Abstract
Most physical systems operate in continuous time. However, to interact with such systems one needs to take samples. This raises the question of the relationship between the sampled response and the response of the underlying continuous-time system. In this paper we review several aspects of the sampling process. In particular, we examine the role played by variance and spectral density in describing discrete random processes. We argue that spectral density has several advantages over variance. We illustrate the ideas by reference to the problem of state estimation using the discrete-time Kalman filter.
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References
Anderson B., Moore J.: Optimal Filtering. Prentice Hall, Prentice (1979)
Åström K.: Introduction to Stochastic Control Theory. Academic Press, London (1970)
Åström K.J., Wittenmark B.: Computer Controlled Systems—Theory and design. Prentice-Hall, Prentice (1997)
Christodoulos, F., Pardalos, P.M. (eds): Encyclopedia of Optimization. Springer, Berlin (2009)
Churchill R.V., Brown J.W.: Complex variables and applications. McGraw-Hill, New York (1990)
Feuer A., Goodwin G.: Sampling in Digital Signal Processing and Control. Birkhäuser, Boston (1996)
Goodwin G., Middleton R., Poor H.: High-speed digital signal processing and control. Proc. IEEE 80(2), 240–259 (1992)
Goodwin G., Graebe S., Salgado M.: Control System Design. Prentice Hall, Prentice (2001)
Jazwinski A.: Stochastic Processes and Filtering Theory. Academic Press, London (1970)
Kailath T.: Lecture on Wiener and Kalman Filtering. Springer, Berlin (1981)
Kloeden P., Platen E.: Numerical Solution of Stochastic Differential Equations. Springer, Berlin (1992)
Mariani F., Pacelli G., Zirilli F.: Maximum likelihood estimation of the Heston stochastic volatility model using asset and option prices: an application of nonlinear filtering theory. Optim. Lett. 2(2), 177–222 (2008)
Middleton R., Goodwin G.: Digital Control and Estimation. A Unified Approach. Prentice Hall, Prentice (1990)
Pardalos P.M., Yatsenko V.: Optimization and Control of Bilinear Systems. Springer, Berlin (2009)
Salgado M., Middleton R., Goodwin G.: Connection between continuous and discrete Riccati equations with applications to Kalman filtering. Control Theory Appl. IEE Proc. D 135(1), 28–34 (1988)
Söderström T.: Discrete-Time Stochastic Systems—Estimation and Control. Springer, Berlin (2002)
Suchomski P.: Numerical conditioning of delta-domain Lyapunov and Riccati equations. Control Theory Appl. IEE Proc. 148(6), 497–501 (2001)
Villemonteix J., Vazquez E., Sidorkiewicz M., Walter E.: Global optimization of expensive-to-evaluate functions: an empirical comparison of two sampling criteria. J. Glob. Optim. 43(2–3), 373–389 (2009)
Wood G., Alexander D., Bulger D.: Approximation of the distribution of convergence times for stochastic global optimisation. J. Glob. Optim. 22(1–4), 271–284 (2002)
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Goodwin, G.C., Yuz, J.I., Salgado, M.E. et al. Variance or spectral density in sampled data filtering?. J Glob Optim 52, 335–351 (2012). https://doi.org/10.1007/s10898-011-9675-4
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DOI: https://doi.org/10.1007/s10898-011-9675-4