Based on the least-square minimization a computationally efficient learning algorithm for the Principal Component Analysis(PCA) is derived. The dual learning rate parameters are adaptively introduced to make the propo...Based on the least-square minimization a computationally efficient learning algorithm for the Principal Component Analysis(PCA) is derived. The dual learning rate parameters are adaptively introduced to make the proposed algorithm providing the capability of the fast convergence and high accuracy for extracting all the principal components. It is shown that all the information needed for PCA can be completely represented by the unnormalized weight vector which is updated based only on the corresponding neuron input-output product. The convergence performance of the proposed algorithm is briefly analyzed.The relation between Oja’s rule and the least squares learning rule is also established. Finally, a simulation example is given to illustrate the effectiveness of this algorithm for PCA.展开更多
This paper proposes a recursive least squares algorithm for a nonlinear additive system with time delay.By the Weierstrass approximation theorem and the key term separation principle, the model can be simplified as an...This paper proposes a recursive least squares algorithm for a nonlinear additive system with time delay.By the Weierstrass approximation theorem and the key term separation principle, the model can be simplified as an identification model. Based on the identification model, a recursive least squares identification algorithm is used to estimate all the unknown parameters of the time-delayed additive system. An example is provided to show the effectiveness of the proposed algorithm.展开更多
Order-recursive least-squares(ORLS)algorithms are applied to the prob-lems of estimation and identification of FIR or ARMA system parameters where a fixedset of input signal samples is available and the desired order ...Order-recursive least-squares(ORLS)algorithms are applied to the prob-lems of estimation and identification of FIR or ARMA system parameters where a fixedset of input signal samples is available and the desired order of the underlying model isunknown.On the basis of several universal formulae for updating nonsymmetric projec-tion operators,this paper presents three kinds of LS algorithms,called nonsymmetric,symmetric and square root normalized fast ORLS algorithms,respectively.As to the au-thors’ knowledge,the first and the third have not been so far provided,and the second isone of those which have the lowest computational requirement.Several simplified versionsof the algorithms are also considered.展开更多
In this paper,a new recursive least squares(RLS)identification algorithm with variable-direction forgetting(VDF)is proposed for multi-output systems.The objective is to enhance parameter estimation performance under n...In this paper,a new recursive least squares(RLS)identification algorithm with variable-direction forgetting(VDF)is proposed for multi-output systems.The objective is to enhance parameter estimation performance under non-persistent excitation.The proposed algorithm performs oblique projection decomposition of the information matrix,such that forgetting is applied only to directions where new information is received.Theoretical proofs show that even without persistent excitation,the information matrix remains lower and upper bounded,and the estimation error variance converges to be within a finite bound.Moreover,detailed analysis is made to compare with a recently reported VDF algorithm that exploits eigenvalue decomposition(VDF-ED).It is revealed that under non-persistent excitation,part of the forgotten subspace in the VDF-ED algorithm could discount old information without receiving new data,which could produce a more ill-conditioned information matrix than our proposed algorithm.Numerical simulation results demonstrate the efficacy and advantage of our proposed algorithm over this recent VDF-ED algorithm.展开更多
The recursive least square is widely used in parameter identification. But if is easy to bring about the phenomena of parameters burst-off. A convergence analysis of a more stable identification algorithm-recursive da...The recursive least square is widely used in parameter identification. But if is easy to bring about the phenomena of parameters burst-off. A convergence analysis of a more stable identification algorithm-recursive damped least square is proposed. This is done by normalizing the measurement vector entering into the identification algorithm. rt is shown that the parametric distance converges to a zero mean random variable. It is also shown that under persistent excitation condition, the condition number of the adaptation gain matrix is bounded, and the variance of the parametric distance is bounded.展开更多
A multi-loop adaptive internal model control (IMC) strategy based on a dynamic partial least squares (PLS) frame-work is proposed to account for plant model errors caused by slow aging,drift in operational conditions,...A multi-loop adaptive internal model control (IMC) strategy based on a dynamic partial least squares (PLS) frame-work is proposed to account for plant model errors caused by slow aging,drift in operational conditions,or environmental changes.Since PLS decomposition structure enables multi-loop controller design within latent spaces,a multivariable adaptive control scheme can be converted easily into several independent univariable control loops in the PLS space.In each latent subspace,once the model error exceeds a specific threshold,online adaptation rules are implemented separately to correct the plant model mismatch via a recursive least squares (RLS) algorithm.Because the IMC extracts the inverse of the minimum part of the internal model as its structure,the IMC controller is self-tuned by explicitly updating the parameters,which are parts of the internal model.Both parameter convergence and system stability are briefly analyzed,and proved to be effective.Finally,the proposed control scheme is tested and evaluated using a widely-used benchmark of a multi-input multi-output (MIMO) system with pure delay.展开更多
