Stochastic observability test for discrete-time kalman filters

Journal of Guidance, Control, and Dynamics

Volumn 32, Issue 4, 2009, Pages 1356-1370

  Bageshwar, Vibhor L ^a   Gebre Egziabher, Demoz ^a   Garrard, William L ^a   Georgiou, Tryphon T ^a  

^a University of Minnesota   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

OBSERVABILITY; STOCHASTIC SYSTEMS; TESTING;

AIDED INERTIAL NAVIGATION; DISCRETE-TIME KALMAN FILTERS; ESTIMATED STATE; INITIAL STATE VECTORS; LINEAR TIME VARYING; NON-LINEAR STOCHASTIC SYSTEMS; STATE VECTOR; SYSTEM MATRICES;

KALMAN FILTERS;

EID: 68049143185     PISSN: 07315090     EISSN: 15333884     Source Type: Journal    
DOI: 10.2514/1.38128     Document Type: Article

References (29)

1. Kalman, R. E., "New Methods in Wiener Filtering Theory, " Proceedings of the First Symposium on Engineering Applications of Random Function Theory and Probability, edited by J. L. Bogdanoff, and F. Kozin, Wiley, New York, 1963, pp. 270-388.
2. Bryson, A. E., and Ho, Y. C., Applied Optimal Control: Optimization, Estimation, and Control, Blaisdell, Waltham, MA, 1969, Chap. 8.
3. Anderson, B. D. O., and Moore, J. B., "Detectability and Stabilizability of Time-Varying Discrete-Time Linear Systems, " SIAM Journal on Control and Optimization, Vol.19, No. 1, Jan. 1981, pp. 20-32. doi: 10.1137/0319002
4. Lewis, F. L., Optimal Estimation, Wiley, New York, 1986, Chap. 2.
5. Delyon, B., "ANote on Uniform Observability, " IEEE Transactions on Automatic Control, Vol.46, No. 8, Aug. 2001, pp. 1326-1327. doi: 10.1109/9.940944
6. Sorenson, H. W., "On the Error Behavior in Linear Minimum Variance Estimation Problems, " IEEE Transactions on Automatic Control, Vol.12, No. 5, Oct. 1967, pp. 557-562. doi: 10.1109/TAC.1967.1098679
7. Deyst, J. J., and Price, C. F., "Conditions for Asymptotic Stability of the Discrete Minimum Variance Linear Estimator, " IEEE Transactions on Automatic Control, Vol.13, No. 6, Dec. 1968, pp. 702-705. doi: 10.1109/TAC.1968.1099024
8. Deyst, J. J., "Correction to Conditions for Asymptotic Stability of the Discrete Minimum-Variance Linear Estimator, " IEEE Transactions on Automatic Control, Vol.18, No. 5, Oct. 1973, pp. 562-563. doi: 10.1109/TAC.1973.1100397
9. Aliev, F. A., and Ozbek, L., "Evaluation of Convergence Rate in the Central Limit Theorem for the Kalman Filter, " IEEE Transactions on Automatic Control, Vol.44, No. 10, Oct. 1999, pp. 1905-1909. doi: 10.1109/9.793734 (Pubitemid 30546886)
10. Bougerol, P., "Kalman Filtering with Random Coefficients and Contractions, " SIAM Journal on Control and Optimization, Vol.31, No. 4, July 1993, pp. 942-959. doi: 10.1137/0331041
11. Solo, V., "Stability of the Kalman Filter with Stochastic Time-Varying Parameters, " Proceedings of the 35th IEEE Conference on Decision and Control, Inst. of Electrical and Electronics Engineers, Piscataway, NJ, Dec. 1996, pp. 57-61.
12. Bitmead, R. R., and Anderson , B. D. O., "Lyapunov Techniques for the Exponential Stability of Linear Difference Equations with Random Coefficients, " IEEE Transactions on Automatic Control, Vol.25, No. 4, Aug. 1980, pp. 782-787. doi: 10.1109/TAC.1980.1102427
13. Ljung, L., "Asymptotic Behavior of the Extended Kalman Filter as a Parameter Estimator for Linear Systems, " IEEE Transactions on Automatic Control, Vol.24, No. 1, Feb. 1979, pp. 36-50. doi: 10.1109/TAC.1979.1101943
