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This paper introduces a reformulation of the extended Kalman Filter using the Gauss-Helmert model for least squares estimation. By proving the equivalence of both estimators it is shown how the methods of statistical analysis in least squares estimation can be applied to the prediction and update process in Kalman Filtering. Especially the efficient computation of the reliability (or redundancy) matrix allows the implementation of self supervising systems. As an application an unparameterized method for estimating the variances of the filters process noise is presented.