Derivation of linear estimation algorithms from measurements affected by multiplicative and additive noises

García-Ligero, María J.; Hermoso-Carazo, Aurora; Linares-Pérez, Josefa; Nakamori, Seiichi

doi:10.1016/j.cam.2010.01.043

Cited by 7 publications

(7 citation statements)

References 20 publications

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“…Using expression (7) based on statistical sample of 500 realizations of sequence (14), (15), for N=4 we obtained histograms of frequencies of n random coefficients W i 1,7 (Fig. 3-16).…”

Section: Discussion Of Results Of the Numerical Experimentsmentioning

confidence: 99%

“…3-16). The procedure of obtaining realizations of vector random sequence (14), (15) on the basis of canonical decomposition (6) comes down to the generation of values of the random variables (1) (1) i1 i2 W , W , = i 1,7 with the appropriate assigned laws of distribution ( Fig. 3-16) and to the conversion of the obtained values by expression (6).…”

Section: Discussion Of Results Of the Numerical Experimentsmentioning

confidence: 99%

“…Doctor of Technical Sciences, Professor, Rector* of stationary normal sequences is also rather well examined on the basis of two operators of generation of values, proposed in [14], as well as the developed [15] approaches to determining their parameters. In this case, the problem of simulation of Markovian sequences is solved most easily [16], which comes down to implementation of the method of conditional distributions for the simplest case -only with the two-dimensional distribution density.…”

Section: Simulation Of Vector Random Sequences Based On Polynomial Dementioning

confidence: 99%

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Simulation of vector random sequences based on polynomial degree canonical decomposition

Shebanin

Atamanyuk

Kondratenko

2016

EEJET

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“…Using expression (7) based on statistical sample of 500 realizations of sequence (14), (15), for N=4 we obtained histograms of frequencies of n random coefficients W i 1,7 (Fig. 3-16).…”

Section: Discussion Of Results Of the Numerical Experimentsmentioning

confidence: 99%

Section: Discussion Of Results Of the Numerical Experimentsmentioning

confidence: 99%

Section: Simulation Of Vector Random Sequences Based On Polynomial Dementioning

confidence: 99%

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Simulation of vector random sequences based on polynomial degree canonical decomposition

Shebanin

Atamanyuk

Kondratenko

2016

EEJET

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“…The state estimation problem for nonlinear systems with multiplicative noises has also been widely studied during the past few years. For example, a recursive finite-horizon filter for a class of nonlinear time-varying systems subject to multiplicative noises, missing measurements and quantisation effects was designed in [15], and recursive filtering and fixed-point smoothing algorithms for systems with unknown state-space model and subject to multiplicative noises were derived in [16]. However, all of the aforementioned literatures require the constraint that the additive measurement noise affecting the system must be white.…”

Section: Introductionmentioning

confidence: 99%

Optimal Estimation for Discrete-Time Linear Systems in the Presence of Multiplicative and Time-Correlated Additive Measurement Noises

Liu

2015

IEEE Trans. Signal Process.

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In this paper, the state estimation problem for discrete-time linear systems influenced by multiplicative and time-correlated additive measurement noises is considered where the multiplicative noises are zero-mean white noise sequences, and the time-correlated additive noise is described by a linear system model with white noise. An optimal linear estimator for the system under consideration is proposed, which does not require computing the inverse of state transition matrix. The proposed estimator has a recursive structure, and has time-independent computation and storage load. Computer simulations are carried out to demonstrate the performance of the proposed estimator. The simulation results show the superiority of the proposed estimator.

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“…16 and references therein) or signal-dependent Poisson noise [typical for charge-coupled device (CCD) sensors]. [17][18][19][20][21][22][23][24][25][26][27][28] A threshold that is a function of noise standard deviation can be used with an edge detector. 13 In Refs.…”

Section: Introductionmentioning

confidence: 99%

Image informative maps for component-wise estimating parameters of signal-dependent noise

Uss

Vozel²,

Lukin

et al. 2013

J. Electron. Imaging

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We deal with the problem of blind parameter estimation of signal-dependent noise from mono-component image data. Multispectral or color images can be processed in a componentwise manner. The main results obtained rest on the assumption that the image texture and noise parameters estimation problems are interdependent. A two-dimensional fractal Brownian motion (fBm) model is used for locally describing image texture. A polynomial model is assumed for the purpose of describing the signal-dependent noise variance dependence on image intensity. Using the maximum likelihood approach, estimates of both fBm-model and noise parameters are obtained. It is demonstrated that Fisher information (FI) on noise parameters contained in an image is distributed nonuniformly over intensity coordinates (an image intensity range). It is also shown how to find the most informative intensities and the corresponding image areas for a given noisy image. The proposed estimator benefits from these detected areas to improve the estimation accuracy of signal-dependent noise parameters. Finally, the potential estimation accuracy (Cramér-Rao Lower Bound, or CRLB) of noise parameters is derived, providing confidence intervals of these estimates for a given image. In the experiment, the proposed and existing state-of-the-art noise variance estimators are compared for a large image database using CRLB-based statistical efficiency criteria.

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Derivation of linear estimation algorithms from measurements affected by multiplicative and additive noises

Cited by 7 publications

References 20 publications

Simulation of vector random sequences based on polynomial degree canonical decomposition

Simulation of vector random sequences based on polynomial degree canonical decomposition

Optimal Estimation for Discrete-Time Linear Systems in the Presence of Multiplicative and Time-Correlated Additive Measurement Noises

Image informative maps for component-wise estimating parameters of signal-dependent noise

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