Recursive Relations of the Cost Functions for the Least-Squares Algorithms for Multivariable Systems

Ma, Junxia; Ding, Feng

doi:10.1007/s00034-012-9448-4

Cited by 15 publications

(5 citation statements)

References 56 publications

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“…The simulation results verifies the proposed convergence theorem. The method used in the paper can be used to study the convergence of other identification algorithms for linear and nonlinear systems with colored noises [14,16,27,34].…”

Section: Discussionmentioning

confidence: 99%

Performance Analysis of the Auxiliary Model-Based Stochastic Gradient Parameter Estimation Algorithm for State-Space Systems with One-Step State Delay

Ding

2012

Circuits Syst Signal Process

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How to use the observation data to build the mathematical models of timedelay systems and how to estimate the parameters of the obtained models are important for studying the laws of motion of systems. This paper presents an auxiliary model-based stochastic gradient parameter estimation algorithm and studies its convergence for the input-output representation for state-space systems with one-step delays, by means of the auxiliary model identification idea. The simulation results indicate that the proposed algorithm can effectively estimate the parameters of the systems.

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Section: Discussionmentioning

confidence: 99%

Performance Analysis of the Auxiliary Model-Based Stochastic Gradient Parameter Estimation Algorithm for State-Space Systems with One-Step State Delay

Ding

2012

Circuits Syst Signal Process

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“…To solve the problems of identification of dynamic object in real time in finding the model parameters from all common methods should be used recursive least squares method [9,14]. To implement the method, at first it is necessary to determine the initial estimate of the vector of model parameters A [m] based on a sample of observations of length m, which can be found from the equation…”

Section: Modeling Of Acoustic Signals Of Electrical Equipment By the Autoregressive Moving-average Model (Arma)mentioning

confidence: 99%

Research of Acoustic Signals Digital Processing Methods Application Efficiency for the Electromechanical System Functional Diagnostics

Rudakova

Polyvoda

Kondratieva

et al. 2021

Lecture Notes in Computational Intelligence and Decision Making

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The article is devoted to researching of application efficiency of acoustic signals digital processing methods for the electromechanical systems (EMS) functional diagnostics in real time. The steps according to which it is necessary to carry out the analysis of the acoustic signals generated during operation of EMS for construction and adjustment of functional diagnostics systems are offered. The primary task is to study the statistical properties of acoustic signals. The next step is spectral analysis of acoustic signals. In the process of acoustic signal conversion after its hardware processing, the limits of the informative part of the signal are determined on the basis of spectral analysis based on Fourier transform of the signal. It is proposed to use logic-time processing based on the estimation of the normalized energy spectrum and spectral entropy to determine the frequency range of the informative part of the signal. The expediency of using the autoregressive model of the moving average as an acoustic signal model is substantiated. The problem of building mathematical models on the basis of which it is possible to adequately identify the intensity of work and the state of the equipment is solved. The procedure for identifying the parameters of the signal model by the recurrent least squares method is given, which allows to analyze the state of the equipment in real time. It is proposed to use multiplescale analysis to speed up the process of signal analysis and reduce the amount of calculations.

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“…[8,9]. As a result, there is active research effort directed towards the modelling and identification of multivariable systems [10][11][12][13][14][15]. For example, Ding et al proposed a multiinnovation least squares identification algorithm based on the auxiliary model, by replacing the unknown inner variables with their estimates computed by an auxiliary model [10]; Schon et al studied the maximum likelihood estimation of multivariable dynamic systems [11].…”

Section: Introductionmentioning

confidence: 98%

“…For example, Ding et al proposed a multiinnovation least squares identification algorithm based on the auxiliary model, by replacing the unknown inner variables with their estimates computed by an auxiliary model [10]; Schon et al studied the maximum likelihood estimation of multivariable dynamic systems [11]. Ma and Ding [12] studied the recursive computation of the cost functions for the least squares type algorithms for multivariable models and Han and Ding [16] derived the convergence of the stochastic gradient algorithm for multivariable systems by expanding an innovation vector to an innovation matrix.…”

Section: Introductionmentioning

confidence: 99%

Bias compensation based partially coupled recursive least squares identification algorithm with forgetting factors for MIMO systems: Application to PMSMs

Shi

Wang

2016

Journal of the Franklin Institute

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Recursive Relations of the Cost Functions for the Least-Squares Algorithms for Multivariable Systems

Cited by 15 publications

References 56 publications

Performance Analysis of the Auxiliary Model-Based Stochastic Gradient Parameter Estimation Algorithm for State-Space Systems with One-Step State Delay

Performance Analysis of the Auxiliary Model-Based Stochastic Gradient Parameter Estimation Algorithm for State-Space Systems with One-Step State Delay

Research of Acoustic Signals Digital Processing Methods Application Efficiency for the Electromechanical System Functional Diagnostics

Bias compensation based partially coupled recursive least squares identification algorithm with forgetting factors for MIMO systems: Application to PMSMs

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