For the unforced dynamical non-linear state–space model,a new Q1 and efficient square root extended kernel recursive least square estimation algorithm is developed in this article.The proposed algorithm lends itself ...For the unforced dynamical non-linear state–space model,a new Q1 and efficient square root extended kernel recursive least square estimation algorithm is developed in this article.The proposed algorithm lends itself towards the parallel implementation as in the FPGA systems.With the help of an ortho-normal triangularization method,which relies on numerically stable givens rotation,matrix inversion causes a computational burden,is reduced.Matrix computation possesses many excellent numerical properties such as singularity,symmetry,skew symmetry,and triangularity is achieved by using this algorithm.The proposed method is validated for the prediction of stationary and non-stationary Mackey–Glass Time Series,along with that a component in the x-direction of the Lorenz Times Series is also predicted to illustrate its usefulness.By the learning curves regarding mean square error(MSE)are witnessed for demonstration with prediction performance of the proposed algorithm from where it’s concluded that the proposed algorithm performs better than EKRLS.This new SREKRLS based design positively offers an innovative era towards non-linear systolic arrays,which is efficient in developing very-large-scale integration(VLSI)applications with non-linear input data.Multiple experiments are carried out to validate the reliability,effectiveness,and applicability of the proposed algorithm and with different noise levels compared to the Extended kernel recursive least-squares(EKRLS)algorithm.展开更多
A modified RAKE receiver based on novel Recursive Least Squares （RLS） adaptive algorithm is proposed. The receiver uses L-fingered correlators, which are composed of RLS adaptive filters, to enhance the performance ...A modified RAKE receiver based on novel Recursive Least Squares （RLS） adaptive algorithm is proposed. The receiver uses L-fingered correlators, which are composed of RLS adaptive filters, to enhance the performance of multipath receiving. It can also track the amplitude of the received signal to form a real-time amplitude estimation which is correlated with the power of excess delay bin. The simulation results based on the IEEE UltraWide Band （UWB） channel models （CMI to CM4） show that the novel RLS algorithm can alter the attenuation estimation with the finger＇s power delay profile, and RAKE receiver with few fingers can be employed to get high performance.展开更多
The Bit Error Rate （BER） performance of a Turbo Product Code （TPC） based Space-Time Block Coding （STBC） multiuser wireless system in the frequency-selective channels has been investigated. Both of the good error...The Bit Error Rate （BER） performance of a Turbo Product Code （TPC） based Space-Time Block Coding （STBC） multiuser wireless system in the frequency-selective channels has been investigated. Both of the good error correcting capability of TPC and the large diversity gain of STBC can be achieved simultaneously. A Least Square Error-Recursive Least Square （LSE-RLS） algorithm is applied to estimate the channel and cancel the interference. Simulations show that the proposed system can obtain about 2.7dB gain in Es/N0 at the BER of 10^-3.展开更多
While positive feedback exists in an active vibration control system, it may cause instability of the whole system. To solve this problem, a feedforward adaptive controller is proposed based on the Fihered-U recursive...While positive feedback exists in an active vibration control system, it may cause instability of the whole system. To solve this problem, a feedforward adaptive controller is proposed based on the Fihered-U recursive least square （FURLS） algorithm. Algorithm development process is presented in this paper. Real time active vibration control experimental tests were done. The experiment resuits show that the active control algorithm proposed in this paper has good control performance for both narrow band disturbances and broad band disturbances.展开更多
Modified constant modulus and recursive least squares （MCMA-RLS） algorithm is proposed to cancel interference caused by the variable frequency offset （FO） in the orthogonal frequency division multiplexing （OFDM）...Modified constant modulus and recursive least squares （MCMA-RLS） algorithm is proposed to cancel interference caused by the variable frequency offset （FO） in the orthogonal frequency division multiplexing （OFDM） system. The MCMA-RLS algorithm is composed of two stages including MCMA scheme and RLS scheme. MCMA is selected to pre-cancel the variable frequency offset firstly, and then the residual interference has been canceled by the RLS scheme. BR error rate is simulated to demonstrate that the proposed method is robust for canceling the variable frequency offset.展开更多
基金Supported by the National Natural Science Foundation of Chinathe Science foundation of Guangxi Educational Administration
文摘Based on the least-square minimization a computationally efficient learning algorithm for the Principal Component Analysis(PCA) is derived. The dual learning rate parameters are adaptively introduced to make the proposed algorithm providing the capability of the fast convergence and high accuracy for extracting all the principal components. It is shown that all the information needed for PCA can be completely represented by the unnormalized weight vector which is updated based only on the corresponding neuron input-output product. The convergence performance of the proposed algorithm is briefly analyzed.The relation between Oja’s rule and the least squares learning rule is also established. Finally, a simulation example is given to illustrate the effectiveness of this algorithm for PCA.
