Abstract
In the robot navigation problem, noisy sensor data must be filtered to obtain the best estimate of the robot position. The discrete Kalman filter, commonly used for prediction and detection of signals in communication and control problems, has become a popular method to reduce the effect of uncertainty from the sensor data. However, in the domain of robot navigation, sensor readings are not only uncertain, but can also be relatively infrequent compared to traditional signal processing applications. In addition, a good initial estimate of location, critical for Kalman convergence, is often not available. Hence, there is a need for a filter that is capable of converging with a poor initial estimate and many fewer readings than the Kalman filter. To this end, we propose the use of a Recursive Total Least Squares Filter. This filter is easily updated to incorporate new sensor data, and in our experiments converged faster and to greater accuracy than the Kalman filter.
This work was supported jointly by Minnesota Department of Transportation grant 71789-72996-173 and National Science Foundation grant CCR-9405380.
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References
N. Ayache and O. D. Faugeras. Maintaining representations of the environment of a mobile robot. IEEE Transactions on Robotics and Automation, 5(6):804–819. December 1989.
D. L. Boley and K. T. Sutherland. Recursive total least squares: An alternative to the discrete Kalman filter. Technical Report CS TR 93-32, University of Minnesota, April 1993.
N. K. Bose, H. C. Kim, and H. M. Valenzuela. Recursive implementation of total least squares algorithm for image reconstruction from noisy, undersampled multiframes. In Proceedings of 1993 International Conference on Acoustics, Speech and Signal Processing, pages V-269–V-272. IEEE, May 1993.
W. Brogan. Modern Control Theory. Prentice Hall. 3rd edition, 1991.
C. E. Davila. Efficient recursive total least squares algorithm for FIR adaptive filtering. IEEE Trans. Sig. Proc., 42(2):268–280. 1994.
R. D. DeGroat. Noniterative subspace tracking. IEEE Transactions on Signal Processing, 40(3):571–577, March 1992.
H. Durrant-White, E. Bell, and P. Avery. The design of a radar-based navigation system for large outdoor vehicles. In Proceedings of 1995 International Conference on Robotics and Automation, pages 764–769. IEEE, June 1995.
A. Gelb. Applied Optimal Estimation. The M. I. T. Press, 1st edition, 1974.
G. H. Golub and C. F. Van Loan. Matrix Computations. Johns Hopkins, 2nd edition, 1989.
G. Hager and M. Mintz. Computational methods for task-directed sensor data fusion and sensor planning. The International Journal of Robotics Research, 10(4):285–313, August 1991.
S. Haykin. Adaptive Filter Theory. Prentice Hall. 2nd edition, 1991.
S. Hosur, A. H. Tewfik, and D. Boley. Multiple subspace ULV algorithm and LMS tracking. In M. Moonen and B. D. Moor, editors, 3rd Int'l Workshop on SVD and Signal Processing, pages 295–302. Elsevier, August 1995. Leuven, Belgium.
R. E. Kalman. A new approach to linear filtering and prediction problems. Journal of Basic Engineering, pages 35–45. 1960.
A. Kosaka and A. C. Kak. Fast vision-guided mobile robot navigation using model-based reasoning and prediction of uncertainties. CVGIP: Image Understanding. 56(3):271–329, November 1992.
H. Schneiderman and M. Nashman. A discriminating feature tracker for vision-based autonomous driving. IEEE Transactions on Robotics and Automation. 10(6):769–775. December 1994.
R. C. Smith and P. Cheeseman. On the representation and estimation of spatial uncertainty. The International Journal of Robotics Research. 5(4):56–68, Winter 1986.
H. W. Sorenson. Least-squares estimation: from Gauss to Kalman. IEEE Spectrum, pages 63–68, July 1970.
G. W. Stewart. Updating a rank-revealing ULV decomposition. SIAM J. Matrix Analysis. 14(2), 1993.
G. Strang. Introduction to Applied Mathematics. Wellesley-Cambridge Press. 1986.
K. T. Sutherland. Ordering landmarks in a view. In Proceedings 1994 ARPA Image Understanding Workshop, November 1994.
K. T. Sutherland and W. B. Thompson. Localizing in unstructured environments: Dealing with the errors. IEEE Transactions on Robotics and Automation. 10(6):740–754, December 1994.
S. Van Huffel and J. Vandewalle. The Total Least Squares Problem — Computational Aspects and Analysis. SIAM. Philadelphia, 1991.
S. Van Huffel and H. Zha. An efficient total least squares algorithm based on a rank-revealing two-sided orthogonal decomposition. Numerical Algorithms. 4(1–2):101–133, January 1993.
K.-B. Yu. Recursive updating the eigenvalue decomposition of a covariance matrix. IEEE Transactions on Signal Processing, 39(5):1136–1145, May 1991.
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© 1996 Springer-Verlag Berlin Heidelberg
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Boley, D.L., Steinmetz, E.S., Sutherland, K.T. (1996). Recursive total least squares: An alternative to using the discrete kalman filter in robot navigation. In: Dorst, L., van Lambalgen, M., Voorbraak, F. (eds) Reasoning with Uncertainty in Robotics. RUR 1995. Lecture Notes in Computer Science, vol 1093. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0013963
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DOI: https://doi.org/10.1007/BFb0013963
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