Recursive Least Squares and Multi-innovation Stochastic Gradient Parameter Estimation Methods for Signal Modeling
TL;DR: This paper studies the parameter estimation problem for the sine combination signals and periodic signals and presents the multi-innovation stochastic gradient parameter estimation method, derived by means of the trigonometric function expansion.
Abstract: The sine signals are widely used in signal processing, communication technology, system performance analysis and system identification. Many periodic signals can be transformed into the sum of different harmonic sine signals by using the Fourier expansion. This paper studies the parameter estimation problem for the sine combination signals and periodic signals. In order to perform the online parameter estimation, the stochastic gradient algorithm is derived according to the gradient optimization principle. On this basis, the multi-innovation stochastic gradient parameter estimation method is presented by expanding the scalar innovation into the innovation vector for the aim of improving the estimation accuracy. Moreover, in order to enhance the stabilization of the parameter estimation method, the recursive least squares algorithm is derived by means of the trigonometric function expansion. Finally, some simulation examples are provided to show and compare the performance of the proposed approaches.
Citations
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TL;DR: A filtering based extended stochastic gradient algorithm and a filtering based multi-innovation ESG algorithm for improving the parameter estimation accuracy for a multivariable system with moving average noise.
Abstract: For a multivariable system with moving average noise (i.e., a multivariable controlled autoregressive moving average system), this paper proposes a filtering based extended stochastic gradient (ESG) algorithm and a filtering based multi-innovation ESG algorithm for improving the parameter estimation accuracy. The key is using the filtering technique and the multi-innovation identification theory. The proposed algorithms can identify the parameters of the system model and the noise model. The filtering based multi-innovation ESG algorithm can give more accurate parameter estimates. The numerical simulation results demonstrate that the proposed algorithms work well.
234 citations
TL;DR: This paper proposes a state filtering method for the single-input–single-output bilinear systems by minimizing the covariance matrix of the state estimation errors by extending the extended Kalman filter algorithm to multiple- input–multiple-output Bilinear Systems.
Abstract: This paper considers the state estimation problem of bilinear systems in the presence of disturbances. The standard Kalman filter is recognized as the best state estimator for linear systems, but it is not applicable for bilinear systems. It is well known that the extended Kalman filter (EKF) is proposed based on the Taylor expansion to linearize the nonlinear model. In this paper, we show that the EKF method is not suitable for bilinear systems because the linearization method for bilinear systems cannot describe the behavior of the considered system. Therefore, this paper proposes a state filtering method for the single-input–single-output bilinear systems by minimizing the covariance matrix of the state estimation errors. Moreover, the state estimation algorithm is extended to multiple-input–multiple-output bilinear systems. The performance analysis indicates that the state estimates can track the true states. Finally, the numerical examples illustrate the specific performance of the proposed method.
195 citations
Additional excerpts
...Obviously, if there exists the departure 𝛿Lk from the filtering gain vector to the optimal gain vector Lk, the estimation error covariance matrix obtained from (15) will deviate from the minimal Pk+1 and reaches Pk+1 + 𝛿Pk+1, where 𝛿Pk+1 is the nonnegative definite matrix....
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...Substituting (15) into (16) gives δPk+1 = (A − Lkc − δLkc)Pk ( AT − cLk + B uk − cδLk ) + BukPk ( AT − cLk + B uk ) − BukPkcδLk + Rw + LkRvL T k + LkRvδL T k + δLkRvL T k + δLkRvδL T k − Pk+1 = −δLk ( cPkA − cPkcLk + cPkB uk − RvLk ) − ( cPkA − cPkcLk + cPkB uk − RvLk )T δLk + δLk(cPkc T + Rv)δLk = W k + Wk + δLk(cPkc T + Rv)δLk , (17) where W k ∶= −δLk(cPkA − cPkcLk + cPkB uk − RvLk )....
