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Robust H2/H∞-state estimation for systems with error variance constraints: the continuous-time case
Copyright [1999] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.The paper is concerned with the state estimator design problem for perturbed linear continuous-time systems with H∞ norm and variance constraints. The perturbation is assumed to be time-invariant and norm-bounded and enters into both the state and measurement matrices. The problem we address is to design a linear state estimator such that, for all admissible measurable perturbations, the variance of the estimation error of each state is not more than the individual prespecified value, and the transfer function from disturbances to error state outputs satisfies the prespecified H∞ norm upper bound constraint, simultaneously. Existence conditions of the desired estimators are derived in terms of Riccati-type matrix inequalities, and the analytical expression of these estimators is also presented. A numerical example is provided to show the directness and effectiveness of the proposed design approac
Maximum L-likelihood estimation
In this paper, the maximum L-likelihood estimator (MLE), a new
parameter estimator based on nonextensive entropy [Kibernetika 3 (1967) 30--35]
is introduced. The properties of the MLE are studied via asymptotic analysis
and computer simulations. The behavior of the MLE is characterized by the
degree of distortion applied to the assumed model. When is properly
chosen for small and moderate sample sizes, the MLE can successfully trade
bias for precision, resulting in a substantial reduction of the mean squared
error. When the sample size is large and tends to 1, a necessary and
sufficient condition to ensure a proper asymptotic normality and efficiency of
MLE is established.Comment: Published in at http://dx.doi.org/10.1214/09-AOS687 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Pathwise Sensitivity Analysis in Transient Regimes
The instantaneous relative entropy (IRE) and the corresponding instanta-
neous Fisher information matrix (IFIM) for transient stochastic processes are
pre- sented in this paper. These novel tools for sensitivity analysis of
stochastic models serve as an extension of the well known relative entropy rate
(RER) and the corre- sponding Fisher information matrix (FIM) that apply to
stationary processes. Three cases are studied here, discrete-time Markov
chains, continuous-time Markov chains and stochastic differential equations. A
biological reaction network is presented as a demonstration numerical example
Information Geometry Approach to Parameter Estimation in Markov Chains
We consider the parameter estimation of Markov chain when the unknown
transition matrix belongs to an exponential family of transition matrices.
Then, we show that the sample mean of the generator of the exponential family
is an asymptotically efficient estimator. Further, we also define a curved
exponential family of transition matrices. Using a transition matrix version of
the Pythagorean theorem, we give an asymptotically efficient estimator for a
curved exponential family.Comment: Appendix D is adde
Time and spectral domain relative entropy: A new approach to multivariate spectral estimation
The concept of spectral relative entropy rate is introduced for jointly
stationary Gaussian processes. Using classical information-theoretic results,
we establish a remarkable connection between time and spectral domain relative
entropy rates. This naturally leads to a new spectral estimation technique
where a multivariate version of the Itakura-Saito distance is employed}. It may
be viewed as an extension of the approach, called THREE, introduced by Byrnes,
Georgiou and Lindquist in 2000 which, in turn, followed in the footsteps of the
Burg-Jaynes Maximum Entropy Method. Spectral estimation is here recast in the
form of a constrained spectrum approximation problem where the distance is
equal to the processes relative entropy rate. The corresponding solution
entails a complexity upper bound which improves on the one so far available in
the multichannel framework. Indeed, it is equal to the one featured by THREE in
the scalar case. The solution is computed via a globally convergent matricial
Newton-type algorithm. Simulations suggest the effectiveness of the new
technique in tackling multivariate spectral estimation tasks, especially in the
case of short data records.Comment: 32 pages, submitted for publicatio
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