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Robust Extended Kalman Filtering in Hybrid Positioning Applications

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4th WORKSHOP ON POSITIONING, NAVIGATION AND COMMUNICATION 2007 (WPNC’07), HANNOVER, GERMANY<br />

best estimates. More sophisticated robust filter should be able<br />

to <strong>in</strong>dentify certa<strong>in</strong> situations and apply the most convenient<br />

robust model to them, but this is beyond the scope of this<br />

paper and left for future study.<br />

ACKNOWLEDGMENT<br />

This study was funded by Nokia Corporation. The EKF<br />

and EKF2 used for reference were implemented by Simo Ali-<br />

Löytty and the simulation test bench was generated us<strong>in</strong>g Niilo<br />

Sirola’s test bench generator [8].<br />

REFERENCES<br />

[1] S. Ali-Löytty, N. Sirola, and R. Piché, “Consistency of Three <strong>Kalman</strong><br />

Filter Extensions <strong>in</strong> <strong>Hybrid</strong> Navigation,” <strong>in</strong> Proceed<strong>in</strong>gs of the European<br />

Navigation Conference GNSS, July 19-22 2005.<br />

[2] P. J. Huber, “<strong>Robust</strong> Estimation of a Location Parameter,” Ann. Math.<br />

Statis., vol. 35, pp. 73–101, 1964.<br />

[3] R. D. Mart<strong>in</strong> and C. J. Masreliez, “<strong>Robust</strong> Estimation via Stochastic<br />

Approximation,” IEEE Transactions on Information Theory, vol. IT-21,<br />

no. 3, pp. 263–271, May 1975.<br />

[4] D. F. Andrews, P. J. Bickel, F. R. Hampel, P. J. Huber, W. H. Rogers,<br />

andJ.W.Tukey,<strong>Robust</strong> Estimates of Location: Survey and Advances.<br />

Pr<strong>in</strong>ceton University Press, 1972.<br />

[5] A. Carosio, A. C<strong>in</strong>a, and M. Piras, “The <strong>Robust</strong> Statistics Method<br />

Applied to the <strong>Kalman</strong> Filter: Theory and Application,” ION GNSS 18th<br />

International Technical Meet<strong>in</strong>g of the Satellite Division, September 13-<br />

16 2005.<br />

[6] A. E. Bryson and Y.-C. Ho, Applied Optimal Control: Optimization,<br />

Estimation, and Control. Taylor & Francis, 1975.<br />

[7] C. J. Masreliez and R. D. Mart<strong>in</strong>, “<strong>Robust</strong> Bayesian Estimation for the<br />

L<strong>in</strong>ear Model and <strong>Robust</strong>ify<strong>in</strong>g the <strong>Kalman</strong> Filter,” IEEE Transactions<br />

on Automatic Control, vol. AC–22, no. 3, pp. 361–371, 1977.<br />

[8] N. Sirola, S. Ali-Löytty, and R. Piché, “Benchmark<strong>in</strong>g nonl<strong>in</strong>ear filters,”<br />

<strong>in</strong> Nonl<strong>in</strong>ear Statistical Signal Process<strong>in</strong>g Workshop NSSPW06, Cambridge,<br />

September 2006.<br />

60

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