Minimax estimation by probabilistic criterion

Pankov, A. R.; Semenikhin, K. V.

doi:10.1134/s0005117907030058

Cited by 11 publications

(4 citation statements)

References 12 publications

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“…Method (8) is sufficiently effective at zero mean independent disturbances, which is why the behavior of the estimates generated by algorithms (8) and (9) is good at zero mean random disturbances despite the high level of noise in the observations (see Fig. 1).…”

Section: Optimization Of the Algorithm Parameter Selectionmentioning

confidence: 90%

“…Here, Figures 1-4 show the comparative behavior of pre diction errors based on three algorithms in typical cases for four different disturbances (noise): a randomized algorithm (7) an LMS algorithm [1] (a simplified Kalman filter [4]) (8) and the Kalman filter It is known that Kalman filter (9) gives optimal estimates in the case of Gaussian independent noise in observations. Method (8) is sufficiently effective at zero mean independent disturbances, which is why the behavior of the estimates generated by algorithms (8) and (9) is good at zero mean random disturbances despite the high level of noise in the observations (see Fig.…”

Section: Optimization Of the Algorithm Parameter Selectionmentioning

confidence: 99%

“…Here, uncer tainties are considered as boundedness in a certain sense, but in other respects, they may be arbitrary. In formulations with a priori knowledge of the noise level, it is usually sufficient to derive predictions in the form of sets, the sizes of which are stabilized in time [3][4][5][6][7][8][9][10]. In this case, no consideration is given to the possibilities of deriving valid point estimates.…”

Section: Introductionmentioning

confidence: 99%

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Potential of randomization in kalman-type prediction algorithms at arbitrary external noise in observations

Amelin

Granichin

2011

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The problem of predicting the values of a random process is considered. The uncertainties gener ating the process studied are assumed to be of a statistical nature, and observations are carried out with unknown, but bounded, disturbances. A randomized algorithm, which filters out arbitrary external noise in observations, is proposed. The operability of the new algorithm at irregular noises in observations is illustrated by simulation as compared to traditional approaches.

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Section: Optimization Of the Algorithm Parameter Selectionmentioning

confidence: 90%

Section: Optimization Of the Algorithm Parameter Selectionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Potential of randomization in kalman-type prediction algorithms at arbitrary external noise in observations

Amelin

Granichin

2011

Gyroscopy Navig.

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“…Among the immense variety of the minimax formulations of the problems of estimation and filtration (see, for example, [2,3]) we give a brush treatment to those where covariations of the random factors are unknown. The works [4][5][6][7] were devoted to determination of the upper boundary of the root-mean-square error in the problems of estimation and filtration and to minimization of this upper boundary for systems with uncertain parameters in the covariance matrices of measurement noise.…”

Section: Introductionmentioning

confidence: 99%

Optimal estimation and filtration under unknown covariances of random factors

Коган

2014

Autom Remote Control

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The general schemes of linear estimation and filtration were considered on assumption of the unknown covariance matrix of random factors such as unknown parameters, measurement errors, and initial and external perturbations. A new criterion was introduced for the quality of estimate or filter. It is the level of damping random perturbations which is defined by the maximal value over all covariance matrices of the root-mean-square error normalized by the sum of variances of all random factors. The level of damping random perturbations was shown to be equal to the square of the spectral norm of the matrix relating the error of estimation and the random factors, and the optimal estimate minimizing this criterion was established. In the problem of filtration, it was shown how the filter parameters that are optimal in the level of damping random perturbations are expressed in terms of the linear matrix inequalities.

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Distributionally Robust Optimization by Probability Criterion for Estimating a Bounded Signal

Semenikhin

Arkhipov

2023

Lecture Notes in Computer Science

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Minimax estimation by probabilistic criterion

Cited by 11 publications

References 12 publications

Potential of randomization in kalman-type prediction algorithms at arbitrary external noise in observations

Potential of randomization in kalman-type prediction algorithms at arbitrary external noise in observations

Optimal estimation and filtration under unknown covariances of random factors

Distributionally Robust Optimization by Probability Criterion for Estimating a Bounded Signal

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