| Title:
|
Nonlinear Bayesian state filtering with missing measurements and bounded noise and its application to vehicle position estimation (English) |
| Author:
|
Pavelková, Lenka |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
47 |
| Issue:
|
3 |
| Year:
|
2011 |
| Pages:
|
370-384 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper deals with parameter and state estimation and focuses on two problems that frequently occur in many practical applications: (i) bounded uncertainty and (ii) missing measurement data. An algorithm for the state estimation of the discrete-time non-linear state space model whose uncertainties are bounded is proposed. The algorithm also copes with situations when some measurements are missing. It uses Bayesian approach and evaluates maximum a posteriori probability (MAP) estimates of states and parameters. As the model uncertainties are supposed to have a bounded support, the searched estimates lie within an area that is described by the system of inequalities. In consequence, the problem of MAP estimation becomes the problem of nonlinear mathematical programming (NLP). The estimation with missing data reduces to the omission of corresponding inequalities in NLP formulation. The proposed estimation algorithm is applied to the estimation of a moving vehicle position when incomplete data from global positioning system (GPS) together with complete data from vehicle sensors are at disposal. (English) |
| Keyword:
|
non-linear state space model |
| Keyword:
|
bounded uncertainty |
| Keyword:
|
missing measurements |
| Keyword:
|
state filtering |
| Keyword:
|
vehicle position estimation |
| MSC:
|
93E11 |
| MSC:
|
93E12 |
| idZBL:
|
Zbl 1222.93224 |
| idMR:
|
MR2857195 |
| . |
| Date available:
|
2011-06-23T12:53:18Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141591 |
| . |
| Reference:
|
[1] Becis-Aubry, Y., Boutayeb, M., Darouach, M.: State estimation in the presence of bounded disturbances.Automatica 44 (2008), 1867–1873. Zbl 1149.93340, MR 2528139, 10.1016/j.automatica.2007.10.033 |
| Reference:
|
[2] Bemporad, A., Filippi, C., Torrisi., F.: Inner and outer approximations of polytopes using boxes.Computational Geometry 27 (2004), 151–178. Zbl 1044.65016, MR 2030535, 10.1016/S0925-7721(03)00048-8 |
| Reference:
|
[3] Berger, J. O.: Statistical Decision Theory and Bayesian Analysis.Springer-Verlag, New York 1985. Zbl 0572.62008, MR 0804611 |
| Reference:
|
[4] Fletcher, R.: Practical Methods of Optimization.John Wiley & Sons, 2000. MR 0955799 |
| Reference:
|
[5] Goodwin, G. C., Feuer, A.: Estimation with missing data.Mathematical and Computer Modelling of Dynamical Systems 5 (1999), 3, 220–244. Zbl 0940.93069, 10.1076/mcmd.5.3.220.3681 |
| Reference:
|
[6] Gupta, V., Brennan, S.: Terrain-based vehicle orientation estimation combining vision and inertial measurements.J. Field Robotics 25 (2008), 3, 181–202. Zbl 1243.68288, 10.1002/rob.20233 |
| Reference:
|
[7] Imran, M., Hassan, Y., Patterson, D.: GPS-GIS-based procedure for tracking vehicle path on horizontal alignments.Computer-aided Civil and Infrastructure Engineering 21(2006), 5, 383–394. 10.1111/j.1467-8667.2006.00444.x |
| Reference:
|
[8] Jazwinski, A. M.: Stochastic Processes and Filtering Theory.Academic Press, New York 1970. Zbl 0203.50101 |
| Reference:
|
[9] Kárný, M., Böhm, J., Guy, T. V., Jirsa, L., Nagy, I., Nedoma, P., Tesař, L.: Optimized Bayesian dynamic advising: Theory and algorithms.Springer, London 2005. |
| Reference:
|
[10] Lang, L., Chen, B. R., Bakshi, W., Goel, P. G., Ungarala, S.: Bayesian estimation via sequential Monte Carlo sampling – Constrained dynamic systems.Automatica 43 (2007), 1615–1622. Zbl 1128.93387, MR 2327074, 10.1016/j.automatica.2007.02.012 |
| Reference:
|
[11] Park, S., Hwang, J., Kim, E., Kang, H.: Vehicle tracking using a microwave radar for situation awareness.Control Engrg. Practice 18 (2010), 4, 383–395. |
| Reference:
|
[12] Pavelková, L.: Estimation of Models with Uniform Innovations and its Application on Traffic Data.PhD. Thesis, Czech Technical University in Prague, Faculty of Transportation Sciences, Praha 2008. |
| Reference:
|
[13] Pavelková, L.: State Estimation with Missing Data and Bounded Uncertainty.Technical Report No. 2296, ÚTIA AV ČR, Praha 2011. |
| Reference:
|
[14] Polyak, B. T., Nazin, S. A., Durieu, C., Walter, E.: Ellipsoidal parameter or state estimation under model uncertainty.Automatica 49 (2004), 7, 1171–1179. Zbl 1056.93063, MR 2148312, 10.1016/j.automatica.2004.02.014 |
| Reference:
|
[15] Qi, H. H., Moore, J. B.: Direct Kalman filtering approach for GPS/INS integration.IEEE Trans. Aerospace and Electronic Systems 38 (2002), 687–693. 10.1109/TAES.2002.1008998 |
| Reference:
|
[16] Rao, C. V., Rawlings, J. B., Mayne, D. Q.: Constrained state estimation for nonlinear discrete-time systems: stability and moving horizon approximations.IEEE Trans. Automat. Control 48 (2003), 2, 246–258. MR 1957321, 10.1109/TAC.2002.808470 |
| Reference:
|
[17] Savkin, A. V., Petersen, I. R.: Robust filtering with missing data and a deterministic description of noise and uncertainty.Internat. J. Systems Sci. 28 (1997), 373–378. Zbl 0887.93069, 10.1080/00207729708929397 |
| Reference:
|
[18] Simon, D., Simon, D. L.: Constrained Kalman filtering via density function truncation for turbofan engine health estimation.Internat. J. Systems Sci. 41 (2010), 159–171. MR 2605872, 10.1080/00207720903042970 |
| Reference:
|
[19] Sinopoli, B., Schenato, L., Franceschetti, M., Poolla, K., Jordan, M. I., Sastry, S. S.: Kalman filtering with intermittent observations.IEEE Trans. Automat. Control 49 (2004), 9, 1453–1464. DOI 10.1109/TAC.2004.834121. MR 2086911, 10.1109/TAC.2004.834121 |
| Reference:
|
[20] Tsai, W. K., Parlos, A. G., Verghese, G. C.: Bounding the states of systems with unknown-but-bounded disturbances.Internat. J. Control 52 (1990), 4, 881–915. Zbl 0721.93052, 10.1080/00207179008953573 |
| Reference:
|
[21] Venhovens, P. J. T., Naab, K.: Vehicle dynamics estimation using Kalman filters.Vehicle System Dynamics 32 (1999), 2–3, 171–184. 10.1076/vesd.32.2.171.2088 |
| Reference:
|
[22] Wang, C., Lachapelle, G., Cannon, M. E.: Development of an integrated low-cost GPS/rate gyro system for attitude determination.J. Navigation 57 (2004), 1, 85–101. 10.1017/S0373463303002583 |
| Reference:
|
[23] Wang, Z., Ho, D. W. C., Liu, X.: Variance-constrained filtering for uncertain stochastic systems with missing measurements.IEEE Trans. Automat. Control 48 (2003), 1254–1258. MR 1988100, 10.1109/TAC.2003.814272 |
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