Abstract
This book is about state estimation of control systems, nonlinear control systems in particular. Control systems are dynamic systems and exist in engineering, physical sciences as well as in social sciences. The earliest, somehow commonly recognised control system could be traced back to James Watt’s flyball governor in 1769. The study on control systems, analysis and system design, has been continuously developed ever since. Until the mid of last century the control systems under investigation had been single-input-single-output (SISO), time-invariant systems and were mainly deterministic and of lumped parameters. The approaches used were of frequency domain nature, so-called classical approaches. In classical control approaches, control system’s dynamic behaviour is represented by transfer functions. Rapid developments and needs in aerospace engineering in the 1950s and 1960s greatly drove the development of control system theory and design methodology, particularly in the state-space approach that is powerful towards multi-input-multi-output (MIMO) systems. State-space models are used to describe the dynamic changes of the control system. In the state-space approach, the system states determine how the system is dynamically evolving. Therefore, by knowing the system states one can know the system’s properties and by changing the trajectory of system states successfully with specifically designed controllers one can achieve the objectives for a certain control system.
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Notes
- 1.
In general, the term “filter” is frequently used for state estimators in the estimation literature. This is due to Wiener, who studied the continuous-time estimation problem and noted that his algorithm can be implemented using a linear circuit. In circuit theory, the filters are used to separate the signals over different frequency ranges. Wiener’s solution extended the classical theory of filter design to problems of obtaining the filtered signals from noisy measurements (Kailath et al. 2000).
References
Anderson BDO, Moore JB (1979) Optimal filtering, vol 21. Prentice Hall, Englewood Cliffs, pp 22–95
Arasaratnam I, Haykin S (2009) Cubature kalman filters. IEEE Trans Autom Control 54(6):1254–1269
Arulampalam MS, Maskell S, Gordon N, Clapp T (2002) A tutorial on particle filters for online nonlinear/non-gaussian bayesian tracking. IEEE Trans Signal Process 50(2):174–188
Banavar RN, Speyer JL (1991) A linear-quadratic game approach to estimation and smoothing. In: Proceedings of the 1991 American control conference. IEEE, pp 2818–2822
Basar T (1991) Optimum performance levels for minimax filters, predictors and smoothers. Syst Control Lett 16(5):309–317
Bierman G, Belzer MR, Vandergraft JS, Porter DW (1990) Maximum likelihood estimation using square root information filters. IEEE Trans Autom Control 35(12):1293–1298
Campbell ME, Whitacre WW (2007) Cooperative tracking using vision measurements on seascan UAVs. IEEE Trans Control Syst Technol 15(4):613–626
Carlson NA (1990) Federated square root filter for decentralized parallel processors. IEEE Trans Aerosp Electron Syst 26(3):517–525
Doucet A, Godsill S, Andrieu C (2000) On sequential monte carlo sampling methods for bayesian filtering. Stat Comput 10(3):197–208
Grewal M, Andrews A (2001) Kalman filtering: theory and practice using matlab. Wiley, New Jersey
Grimble MJ, El Sayed A (1990) Solution of the \(h_\infty \) optimal linear filtering problem for discrete-time systems. IEEE Trans Acoust Speech Signal Process 38(7):1092–1104
Gu D-W, Petkov PH, Konstantinov MM (2014) Robust control design with MATLAB®. Springer Science & Business Media, Berlin
Hassibi B, Kailath T, Sayed AH (2000) Array algorithms for H/sup/spl infin//estimation. IEEE Trans Autom Control 45(4):702–706
Ito K, Xiong K (2000) Gaussian filters for nonlinear filtering problems. IEEE Trans Autom Control 45(5):910–927
Julier SJ, Uhlmann JK (2004) Unscented filtering and nonlinear estimation. Proc IEEE 92(3):401–422
Julier S, Uhlmann J, Durrant-Whyte HF (2000) A new method for the nonlinear transformation of means and covariances in filters and estimators. IEEE Trans Autom Control 45(3):477–482
Kailath T (1968) An innovations approach to least-squares estimation-part i: linear filtering in additive white noise. IEEE Trans Autom Control 13(6):646–655
Kailath T, Sayed AH, Hassibi B (2000) Linear estimation, vol 1. Prentice Hall, Upper Saddle River
Kalman RE (1960) A new approach to linear filtering and prediction problems. J Basic Eng 82(1):35–45
Kaminski P, Bryson A, Schmidt S (1971) Discrete square root filtering: a survey of current techniques. IEEE Trans Autom Control 16(6):727–736
Kolmogorov AN, Doyle WL, Selin I (1962) Interpolation and extrapolation of stationary random sequences. Bulletin of academic sciences, Mathematics series, USSR, vol 5, 1941. Translation by W. Doyle and J. Selin, RM-3090-PR, Rand Corporation, Santa Monica, California
Lee D-J (2008) Nonlinear estimation and multiple sensor fusion using unscented information filtering. IEEE Signal Process Lett 15:861–864
McGee LA, Schmidt SF (1985) Discovery of the kalman filter as a practical tool for aerospace and industry
Morf M, Kailath T (1975) Square-root algorithms for least-squares estimation. IEEE Trans Autom Control 20(4):487–497
Mracek CP, Clontier J, D’Souza CA (1996) A new technique for nonlinear estimation. In: Proceedings of the 1996 IEEE international conference on control applications. IEEE, pp 338–343
Mutambara AG (1998) Decentralized estimation and control for multisensor systems. CRC press, Boca Raton
Napgal K, Khargonekar P (1991) Filtering and smoothing in an h-infinity setting. IEEE Trans Autom Control 36:152–166
Nemra A, Aouf N (2010) Robust INS/GPS sensor fusion for uav localization using SDRE nonlinear filtering. IEEE Sens J 10(4):789–798
Park P, Kailath T (1995) New square-root algorithms for kalman filtering. IEEE Trans Autom Control 40(5):895–899
Psiaki ML (1999) Square-root information filtering and fixed-interval smoothing with singularities. Automatica 35(7):1323–1331
Sarmavuori J, Sarkka S (2012) Fourier-hermite kalman filter. IEEE Trans Autom Control 57(6):1511–1515
Shaked U (1990) \(h_\infty \)-minimum error state estimation of linear stationary processes. IEEE Trans Autom Control 35(5):554–558
Simon D (2006) Optimal state estimation: Kalman, H infinity, and nonlinear approaches. Wiley, New Jersey
Sorenson HW (1970) Least-squares estimation: from gauss to kalman. IEEE Spectr 7(7):63–68
Vercauteren T, Wang X (2005) Decentralized sigma-point information filters for target tracking in collaborative sensor networks. IEEE Trans Signal Process 53(8):2997–3009
Verhaegen M, Van Dooren P (1986) Numerical aspects of different kalman filter implementations. IEEE Trans Autom Control 31(10):907–917
Wiener N (1949) Extrapolation, interpolation, and smoothing of stationary time series, vol 7. MIT press, Cambridge
Xiong Y, Saif M (2001) Sliding mode observer for nonlinear uncertain systems. IEEE Trans Autom Control 46(12):2012–2017
Yaesh I, Shaked U (1992) Game theory approach to optimal linear state estimation and its relation to the minimum \(h_\infty \) norm estimation. IEEE Trans Autom Control 37(6):828–831
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Chandra, K.P.B., Gu, DW. (2019). Control Systems and State Estimation. In: Nonlinear Filtering. Springer, Cham. https://doi.org/10.1007/978-3-030-01797-2_1
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