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
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
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
Human motion prediction is a critical issue in human-robot collaboration(HRC)tasks.In order to reduce the local error caused by the limitation of the capture range and sampling frequency of the depth sensor,a hybrid h...Human motion prediction is a critical issue in human-robot collaboration(HRC)tasks.In order to reduce the local error caused by the limitation of the capture range and sampling frequency of the depth sensor,a hybrid human motion prediction algorithm,optimized sliding window polynomial fitting and recursive least squares(OSWPF-RLS)was proposed.The OSWPF-RLS algorithm uses the human body joint data obtained under the HRC task as input,and uses recursive least squares(RLS)to predict the human movement trajectories within the time window.Then,the optimized sliding window polynomial fitting(OSWPF)is used to calculate the multi-step prediction value,and the increment of multi-step prediction value was appropriately constrained.Experimental results show that compared with the existing benchmark algorithms,the OSWPF-RLS algorithm improved the multi-step prediction accuracy of human motion and enhanced the ability to respond to different human movements.展开更多
Aimed at the problem of adaptive noise canceling(ANC),three implementary algorithms which are least mean square(LMS) algorithm,recursive least square(RLS) algorithm and fast affine projection(FAP) algorithm,have been ...Aimed at the problem of adaptive noise canceling(ANC),three implementary algorithms which are least mean square(LMS) algorithm,recursive least square(RLS) algorithm and fast affine projection(FAP) algorithm,have been researched.The simulations were made for the performance of these algorithms.The extraction of fetal electrocardiogram(FECG) is applied to compare the application effect of the above algorithms.The proposed FAP algorithm has obvious advantages in computational complexity,convergence speed and steadystate error.展开更多
A pair of multichannel recursive least squares (RLS) adaptive lattice algorithms based on the order recursive of lattice filters and the superior numerical properties of Givens algorithms is derived in this paper. The...A pair of multichannel recursive least squares (RLS) adaptive lattice algorithms based on the order recursive of lattice filters and the superior numerical properties of Givens algorithms is derived in this paper. The derivation of the first algorithm is based on QR decomposition of the input data matrix directly, and the Givens rotations approach is used to compute the QR decomposition. Using first a prerotation of the input data matrix and then a repetition of the single channel Givens lattice algorithm, the second algorithm can be obtained. Both algorithms have superior numerical properties, particularly the robustness to wordlength limitations. The parameter vector to be estimated can be extracted directly from internal variables in the present algorithms without a backsolve operation with an extra triangular array. The results of computer simulation of the parameter identification of a two-channel system are presented to confirm efficiently the derivation.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
In this paper, we propose a simple learning algorithm for non\|linear function approximation and system modeling using minimal radial basis function neural network with high generalization performance. A hybrid algori...In this paper, we propose a simple learning algorithm for non\|linear function approximation and system modeling using minimal radial basis function neural network with high generalization performance. A hybrid algorithm is constructed, which combines recursive n \|means clustering algorithm with a simple recursive regularized least squares algorithm (SRRLS). The n \|means clustering algorithm adjusts the centers of the network, while the SRRLS constructs a parsimonious network which makes the generalization performance of the network well. The SRRLS algorithm needs no matrix computing, so it has a lower computational cost and no ill\|conditional problem. Because of the recursive manner, this algorithm is suitable for on\|line applications. The effectiveness of this algorithm is demonstrated by two benchmark examples.展开更多
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.
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 National Natural Science Foundation of China(61701270)the Young Doctor Cooperation Foundation of Qilu University of Technology(Shandong Academy of Sciences)(2017BSHZ008)。
文摘Human motion prediction is a critical issue in human-robot collaboration(HRC)tasks.In order to reduce the local error caused by the limitation of the capture range and sampling frequency of the depth sensor,a hybrid human motion prediction algorithm,optimized sliding window polynomial fitting and recursive least squares(OSWPF-RLS)was proposed.The OSWPF-RLS algorithm uses the human body joint data obtained under the HRC task as input,and uses recursive least squares(RLS)to predict the human movement trajectories within the time window.Then,the optimized sliding window polynomial fitting(OSWPF)is used to calculate the multi-step prediction value,and the increment of multi-step prediction value was appropriately constrained.Experimental results show that compared with the existing benchmark algorithms,the OSWPF-RLS algorithm improved the multi-step prediction accuracy of human motion and enhanced the ability to respond to different human movements.
基金the National Key Technologies R&D Program (No. 2006BAI22B01)
文摘Aimed at the problem of adaptive noise canceling(ANC),three implementary algorithms which are least mean square(LMS) algorithm,recursive least square(RLS) algorithm and fast affine projection(FAP) algorithm,have been researched.The simulations were made for the performance of these algorithms.The extraction of fetal electrocardiogram(FECG) is applied to compare the application effect of the above algorithms.The proposed FAP algorithm has obvious advantages in computational complexity,convergence speed and steadystate error.
基金Foundation of the Academy of Electronic Science,China
文摘A pair of multichannel recursive least squares (RLS) adaptive lattice algorithms based on the order recursive of lattice filters and the superior numerical properties of Givens algorithms is derived in this paper. The derivation of the first algorithm is based on QR decomposition of the input data matrix directly, and the Givens rotations approach is used to compute the QR decomposition. Using first a prerotation of the input data matrix and then a repetition of the single channel Givens lattice algorithm, the second algorithm can be obtained. Both algorithms have superior numerical properties, particularly the robustness to wordlength limitations. The parameter vector to be estimated can be extracted directly from internal variables in the present algorithms without a backsolve operation with an extra triangular array. The results of computer simulation of the parameter identification of a two-channel system are presented to confirm efficiently the derivation.
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This work is supported by the International Pioneering Center of TEDATianjinP.R China
文摘In this paper, we propose a simple learning algorithm for non\|linear function approximation and system modeling using minimal radial basis function neural network with high generalization performance. A hybrid algorithm is constructed, which combines recursive n \|means clustering algorithm with a simple recursive regularized least squares algorithm (SRRLS). The n \|means clustering algorithm adjusts the centers of the network, while the SRRLS constructs a parsimonious network which makes the generalization performance of the network well. The SRRLS algorithm needs no matrix computing, so it has a lower computational cost and no ill\|conditional problem. Because of the recursive manner, this algorithm is suitable for on\|line applications. The effectiveness of this algorithm is demonstrated by two benchmark examples.
