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The least squares method is one of the most effective approaches for estimating an impulse response of discrete-time systems. However, when colored smooth input signals are utilized for parameter identification, the least squares estimates tend to fluctuate seriously and converge very slowly to their true values. In these circumstances, the corresp...
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Citations
In the control system design, the robust control theory has been studied actively. However, in order to apply the robust control theory to real plants, it is necessary to evaluate model uncertainty as well as a nominal model. In this paper, a new and practical identification method for the model uncertainty is proposed. The identification method is based on the ordinary least-squares identfication method in cooperation with the decimation. The key idea of the method is a frequency division by the decimation. The frequency band of the plant is divided into two parts,that is, one corresponds to the nominal model and the other corresponds to unmodeled dynamics. Effectiveness of the method is examined through actual data that is collected thorogh identification experiments of a ground-based test model for a large space structure (LSS).
It is well known that employment of nonwhite input in system identification often causes large estimation errors. While the mechanism of inducing these errors has been well understood for linear system identification, it has not been made clear yet for nonlinear systems.
This paper analyzes this mechanism for nonlinear system identification with Volterra functional series models. A vector space approach gives a clear physical interpretation of the error generation from a viewpoint of the excitation intensity of the input against the identified system. Based on this analysis, new algorithms of reducing estimation errors are proposed.
When the ordinary least-square method is applied in the estimation of the impulse response of the linear system using a nonwhite input, the result is affected greatly by the observation noise and the error in the numerical calculation, and the accuracy of the estimation is greatly deteriorated.
This paper presents a mathematical analysis based on a geometrical approach for the error generation mechanism and provides a clear physical description from the standpoint of the system identification. It is shown that the nonwhite input has the following problem.
The excitation turns out to be weak for the linear system in which the impulse response vector corresponds to the eigenvector for a small eigenvalue of the autocorrelation matrix. This weakness of the excitation is the major cause of the deterioration of the estimation accuracy in the ordinary least-square method.
Based on those results, a new physical interpretation is given to the eigenvalue truncation method and the regularization method, which are already proposed as improvements of the ordinary least-square method. The proposed error analysis can also be considered as the basic theory which can be applied not only to the estimation of the impulse response, but also to the parameter estimation of the transfer function model and the design of the optimal input for the identification.
In order to attain stabilized convergence, the authors propose a
generalized regularization scheme using multiple regularization
parameters and an a priori estimate, and they obtain analytically the
parameter values that minimize the mean square error (MSE) or the
estimated MSE using only accessible data signals. They show that method
can give simultaneously the optimal regularization parameters and the
optical truncation of smaller eigenvalues in the singular value (or
eigenvalue) decomposition (SVD or EVD). The proposed schemes for the
optimized regularization and SVD are exemplified in impulse response
identification using low-pass input and optimized extrapolation of the
bandlimited signal
The design of a discrete-time model reference robust adaptive
control system for a plant in the presence of bounded disturbances is
investigated. The system uses a robust adaptive algorithm with multiple
regularization parameters. This algorithm belongs to the class of leaky
integration methods; thus the designed regularization parameters
correspond to σ in the σ-modification approach. It is shown
how to determine these regularization parameters theoretically such that
minimization of the parameter error is attained in the presence of the
disturbances, and it is not necessary for the upper bound of the
disturbances to be known a priori. Furthermore, persistent spanning is
ensured, regardless of the size of the disturbance
The paper proposes an algorithm for active noise control (ANC) using the least squares lattice (LSL) algorithm. As a main algorithm for ANC, the LMS algorithm has been used for its simplicity. However, the LMS algorithm has problems of both convergence speed and estimation accuracy in the case of the broadband noise such as road noise which is one of the passenger compartment noises in a car running on rough roads. In order to solve these problems, the LSL algorithm for ANC is considered. By computer simulations, the LSL algorithm turns out to be more effective than the LMS algorithm in both convergence speed and estimation accuracy, especially for the colored input signal used in ANC of road noise.
