Alberto Cina and Marco Piras

Abstract:	This research deals with the possibility of using the robust methods, particularly the Huber-estimator, in a sequential approach. The Kalman filter is a frequently used sequential technique, which foresees the use of velocity filter in the algorithm. The disadvantage, as in all non robust methods, is that any possible errors , that are not removed in the original dataset, could lead to an incorrect solution. There are different methods in literature devoted to analyzing and detecting of outliers, that can be applied the Kalman filter. In robust statistics, the Huber estimator foresees three ways of verifying the basic conditions in the objective function: the first is to modify the normal matrix, the second is to modify the weight matrix and the last is to modify the observation vector. The last method has been applied to the Kalman filter and a particular Robust Kalman Filter has been generated. This method is based on sequential calculus using the Kalman filter applied to robust statistics. This operation makes the relative residual equal to the k parameter, for each modified observation. In this situation the Least Squares method can also be applied for these observations. The RKF has also been applied to a dataset with different outlier and the results obtained with other typical sequential techniques (Sequential Least Squares) have been compared. The method, using the robust statistics, suffers less from the presence of outlier because it has a breakpoint of about 0,2. This allows many errors to be present in the data, in the same epoch, but a correct solution to be obtained. The technique could play an important role in sequential applications, for example in the control of area correction parameters, calculated from a control center. which manages a GPS stations permanent network. Another possible case is that of real time deformation control. The implemented method could therefore be a good solution for outlier detection or for to calculate the estimated solution with a low dependence on the outliers.
Published in:	Proceedings of the 18th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2005) September 13 - 16, 2005 Long Beach Convention Center Long Beach, CA
Pages:	525 - 535
Cite this article:	Carosio, Alessandro, Cina, Alberto, Piras, Marco, "The Robust Statistics Method Applied to the Kalman Filter: Theory and Application," Proceedings of the 18th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2005), Long Beach, CA, September 2005, pp. 525-535.
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