Robust identification of non-stationary objects with nongaussian interference

Rudenko, Oleg; Bezsonov, Oleksandr; Lebediev, Oleh; Serdiuk, Nataliia

doi:10.15587/1729-4061.2019.181256

Cited by 4 publications

(9 citation statements)

References 33 publications

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“…In conclusion, the study reported in this paper is a continuation and the advancement of earlier research, the results of which are described in [18,33].…”

Section: Discussion Of Results Of Studying the Convergence Of A Gradisupporting

confidence: 65%

“…Works [14][15][16][17][18] developed a simpler approach to building combined functionals, consisting of both quadric and modular, and without the specified flaw.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

“…Such a criterion was for the first time proposed in [14]. In [14][15][16][17][18], this criterion was used to solve the problem of identification in the presence of pulse interference. The stability of the normalized algorithm was studied in [15]; the applied identification problem was solved in [16].…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

“…The stability of the normalized algorithm was studied in [15]; the applied identification problem was solved in [16]. An adaptive combination of normalized filters was proposed in [17]; the convergence of the identification algorithm was studied in [18], where the task of selecting the optimal parameters' values of the algorithm was addresses.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

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Studying the properties of a robust algorithm for identifying linear objects, which minimizes a combined functional

Rudenko

Bezsonov

Lebediev

et al. 2020

EEJET

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This paper addresses the task of identifying the parameters of a linear object in the presence of non-Gaussian interference. The identification algorithm is a gradient procedure for minimizing the combined functional. The combined functional, in turn, consists of the fourth-degree functional and a modular functional, whose weights are set using a mixing parameter. Such a combination of functionals makes it possible to obtain estimates that demonstrate robust properties. We have determined the conditions for the convergence of the applied procedure in the mean and root-mean-square measurements in the presence of non-Gaussian interference. In addition, expressions have been obtained to determine the optimal values of the algorithm's parameters, which ensure its maximum convergence rate. Based on the estimates obtained, the asymptomatic and non-asymptotic values of errors in estimating the parameters and identification errors. Because the resulting expressions contain a series of unknown parameters (the values of signal and interference variances), their practical application requires that the estimates of these parameters should be used. We have investigated the issue of stability of the steady identification process and determined the conditions for this stability. It has been shown that determining these conditions necessitates solving the third-degree equations, whose coefficients depend on the specificity of the problem to be solved. The resulting ratios are rather cumbersome but their simplification allows for a qualitative analysis of stability issues. It should be noted that all the estimates reported in this work depend on the choice of a mixing parameter, the task of determining which remains to be explored. The estimates obtained in this paper allow the researcher to pre-evaluate the capabilities of the identification algorithm and the effectiveness of its use in solving practical problems

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“…In conclusion, the study reported in this paper is a continuation and the advancement of earlier research, the results of which are described in [18,33].…”

Section: Discussion Of Results Of Studying the Convergence Of A Gradisupporting

confidence: 65%

“…Works [14][15][16][17][18] developed a simpler approach to building combined functionals, consisting of both quadric and modular, and without the specified flaw.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

Section: Literature Review and Problem Statementmentioning

confidence: 99%

Section: Literature Review and Problem Statementmentioning

confidence: 99%

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Studying the properties of a robust algorithm for identifying linear objects, which minimizes a combined functional

Rudenko

Bezsonov

Lebediev

et al. 2020

EEJET

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“…Вперше такий критерій запропоновано в [11]. У роботах [12][13][14][15] даний критерій застосовувався для розв'язання задачі ідентифікації за наявністю імпульсних завад. В [16] був запропонований критерій найменшого четвертого ступеня, властивості якого вивчалися в роботах [17][18][19][20][21].…”

Section: вступunclassified

Робастна Ідентифікація Об'єктів На Основі Мінімізації Комбінованого Функціоналу

Rudenko¹,

Bezsonov²,

Сердюк³

et al. 2020

soi

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Розглянуто задачу ідентифікації параметрів лінійного об'єкта за наявністю негаусівських завад на основі мінімізації комбінованого функціоналу, який поєднує властивості МНК та МНМ та забезпечує робастність одержуваних оцінок. Досліджено статистичні властивості градієнтного алгоритму ідентифікації, в результаті чого визначено умови його збіжності в середньому і середньоквадратичному. Для дослідження властивостей в алгоритму використано функції Ляпунова. Отримано аналітичні оцінки неасимпотичних та асимптотичних значень помилки оцінювання параметрів і точності ідентифікації. Показано, що ці значення помилки оцінювання і точності ідентифікації залежать від вибору параметра змішування. Отримані оцінки є досить загальними і залежать від статистичних характеристик корисних сигналів і завад. Тому для їх практичного застосування слід скористатися оцінками цих параметрів. Результати експериментального дослідження властивостей алгоритму при ідентифікації об’єкту, вихід якого вимірюється з незалежним шумом з розподілом Релея, некорельованим з сигналами, свідчать про ефективність підходу, що розвивається. Отримані в роботі оцінки дозволяють досліднику при вирішенні практичних завдань попередньо оцінити можливості досліджуваного алгоритму і ефективність його застосування.

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Developing a multi-step recurrent algorithm to maximize the criteria of correntropy

Rudenko

Bezsonov

Borysenko

et al. 2021

EEJET

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This paper considers the task of constructing a linear model of the object studied using a robust criterion. The functionality applied, in this case, is correntropy. That makes it possible to obtain estimates that have robust properties. The evaluation algorithm is a multi-step procedure that employs a limited number of information measurements, that is, it has limited memory. The feature of the algorithm is that the matrices and observation vectors involved in estimate construction are formed in the following way: they include information about the newly arrived measurements and exclude information about the oldest ones. Depending on the way these matrices and vectors are built (new information is added first, and then outdated is excluded, or the outdated is first excluded, and then a new one is added), two estimate forms are possible. The second Lyapunov method is used to study the convergence of the algorithm. The conditions of convergence for a multi-step algorithm have been defined. The analysis of the established regime has revealed that the algorithm ensures that unbiased estimates are obtained. It should be noted that all the estimates reported in this work depend on the choice of the width of the nucleus, the information weighting factor, and the algorithm memory, the task of determining which remains open. Therefore, these parameters' estimates should be applied for the practical use of such multi-step algorithms. The estimates obtained in this paper allow the researcher to pre-evaluate the possibilities of identification using a multi-step algorithm, as well as the effectiveness of its application when solving practical tasks

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Robust identification of non-stationary objects with nongaussian interference

Cited by 4 publications

References 33 publications

Studying the properties of a robust algorithm for identifying linear objects, which minimizes a combined functional

Studying the properties of a robust algorithm for identifying linear objects, which minimizes a combined functional

Робастна Ідентифікація Об'єктів На Основі Мінімізації Комбінованого Функціоналу

Developing a multi-step recurrent algorithm to maximize the criteria of correntropy

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