4th WORKSHOP ON POSITIONING, NAVIGATION AND COMMUNICATION 2007 (WPNC’07), HANNOVER, GERMANY best estimates. More sophisticated robust filter should be able to <strong>in</strong>dentify certa<strong>in</strong> situations and apply the most convenient robust model to them, but this is beyond the scope of this paper and left for future study. ACKNOWLEDGMENT This study was funded by Nokia Corporation. The EKF and EKF2 used for reference were implemented by Simo Ali- Löytty and the simulation test bench was generated us<strong>in</strong>g Niilo Sirola’s test bench generator [8]. REFERENCES [1] S. Ali-Löytty, N. Sirola, and R. Piché, “Consistency of Three <strong>Kalman</strong> Filter Extensions <strong>in</strong> <strong>Hybrid</strong> Navigation,” <strong>in</strong> Proceed<strong>in</strong>gs of the European Navigation Conference GNSS, July 19-22 2005. [2] P. J. Huber, “<strong>Robust</strong> Estimation of a Location Parameter,” Ann. Math. Statis., vol. 35, pp. 73–101, 1964. [3] R. D. Mart<strong>in</strong> and C. J. Masreliez, “<strong>Robust</strong> Estimation via Stochastic Approximation,” IEEE Transactions on Information Theory, vol. IT-21, no. 3, pp. 263–271, May 1975. [4] D. F. Andrews, P. J. Bickel, F. R. Hampel, P. J. Huber, W. H. Rogers, andJ.W.Tukey,<strong>Robust</strong> Estimates of Location: Survey and Advances. Pr<strong>in</strong>ceton University Press, 1972. [5] A. Carosio, A. C<strong>in</strong>a, and M. Piras, “The <strong>Robust</strong> Statistics Method Applied to the <strong>Kalman</strong> Filter: Theory and Application,” ION GNSS 18th International Technical Meet<strong>in</strong>g of the Satellite Division, September 13- 16 2005. [6] A. E. Bryson and Y.-C. Ho, Applied Optimal Control: Optimization, Estimation, and Control. Taylor & Francis, 1975. [7] C. J. Masreliez and R. D. Mart<strong>in</strong>, “<strong>Robust</strong> Bayesian Estimation for the L<strong>in</strong>ear Model and <strong>Robust</strong>ify<strong>in</strong>g the <strong>Kalman</strong> Filter,” IEEE Transactions on Automatic Control, vol. AC–22, no. 3, pp. 361–371, 1977. [8] N. Sirola, S. Ali-Löytty, and R. Piché, “Benchmark<strong>in</strong>g nonl<strong>in</strong>ear filters,” <strong>in</strong> Nonl<strong>in</strong>ear Statistical Signal Process<strong>in</strong>g Workshop NSSPW06, Cambridge, September 2006. 60
4th WORKSHOP ON POSITIONING, NAVIGATION AND COMMUNICATION 2007 (WPNC’07), HANNOVER, GERMANY −k2 −k −y −k1 ψH(t) k −k ψM(t) y −y ωD(t) 1 k y k1 k2 t Fig. 1. The ψ- and the ω-functions t t 61 −k2 −k1 ψD(t) k1 −k1 ωH(t) 1 −k k ωM (t) 1 −y y k1 k2 t t t