Variance or spectral density in sampled data filtering?

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.

[1]  G. Goodwin,et al.  High-speed digital signal processing and control , 1992, Proc. IEEE.

[2]  Karl Johan Åström,et al.  Computer-Controlled Systems: Theory and Design , 1984 .

[3]  Graziella Pacelli,et al.  Maximum likelihood estimation of the Heston stochastic volatility model using asset and option prices: an application of nonlinear filtering theory , 2008, Optim. Lett..

[4]  P. Suchomski,et al.  Numerical conditioning of delta-domain Lyapunov and Riccati equations , 2001 .

[5]  Graham C. Goodwin,et al.  Control System Design , 2000 .

[6]  A. Jazwinski.  Stochastic Processes and Filtering Theory , 1970 .

[7]  B. Anderson,et al.  Optimal Filtering , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[8]  Eric Walter,et al.  Global optimization of expensive-to-evaluate functions: an empirical comparison of two sampling criteria , 2009, J. Glob. Optim..

[9]  P. Kloeden,et al.  Numerical Solution of Stochastic Differential Equations , 1992 .

[10]  Panos M. Pardalos,et al.  Encyclopedia of Optimization , 2006 .

[11]  G. Goodwin,et al.  Connection between continuous and discrete Riccati equations with applications to kalman filtering , 1988 .

[12]  M Pardalos Panos,et al.  Optimization and Control of Bilinear Systems , 2008 .

[13]  Graham C. Goodwin,et al.  Digital control and estimation : a unified approach , 1990 .

[14]  McCarthyEd,et al.  A Unified Approach , 2005 .

[15]  Graham C. Goodwin,et al.  Sampling in Digital Sig-nal Processing and Control , 1996 .

[16]  K. Åström.  Introduction to Stochastic Control Theory , 1970 .

[17]  T. Söderström.  Discrete-Time Stochastic Systems: Estimation and Control , 1995 .

[18]  J. W. Brown,et al.  Complex Variables and Applications , 1985 .

[19]  Graham R. Wood,et al.  Approximation of the distribution of convergence times for stochastic global optimisation , 2002, J. Glob. Optim..