Tommi Perälä
ABSTRACT
A family of Kalman-type filters that estimate the user's position indoors, using range measurements and floor plan data, is presented. The floor plan information is formulated as a set of linear constraints and is used to truncate the Gaussian posterior probability densities occurring in the Kalmantype filters. The truncated Gaussian is approximated with a new Gaussian density such that the mean and the covariance matrix coincide approximately with the mean and the covariance matrix of the truncated Gaussian. The linear constraints may be used all at once or imposed one after another. Both strategies are studied in this paper and their advantages and disadvantages are discussed.
Simulation data has been processed using the Extended Kalman filter, the second order Extended Kalman filter and the Unscented Kalman filter, and the results are compared to a reference solution computed with a sequential Monte Carlo particle filter. The simulations indicate that the proposed method for using floor plan information increases the accuracy of the estimates without significantly increasing the computation or the memory requirements. The low computational demand and the absence of the training phase make it a useful addition to existing indoor positioning systems.
- Monte carlo sampling based in-home location tracking with minimal rf infrastructure requirements. In G. V. Záruba, M. Huber, F. A. Kamangar, and I. Chlamtac, editors, Proceedings of IEEE Global Telecommunications Conference 2004 GLOBECOM 04 GLOCOM-04, pages 3624--3629, 2004.Google Scholar
- S. Ali-Löytty. Efficient Gaussian mixture filter for hybrid positioning. In 2008 IEEE/ION Position Location and Navigation Symposium, pages 60--66, Monterey, California, May 2008.Google ScholarCross Ref
- S. Ali-Löytty and N. Sirola. A modified Kalman filter for hybrid positioning. In Proceedings of ION GNSS 2006, pages 1679--1686, September 2006.Google Scholar
- S. Ali-Löytty and N. Sirola. Gaussian mixture filter in hybrid navigation. In Proceedings of The European Navigation Conference GNSS 2007, pages 831--837, Switzerland, May 2007.Google Scholar
- S. Ali-Löytty, N. Sirola, and R. Piché. Consistency of three Kalman filter extensions in hybrid navigation. In Proceedings of the European Navigation Conference GNSS 2005, July 19--22, 2005, Munchen, 2005.Google Scholar
- Y. Bar-Shalom, R. X. Li, and T. Kirubarajan. Estimation with Applications to Tracking and Navigation, Theory Algorithms and Software. John Wiley & Sons, 2001. Google ScholarDigital Library
- R. G. Brown. Introduction to Random Signal Analysis and Kalman Filtering. John Wiley & Sons, 1983.Google Scholar
- A. H. Jazwinski. Stochastic Processes and Filtering Theory, volume 64 of Mathematics in Science and Engineering. Academic Press, 1970.Google Scholar
- S. J. Julier and J. K. Uhlmann. Unscented filtering and nonlinear estimation. Proceedings of the IEEE, 92(3):401--422, March 2004.Google Scholar
- N. Shimada, Y. Shirai, Y. Kuno, and J. Miura. Hand gesture estimation and model refinement using monocular camera - ambiguity limitation by inequality constraints. In FG '98: Proceedings of the 3rd. International Conference on Face & Gesture Recognition, page 268, Washington, DC, USA, 1998. IEEE Computer Society. Google ScholarDigital Library
- D. Simon and D. L. Simon. Constrained Kalman filtering via density function truncation for turbofan engine health estimation. Technical memorandum NASA/TM-2006-214129, National Aeronautics and Space Administration, Washington, DC, 2006.Google Scholar
- H. W. Sorenson and D. L. Alspach. Recursive Bayesian estimation using Gaussian sums. Automatica, 7(4):465--479, July 1971.Google Scholar
- Widyawan, M. Klepal, and S. Beauregard. A backtracking particle filter for fusing building plans with pdr displacement estimates. In Proceedings of the 5th Workshop on Positioning, Navigation and Communication 2008 (WPNC'08), pages 207--212, 2008.Google Scholar
Index Terms
- Kalman-type positioning filters with floor plan information
Recommendations
Accuracy analysis of sigma-point Kalman filters
CCDC'09: Proceedings of the 21st annual international conference on Chinese control and decision conferenceSigma-point Kalman filters are new filters with high precision aimed at nonlinear system. Within the framework of linear minimum variance recursive algorithm, the accuracy of state estimation using the sigma-point Kalman filters mainly depends on the ...
Kalman filter/smoother-based design and implementation of digital IIR filters
Highlights- A Kalman filter framework for finding the optimal response of digital IIR filters is proposed.
AbstractRecently, a unified framework was proposed for forward-backward filtering and penalized least-squares optimization. It was shown that forward-backward filtering can be presented as instances of penalized least-squares optimization. In ...
Kalman filter vs. particle filter in improving K-NN indoor positioning
KES'11: Proceedings of the 15th international conference on Knowledge-based and intelligent information and engineering systems - Volume Part IIThe Kalman filter has been widely used in estimating the state of a process and it is well known that no other algorithm can out-perform it if the assumptions of the Kalman filter hold. For a non-Gaussian estimation problem, both the extended Kalman ...
Comments