Delay structure of wideband noises with application to filtering problems

Bashirov, Agamirza E.; Mazhar, Zeka; Etikan, Hüseyin; Ertürk, Sinem

doi:10.1002/oca.1029

Cited by 6 publications

(3 citation statements)

References 23 publications

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“…Thus, the formula in (1) presents a wide band noise as a distributed delay of a white noise. This issue is studied in Bashirov et al [29,30]. For a moment, consider a simplest case when ϕ is a one-dimensional wide band noise being stationary since the instant ε and having the autocovariance function Λ : [0, ε] → R. Then, by (2), in order to be represented as…”

Section: Wide Band Noisesmentioning

confidence: 99%

Linear Filtering for Wide Band Noise Driven Observation Systems

Bashirov

2016

Circuits Syst Signal Process

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Filtering of wide band noise driven systems accounts the following problem. Given an autocovariance function, there are infinitely many wide band noise processes, which have this autocovariance function. Each of them produces its own best estimate. The problem is a selection of the best one of these best estimates. A similar problem arises in control theory as a selection of optimal one of the optimal controls. In this paper we investigate this problem for a wide class of wide band noises. It is proved that in the case of independent wide band and white noises corrupting, respectively, the signal and observations, the best estimates and the optimal controls in the linear filtering and LQG problems are independent of the respective wide band noises. We present a complete set of formulae for the best estimate and, respectively, for the optimal control in terms of the system parameters and autocovariance function of the wide band noise disturbing the signal system.

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Section: Wide Band Noisesmentioning

confidence: 99%

Linear Filtering for Wide Band Noise Driven Observation Systems

Bashirov

2016

Circuits Syst Signal Process

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“…Bashirov in [], discovered that under general conditions, a wide band noise can be modeled as distributed delay of a white noise. Bashirov et al in [] developed different problems on the basis of this discovery; in spite of this it is not part of our work since it moves us to the stochastic systems where noise is a significant component in control systems. This is the reason that we mention the delays in noises to emphasize the importance of them in processes.…”

Section: Introductionmentioning

confidence: 99%

Impulsive semilinear heat equation with delay in control and in state

Camacho

Leiva

2019

Asian Journal of Control

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In this paper, we prove the interior approximate controllability of the impulsive semilinear heat equation with delay in control and in state by proving first that the linear heat equation with delay in control is approximately controllable.After that, we add impulses and a nonlinear perturbation with delay in state, and using Rothe's fixed point theorem, we prove that the interior approximate controllability of the impulsive semilinear system. Finally, we present some open problems and a possible general framework to study the controllability of impulsive semilinear diffusion process in Hilbert spaces with delay in control and in state.

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“…In [15][16][17][18][19][20][21][22][23] wide band noise driven systems are investigated by a method of approximation. A different method by integral representation was suggested in [24][25][26] which leads to modelling wide band noises as a distributed delay of white noises [27,28].…”

Section: Introductionmentioning

confidence: 99%

Invariant Kalman Filter for Correlated Wide Band Noises

Bashirov

Abuassba

2018

Asian Journal of Control

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Kalman filtering is a powerful estimation method. One of its weaknesses is related to the white or coloured nature of the disturbing noises in the Kalman filtering model. At the same time, real noises are rarely white or coloured. They are mostly wide band. In this regard, white or coloured noise Kalman filtering makes concessions on adequacy. This pushes system scientists to develop mathematical methods of estimation for systems corrupted by wide band noises. In applications, wide band noises are detected by their autocovariance and cross‐covariance functions, which do not allow to model them uniquely. Therefore, it becomes important to develop estimation methods which are independent of a class of wide band noises, but dependent on the unique autocovariance and cross‐covariance functions. Such results are called invariant results. In this paper, we prove a complete set of invariant equations for Kalman type filter for a linear signal‐observation system corrupted by correlated wide band noises. This filter has a ready form to be used in applications, just respective numerical methods must be developed.

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Delay structure of wideband noises with application to filtering problems

Cited by 6 publications

References 23 publications

Linear Filtering for Wide Band Noise Driven Observation Systems

Linear Filtering for Wide Band Noise Driven Observation Systems

Impulsive semilinear heat equation with delay in control and in state

Invariant Kalman Filter for Correlated Wide Band Noises

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