基金the National Natural Science Foundation of China(No.61403165)the Natural Science Foundation of Jiangsu Province(Nos.BK20131109 and BK20141115)+1 种基金the Project of Philosophy and Social Science Research in Colleges and Universities in Jiangsu Province(No.2014SJD381)the Post Doctoral Foundation of Jiangsu Province(No.1501015A)
文摘This paper proposes a recursive least squares algorithm for a nonlinear additive system with time delay.By the Weierstrass approximation theorem and the key term separation principle, the model can be simplified as an identification model. Based on the identification model, a recursive least squares identification algorithm is used to estimate all the unknown parameters of the time-delayed additive system. An example is provided to show the effectiveness of the proposed algorithm.
文摘Order-recursive least-squares(ORLS)algorithms are applied to the prob-lems of estimation and identification of FIR or ARMA system parameters where a fixedset of input signal samples is available and the desired order of the underlying model isunknown.On the basis of several universal formulae for updating nonsymmetric projec-tion operators,this paper presents three kinds of LS algorithms,called nonsymmetric,symmetric and square root normalized fast ORLS algorithms,respectively.As to the au-thors’ knowledge,the first and the third have not been so far provided,and the second isone of those which have the lowest computational requirement.Several simplified versionsof the algorithms are also considered.
基金supported by the National Natural Science Foundation of China(61803163,61991414,61873301)。
文摘In this paper,a new recursive least squares(RLS)identification algorithm with variable-direction forgetting(VDF)is proposed for multi-output systems.The objective is to enhance parameter estimation performance under non-persistent excitation.The proposed algorithm performs oblique projection decomposition of the information matrix,such that forgetting is applied only to directions where new information is received.Theoretical proofs show that even without persistent excitation,the information matrix remains lower and upper bounded,and the estimation error variance converges to be within a finite bound.Moreover,detailed analysis is made to compare with a recently reported VDF algorithm that exploits eigenvalue decomposition(VDF-ED).It is revealed that under non-persistent excitation,part of the forgotten subspace in the VDF-ED algorithm could discount old information without receiving new data,which could produce a more ill-conditioned information matrix than our proposed algorithm.Numerical simulation results demonstrate the efficacy and advantage of our proposed algorithm over this recent VDF-ED algorithm.
文摘The recursive least square is widely used in parameter identification. But if is easy to bring about the phenomena of parameters burst-off. A convergence analysis of a more stable identification algorithm-recursive damped least square is proposed. This is done by normalizing the measurement vector entering into the identification algorithm. rt is shown that the parametric distance converges to a zero mean random variable. It is also shown that under persistent excitation condition, the condition number of the adaptation gain matrix is bounded, and the variance of the parametric distance is bounded.
