Robust minimum variance linear state estimators for multiple sensors with different failure rates. (English) Zbl 1123.93085

Summary: Linear minimum variance unbiased state estimation is considered for systems with uncertain parameters in their state space models and sensor failures. The existing results are generalized to the case where each sensor may fail at any sample time independently of the others. For robust performance, stochastic parameter perturbations are included in the system matrix. Also, stochastic perturbations are allowed in the estimator gain to guarantee resilient operation. An illustrative example is included to demonstrate performance improvement over the Kalman filter which does not include sensor failures in its measurement model.


93E11 Filtering in stochastic control theory
93E03 Stochastic systems in control theory (general)
93A30 Mathematical modelling of systems (MSC2010)
93C73 Perturbations in control/observation systems
Full Text: DOI


[1] DeKoning, W.L., Optimal estimation of linear discrete-time systems with stochastic parameters, Automatica, 20, 113-115, (1984) · Zbl 0542.93062
[2] Horn, R.A.; Johnson, C.R., Topics in matrix analysis, (1991), Cambridge University Press New York · Zbl 0729.15001
[3] Matveev, A.S.; Savkin, A.V., The problem of state estimation via asynchronous communication channels with irregular transmission times, IEEE transactions on automatic control, 48, 4, 670-676, (2003) · Zbl 1364.93779
[4] Nahi, N.E., Optimal recursive estimation with uncertain observation, IEEE transaction on information theory, 15, 457-462, (1969) · Zbl 0174.51102
[5] NaNacara, W.; Yaz, E., Recursive estimator for linear and nonlinear systems with uncertain observations, Signal processing, 62, 215-228, (1997) · Zbl 0908.93061
[6] Petersen, I.R.; Savkin, A.V., Robust Kalman filtering for signals and systems with large uncertainties, (1999), Birkhauser Boston, MA
[7] Rajasekaran, P.K.; Satyanarayana, N.; Srinath, M.D., Optimum linear estimation of stochastic signals in the presence of multiplicative noise, IEEE transactions on aerospace electronic systems, 7, 462, (1971)
[8] Savkin, A.V.; Petersen, I.R., Robust filtering with missing data and a deterministic description of noise and uncertainty, International journal of systems science, 28, 4, 373-378, (1997) · Zbl 0887.93069
[9] Savkin, A.V.; Petersen, I.R.; Moheimani, S.O.R., Model validation and state estimation for uncertain continuous-time systems with missing discrete-continuous data, Computers and electrical engineering, 25, 1, 29-43, (1999)
[10] Sinopoli, B.; Schenato, L.; Franceschetti, M.; Poolla, K.; Jordan, M.I.; Sastry, S.S., Kalman filtering with intermittent observations, IEEE transactions on automatic control, 49, 9, 1453-1464, (2004) · Zbl 1365.93512
[11] Smith, S.; Seiler, P., Estimation with lossy measurements: jump estimators for jump systems, IEEE transactions on automatic control, 48, 12, 2163-2171, (2003) · Zbl 1364.93785
[12] Theodor, Y.; Shaked, U., Robust discrete-time minimum variance filtering, IEEE transactions on signal processing, 44, 2, 181-189, (1996)
[13] Tugnait, J.K., Stability of optimum linear estimators of stochastic signals in white multiplicative noise, IEEE transactions on automatic control, 26, 757-761, (1981) · Zbl 0481.93062
[14] Wang, Z.; Ho, D.W.C.; Liu, X., Variance-constrained filtering for uncertain stochastic systems with missing measurements, IEEE transactions on automatic control, 48, 7, 1254-1258, (2003) · Zbl 1364.93814
[15] Wang, Z.; Yang, F.; Ho, D.W.C.; Liu, X., Robust finite-horizon filtering for stochastic systems with missing measurements, IEEE signal processing letters, 12, 6, 437-440, (2005)
[16] Wang, Z.; Zhu, J.; Unbehauen, H., Robust filter design with time-varying parameter uncertainty and error variance constraints, International journal of control, 72, 1, 30-38, (1999) · Zbl 0953.93069
[17] Wu, P., Yaz, E. E., & Olejniczak, K. J. (1997). Harmonic estimation with random sensor delay. In Proceedings of IEEE CDC, San Diego, CA, pp. 1424-1525.
[18] Yaz, E., Observer design for stochastic-parameter systems, International journal of control, 46, 1213-1217, (1987) · Zbl 0639.93063
[19] Yaz, E., Implications of a result of observer design for stochastic parameter systems, International journal of control, 47, 1355-1360, (1988) · Zbl 0652.93061
[20] Yaz, E., Full and reduced-order observer design for discrete stochastic bilinear systems, IEEE transactions on automatic control, 37, 503-505, (1992)
[21] Yaz, E.E.; Jeong, C.S.; Yaz, Y.I., A LMI approach to discrete-time observer design with stochastic resilience, Journal of computational and applied mathematics, 188, 246-255, (2006) · Zbl 1108.93026
[22] Yaz, E.E.; Jeong, C.S.; Yaz, Y.I.; Bahakeem, A., Resilient design of discrete-time observers with general criteria using lmis, Mathematical and computer modeling, 42, 9-10, 931-938, (2005) · Zbl 1121.93011
[23] Yaz, E., Wu, P., Olejniczak, K., & Yaz, Y. I. (1998). Reduced-order harmonic estimation with probable sensor failures. In Proceedings of IEEE CDC, Tampa, Florida, pp. 1297-1302.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.