14. Guo, L., "Estimating Time-Varying Parameters by the Kalman Filter Based Algorithm: Stability and Convergence, " IEEE Transactions on Automatic Control, Vol.35, No. 2, Feb. 1990, pp. 141-147. doi: 10.1109/9.45169 (Pubitemid 20666486)
15. Boutayeb, M., Rafaralahy, H., and Darouach, M., "Convergence Analysis of the Extended Kalman Filter Used as an Observer for Nonlinear Deterministic Discrete-Time Systems, " IEEE Transactions on Automatic Control, Vol.42. No. 4, Apr. 1997, pp. 581-586. doi: 10.1109/9.566674
16. Song, T. L., and Speyer, J. L., "A Stochastic Analysis of a Modified Gain Extended Kalman Filter with Applications to Estimation with Bearings Only Measurements, " IEEE Transactions on Automatic Control, Vol.30, No. 10, Oct. 1985, pp. 940-949. doi: 10.1109/TAC.1985.1103821
17. Reif, K., Gunther, S., Yaz, E., and Unbehauen, R., "Stochastic Stability of the Continuous-Time Extended Kalman Filter, " IEE Proceedings. Control Theory Applications, Vol.147, No. 1, Jan. 2000, pp. 45-52. doi: 10.1049/ip-cta: 20000125
18. Reif, K., Gunther, S., Yaz, E., and Unbehauen, R., "Stochastic Stability of the Discrete-Time Extended Kalman Filter, " IEEE Transactions on Automatic Control, Vol.44, No. 4, Apr. 1999, pp. 714-728. doi: 10.1109/9.754809
19. Anderson, B. D. O., and Moore, J. B., Optimal Filtering, Dover, Mineola, NY, 1995, Chap. 3.
20. Stengel, R. F., Optimal Control and Estimation, Dover, Mineola, NY, 1994, Chaps. 2, 4.
21. Chen, H. F., Recursive Estimation and Control for Stochastic Systems, Wiley, New York, 1985, p. 237.
22. Ben-Israel, A., and Greville, T. N. E., Generalized Inverses: Theory and Applications, 2nd ed., Springer-Verlag, New York: 2003, Chap. 1.
23. Bar-Itzhack, I. Y., and Berman, N., "Control Theoretic Approach to Inertial Navigation Systems, " Journal of Guidance, Control, and Dynamics, Vol.11, No. 3, May-June 1988, pp. 237-245. doi: 10.2514/3.20299
24. Goshen-Meskin, D., and Bar-Itzhack, I. Y., "Observability Analysis of Piece-Wise Constant Systems-Part 1: Theory, " IEEE Transactions on Aerospace and Electronic Systems, Vol.28, No. 4, Oct. 1992, pp. 1056- 1067. doi: 10.1109/7.165367
25. Goshen-Meskin, D., and Bar-Itzhack, I. Y., "Observability Analysis of Piece-Wise Constant Systems-Part 2: Application to Inertial Navigation In-Flight Alignment, " IEEE Transactions on Aerospace and Electronic Systems, Vol.28, No. 4, Oct. 1992, pp. 1068-1075. doi: 10.1109/7.165368
26. Rhee, I., Abdel-Hafez, M. F., and Speyer, J. L., "Observability of an Integrated GPS/INS During Maneuvers, " IEEE Transactions on Aerospace and Electronic Systems, Vol.40, No. 2, Apr. 2004, pp. 526- 535. doi: 10.1109/TAES.2004.1310002
27. Gebre-Egziabher, D., Hayward, R. C., and Powell, J. D., "Design of Multi-Sensor Attitude Determination Systems, " IEEE Transactions on Aerospace and Electronic Systems, Vol.40 2, Apr. 2004, pp. 627- 649. doi: 10.1109/TAES.2004.1310010
28. Baram, Y., and Kailath, T., "Estimability and Regulability of Linear Systems, " IEEE Transactions on Automatic Control, Vol.33, No. 12, Dec. 1988, pp. 1116-1121. doi: 10.1109/9.14433
29. Bageshwar, V. L., Quantifying Performance Limitations of Kalman Filters in State Vector Estimation Problems, Ph.D. Thesis, Dept. of Aerospace Engineering and Mechanics, Univ. of Minnesota, Minneapolis, MN, 2008, App. B.