基金Project supported by the National Natural Science Foundation of China (No.60574047)the National High-Tech R & D Program (863)of China (No.2007AA04Z168)the Research Fund for the Doctoral Program of Higher Education of China (No.20050335018)
文摘A multi-loop adaptive internal model control (IMC) strategy based on a dynamic partial least squares (PLS) frame-work is proposed to account for plant model errors caused by slow aging,drift in operational conditions,or environmental changes.Since PLS decomposition structure enables multi-loop controller design within latent spaces,a multivariable adaptive control scheme can be converted easily into several independent univariable control loops in the PLS space.In each latent subspace,once the model error exceeds a specific threshold,online adaptation rules are implemented separately to correct the plant model mismatch via a recursive least squares (RLS) algorithm.Because the IMC extracts the inverse of the minimum part of the internal model as its structure,the IMC controller is self-tuned by explicitly updating the parameters,which are parts of the internal model.Both parameter convergence and system stability are briefly analyzed,and proved to be effective.Finally,the proposed control scheme is tested and evaluated using a widely-used benchmark of a multi-input multi-output (MIMO) system with pure delay.
基金funded by Prince Sultan University,Riyadh,Saudi Arabia。
文摘For the unforced dynamical non-linear state–space model,a new Q1 and efficient square root extended kernel recursive least square estimation algorithm is developed in this article.The proposed algorithm lends itself towards the parallel implementation as in the FPGA systems.With the help of an ortho-normal triangularization method,which relies on numerically stable givens rotation,matrix inversion causes a computational burden,is reduced.Matrix computation possesses many excellent numerical properties such as singularity,symmetry,skew symmetry,and triangularity is achieved by using this algorithm.The proposed method is validated for the prediction of stationary and non-stationary Mackey–Glass Time Series,along with that a component in the x-direction of the Lorenz Times Series is also predicted to illustrate its usefulness.By the learning curves regarding mean square error(MSE)are witnessed for demonstration with prediction performance of the proposed algorithm from where it’s concluded that the proposed algorithm performs better than EKRLS.This new SREKRLS based design positively offers an innovative era towards non-linear systolic arrays,which is efficient in developing very-large-scale integration(VLSI)applications with non-linear input data.Multiple experiments are carried out to validate the reliability,effectiveness,and applicability of the proposed algorithm and with different noise levels compared to the Extended kernel recursive least-squares(EKRLS)algorithm.
基金Supported by the Chinese 863 National High Technology Program (No.2002AA783043)the National Natural Science Foundation of China (No.60390540).
文摘A modified RAKE receiver based on novel Recursive Least Squares （RLS） adaptive algorithm is proposed. The receiver uses L-fingered correlators, which are composed of RLS adaptive filters, to enhance the performance of multipath receiving. It can also track the amplitude of the received signal to form a real-time amplitude estimation which is correlated with the power of excess delay bin. The simulation results based on the IEEE UltraWide Band （UWB） channel models （CMI to CM4） show that the novel RLS algorithm can alter the attenuation estimation with the finger＇s power delay profile, and RAKE receiver with few fingers can be employed to get high performance.
文摘The Bit Error Rate （BER） performance of a Turbo Product Code （TPC） based Space-Time Block Coding （STBC） multiuser wireless system in the frequency-selective channels has been investigated. Both of the good error correcting capability of TPC and the large diversity gain of STBC can be achieved simultaneously. A Least Square Error-Recursive Least Square （LSE-RLS） algorithm is applied to estimate the channel and cancel the interference. Simulations show that the proposed system can obtain about 2.7dB gain in Es/N0 at the BER of 10^-3.
基金Supported by the National Natural Science Foundation of China(No.90716027,51175319)
文摘While positive feedback exists in an active vibration control system, it may cause instability of the whole system. To solve this problem, a feedforward adaptive controller is proposed based on the Fihered-U recursive least square （FURLS） algorithm. Algorithm development process is presented in this paper. Real time active vibration control experimental tests were done. The experiment resuits show that the active control algorithm proposed in this paper has good control performance for both narrow band disturbances and broad band disturbances.
基金Supported by the National Natural Science Foundation of China （No. 60532030）.
文摘Modified constant modulus and recursive least squares （MCMA-RLS） algorithm is proposed to cancel interference caused by the variable frequency offset （FO） in the orthogonal frequency division multiplexing （OFDM） system. The MCMA-RLS algorithm is composed of two stages including MCMA scheme and RLS scheme. MCMA is selected to pre-cancel the variable frequency offset firstly, and then the residual interference has been canceled by the RLS scheme. BR error rate is simulated to demonstrate that the proposed method is robust for canceling the variable frequency offset.
