Estimation of non-integral and integral quadratic functions in linear stochastic differential systems
This paper focuses on estimation of an non-integral quadratic function (NIQF) and integral quadratic function (IQF) of a random signal in dynamic system described by a linear stochastic differential equation. The quadratic form of an unobservable signal indicates useful information of a signal for control. The optimal (in mean square sense) and suboptimal estimates of NIQF and IQF represent a function of the Kalman estimate and its error covariance. The proposed estimation algorithms have a closed-form estimation procedure. The obtained estimates are studied in detail, including derivation of the exact formulas and differential equations for mean square errors. The results we demonstrate on practical example of a power of signal , and comparison analysis between optimal and suboptimal estimators is presented.
R. G. Brown and P. Y. C. Hwang, Introduction to Random Signals and Applied Kalman Filtering with Matlab Exercises, 4th Edition, John Wiley & Sons, New York, 2012.
B. Gibbs, Advanced Kalman Filtering, Least Squares and Modelling. A Practical Handbook, John Wiley & Sons, 2011.
M. S. Grewal and A. P. Andrews, Kalman Filtering: Theory and Practice Using MATLAB, 3rd Edition, John Wiley & Sons, New Jersey, 2008.
S. S. Haykin, Kalman Filtering and Neural Networks, John Wiley & Sons, New York, 2004.
V. S. Pugachev and I. N. Sinitsyn, Stochastic Differential Systems. Analysis and Filtering, Wiley & Sons, New York, 1987.
F. L. Lewis, Optimal Estimation with an Introduction to Stochastic Control Theory, Wiley & Sons, New York, 1986.
A. Gelb, Applied Optimal Estimation, MIT Press, Cambridge, MA, 1974.
A. H. Jazwinski, Stochastic Processes and Filtering Theory, Academic Press, New York, 1970.
R. Kan, From moments of sum to moments of product, Journal of Multivariate Analysis, 99 (2008), 542–554.
B. Holmquist, Expectations of products of quadratic forms in normal variables, Stochastic Analysis and Applications, 14 (1996), 149–164.
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