Abstract
In this chapter, the problem of event-based state estimation is analyzed using an approach called “set-valued filtering”. With this approach, the design of an event-based estimator becomes a much simpler task. The main benefit of using the set-valued filtering approach is that the properties of the event-based estimates designed for deterministic event-triggering conditions can be analyzed without relying on any assumptions or approximations of the probability distributions. The properties of the set-valued event-based estimates also lead to a new way of designing event-triggering conditions to simultaneously fulfill requirements on the estimation performance and the sensor-to-estimator communication rate.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Alamo T, Bravo J, Camacho E (2005) Guaranteed state estimation by zonotopes. Automatica 41(6):1035–1043
Bittanti S, Colaneri P, De Nicolao G (1988) The difference periodic Riccati equation for the periodic prediction problem. IEEE Trans Autom Control 33(8):706–712
Chisci L, Garulli A, Zappa G (1996) Recursive state bounding by parallelotopes. Automatica 32(7):1049–1055
De Nicolao G (1992) On the time-varying Riccati difference equation of optimal filtering. SIAM J Control Optim 30(6):1251–1269
Kurzhanski A, Vályi I (1996) Ellipsoidal calculus for estimation and control. Birkhauser
Lutwak E (1988) Intersection bodies and dual mixed volumes. Advances in Mathematicas 71:232–261
Morrell D, Stirling W (1991) Set-valued filtering and smoothing. IEEE Trans Syst Man Cybern 21(1):184–193
Mutambara A (1998) Decentralized estimation and control for multisensor systems. CRC Press Inc., Boca Raton
Noack B, Klumpp V, Hanebeck U (2009) State estimation with sets of densities considering stochastic and systematic errors. In: Proceedings of the 12th international conference on information fusion (Fusion 2009). Seattle, Washington, USA, pp 1751–1758
Noack B, Pfaff F, Hanebeck U (2012) Combined stochastic and set-membership information filtering in multisensor systems. In: Proceedings of the 15th international conference on information fusion (Fusion 2012), Singapore, pp 1218–1224
Odgaard P, Stoustrup J, Kinnaert M (2013) Fault-tolerant control of wind turbines: a benchmark model. IEEE Trans Control Syst Technol 21(4):1168–1182
Schneider R (1996) Convex bodies: the Brunn-Minkowski theory. Cambridge University Press, Cambridge
Shi D, Chen T, Shi L (2015) On set-valued Kalman filtering and its application to event-based state estimation. IEEE Trans Autom Control 60(5):1275–1290
Shi L, Epstein M, Murray R (2010) Kalman filtering over a packet-dropping network: a probabilistic perspective. IEEE Trans Autom Control 55(3):594–604
Stirling W, Morrell D (1991) Convex Bayes decision theory. IEEE Trans Syst Man Cybern 21(1):173–183
Tempo R, Calafiore G, Dabbene F (2005) Randomized algorithms for analysis and control of uncertain systems. Springer, London
Wu J, Jia Q, Johansson K, Shi L (2013) Event-based sensor data scheduling: trade-off between communication rate and estimation quality. IEEE Trans Autom Control 58(4):1041–1046
Zhang X, Zhang Q, Zhao S, Ferrari R, Polycarpou M, Parisini T (2011) Fault detection and isolation of the wind turbine benchmark: an estimation-based approach. In: Proceedings of the 18th IFAC world congress, Milano, Italy
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Shi, D., Shi, L., Chen, T. (2016). A Set-Valued Filtering Approach. In: Event-Based State Estimation. Studies in Systems, Decision and Control, vol 41. Springer, Cham. https://doi.org/10.1007/978-3-319-26606-0_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-26606-0_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-26604-6
Online ISBN: 978-3-319-26606-0
eBook Packages: EngineeringEngineering (R0)