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...From (15), we find that Lk + δLk and Pk+1 + δPk+1 satisfy Pk+1 + δPk+1 = [A − (Lk + δLk)c]Pk[A − c(Lk + δLk) + Buk] + BukPk[A − c(Lk + δLk) + Buk] + Rw + (Lk + δLk)Rv(Lk + δLk), (16)...
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TL;DR: In this paper, a hierarchical multi-innovation stochastic gradient estimation method is derived through parameter decomposition, and the forgetting factor and the convergence factor are introduced to improve the performance of the algorithm.
Abstract: This paper studies the problem of parameter estimation for frequency response signals For a linear system, the frequency response is a sine signal with the same frequency as the input sine signal When a multi-frequency sine signal is applied to a system, the system response also is a multi-frequency sine signal The signal modeling for multi-frequency sine signals is very difficult due to the highly nonlinear relations between the characteristic parameters and the model output In order to obtain the parameter estimates of the multi-frequency sine signal, the signal modeling methods based on statistical identification are proposed by means of the dynamical window discrete measured data By constructing a criterion function with respect to the model parameters to be estimated, a hierarchical multi-innovation stochastic gradient estimation method is derived through parameter decomposition Moreover, the forgetting factor and the convergence factor are introduced to improve the performance of the algorithm The simulation results show the effectiveness of the proposed methods
190 citations
TL;DR: A two-stage least squares based iterative algorithm and a filtering based least squares iterative algorithms are proposed for estimating the parameters of bilinear systems with colored noises by using the hierarchical identification principle and the data filtering technique.
176 citations
TL;DR: In this article, the authors studied the parameter estimation to the system response from the discrete measurement data, by constructing the dynamical rolling cost functions and using the nonlinear optimization, t
Abstract: This article studies the parameter estimation to the system response from the discrete measurement data. By constructing the dynamical rolling cost functions and using the nonlinear optimization, t...
160 citations
Cites background from "Recursive Least Squares and Multi-i..."
...If k = Le, terminate the recursive process and obtain the characteristic parameters from equation (24); otherwise, increase k by 1 and go to Step (2)....
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...If k = Le, terminate the recursive process and obtain the characteristic parameters from equation (24); otherwise, increase k by 1 and go to Step (2)....
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...If k = Le, terminate the recursive process; otherwise, k :1⁄4 k + 1 and go to Step (2)....
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...Increase k by 1 and go to Step (2)....
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...If k = Le, terminate the recursive process; otherwise, k :¼ k + 1 and go to Step (2)....
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References
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TL;DR: A damping parameter estimation algorithm for dynamical systems based on the sine frequency response is proposed and a damping factor is introduced in the proposed iterative algorithm in order to overcome the singular or ill-conditioned matrix during the iterative process.
224 citations
TL;DR: In this article, a new Newton iterative identification method is presented for estimating the parameters of a second-order dynamic system utilizing the obtained data from the step response, in order to obtain the desired dynamic performance, a controller design method based on the root locus is presented to meet the requirement of the dynamic performance of the overshoot.
Abstract: In this paper, a new Newton iterative identification method is presented for estimating the parameters of a second-order dynamic system utilizing the obtained data from the step response. In order to obtain the desired dynamic performance, a controller design method based on the root locus is presented to meet the requirement of the dynamic performance of the overshoot. The simulation results indicate that the proposed Newton iterative identification method is effective and the system response can meet the requirement of system dynamic performances.
222 citations
TL;DR: Gradient based and least-squares based iterative identification algorithms are developed for output error (OE) and output error moving average (OEMA) systems that can produce highly accurate parameter estimation.
205 citations
TL;DR: For a MIMO system whose outputs are contaminated by an ARMA noise process, an auxiliary model based recursive least squares parameter estimation algorithm is presented through filtering input-output data, which has higher estimation accuracy than the existing multivariable identification algorithm.
205 citations
TL;DR: Simulation results show that the obtained models can capture the dynamics of the systems, i.e., the estimated model's outputs are close to the outputs of the actual systems.
153 citations