Comment on "A new method for the nonlinear transformation of means and covariances in filters and estimators" [with authors\´ reply]

The above paper (Julier et al. IEEE Trans. Automat. Contr, vol. 45, pp. 477-82, 2000) generalizes the Kalman filter to nonlinear systems by transforming approximations of the probability distributions through the nonlinear process and measurement functions. This comment derives exactly the same estimator by linearizing the process and measurement functions by a statistical linear regression through some regression points (in contrast with the extended Kalman filter which uses an analytic linearization in one point). This insight allows one: 1) to understand/predict the performance of the estimator for specific applications, and 2) to make adaptations to the estimator (i.e., the choice of the regression points and their weights) in those cases where the original formulation does not assure good results. In reply the authors state that the commenters conclusion is unnecessarily narrow interpretation of results.