A sliding-window variable-regularization recursive-least-squares algorithm is derived, and its convergence properties, computational complexity, and numerical stability are analyzed. The algorithm operates on a finite data window and allows for time-varying regularization in the weighting and the difference between estimates. Numerical examples are provided to compare the performance of this technique with the least mean squares and affine projection algorithms. Copyright (c) 2015 John Wiley & Sons, Ltd.
The structure of tissue paper has great influence on the quality of the resulting paper produced. One method of measuring the crepe wavelength on-line is sought in order to improve process control as well as to promote greater precision and uniform quality of the end product. In this study, a probe was used to read the surface of the paper whilst the paper travelled at a low speed. Light from a light emitting diode was emitted at a specific angle and collected at the corresponding reflecting angle, from the paper surface.
Focusing the lenses at 45º angle produced results matching closest to the expected wavelength, and such measurements were made on a numerous commercial papers to validate the method. The collected signal contains a lot of information from the surface of the paper and from reflected signals inside the paper. The signal was processed using a mathematical approach to extract the most common wavelengths for each paper. The measured wavelength was found to closely match measurements made with commercial off-line equipment. This new method has a good initial potential to work on-line, however further investigation regarding the effects of high speeds upon the sampling still has to be carried out.
The problem of estimating continuous-time autoregressive process parameters from discrete-time data is considered. The basic approach used here is based on replacing the derivatives in the model by discrete-time differences, forming a linear regression, and using the least squares method. Such a procedure is simple to apply, computationally flexible and efficient, and may have good numerical properties. It is known, however, that all standard approximations of the highest order derivative, such as repeated use of the delta operator, gives a biased least squares estimate, even as the sampling interval tends to zero. Some of our previous approaches to overcome this problem are reviewed. Then. two new methods, which avoid the shift in our previous results, are presented. One of them, which is termed bias compensation, is computationally very efficient. Finally, the relationship of the above least squares approaches with an instrumental variable method is investigated. Comparative simulation results are also presented
The complex modulus of a material with linearly viscoelastic behaviour is identified on the basis of strains which are known, from measurements and sometimes from a free end boundary condition, at three or more sections of an axially impacted bar specimen. The aim is to improve existing identification methods based on known strains at three uniformly distributed sections by increasing the number of sections considered and by distributing them non-uniformly. The increased number of sections results in an overdetermined system of equations from which an approximate solution for the complex modulus is determined using the method of least squares. Through the non-uniform distribution of sections, critical conditions with accompanying large errors at certain frequencies are largely eliminated. Experimental tests were carried out at room temperature with two materials, viz., polypropylene and polymethyl methacrylate, five strain gauge configurations and two kinds of impact excitation. Substantial improvement in the quality of the results for complex modulus was obtained.
n this paper, we present a sliding-window variable-regularization recursive least squares algorithm. In contrast to standard recursive least squares, the algorithm presented in this paper operates on a finite window of data, where old data are discarded as new data become available. This property can be beneficial for estimating time-varying parameters. Furthermore, standard recursive least squares uses time-invariant regularization. More specifically, the inverse of the initial covariance matrix in standard recursive least squares can be viewed as a regularization term, which weights the difference between the next estimate and the initial estimate. This regularization is fixed for all steps of the recursion. The algorithm derived in this paper allows for time-varying regularization. In particular, the present paper allows for time varying regularization in the weighting as well as what is being weighted. Specifically, the regularization term can weight the difference between the next estimate and a time-varying vector of parameters rather than the initial estimate.
A continuous-time description of networked control systems is considered and the parameters are estimated. The discrete-time description is time-varying due to the random time-delays in the wireless links and therefore difficult to work with. Off-line as well as on-line situations are considered for parameter estimation. In the off-line situation, a linear regression is formed and then the parameters are estimated by the least squares method. In the on-line situation, the estimates of the parameters are recursively updated for each time instance. A comparative study of two different parameter estimation approaches is presented. In the first approach, the parameters are estimated by a simple linear regression. In the second approach, transformation of the differentiation operator to another casual and stable linear operator is made in linear regression to estimate the parameters. A numerical study of these approaches is also presented for comparison.
System identification for networked control is considered. Due to the time-delays in the network, it can be difficult to work with a discrete-time model and a continuous-time model is therefore chosen. A covariance function based method that relies on the second order statistical properties of the output signal, where it is assumed that the input signal samples are from a discrete-time white noise sequence, is proposed for estimating the parameters. The method is easy to use since the actual time instants when new input signal levels are applied at the actuator do not have to be known. An analysis of the networked system and the effects of the time-delays is made, and the results of the analysis motivate and support the chosen approach. Numerical studies indicate that the method is robust to randomly distributed time-delays, packet drop-outs, and additive measurement noise.
Nuclear quadrupole resonance (NQR) offers an unequivocal method of detecting hidden narcotics and explosives. Unfortunately, the practical use of NQR is restricted by the low signal-to-noise ratio (SNR) and means to improve the SNR are vital to enable a rapid, reliable and convenient system. In this correspondence, we develop two multichannel detectors to counter the typically present radio frequency interference. Numerical simulations indicate that the proposed methods offers a significantly improved robustness to uncertainties in the parameters detailing the examined sample.
Nuclear quadrupole resonance (NQR) offers an unequivocal method of detecting and identifying land mines. Unfortunately, the practical use of NQR is restricted by the low signal-to-noise ratio (SNR), and the means to improve the SNR are vital to enable a rapid, reliable, and convenient system. In this paper, an approximate maximum-likelihood detector (AML) is developed, exploiting the temperature dependency of the NQR frequencies as a way to enhance the SNR. Numerical evaluation using both simulated and real NQR data indicate a significant gain in probability of accurate detection as compared with the current state-of-the-art approach.
Nuclear quadrupole resonance (NQR) offers an unequivocal method of detecting and identifying both hidden explosives, such as land mines, and a variety of narcotics. Unfortunately, the practical use of NQR is restricted by a low signal-to-noise ratio (SNR), and means to improve the SNR are vital to enable a rapid, reliable, and convenient system. In this paper, we introduce a frequency-selective approximate maximum-likelihood (FSAML) detector, operating on a subset of the available frequencies, making it robust to the typically present narrow-band interference. The method exploits the inherent temperature dependency of the NQR frequencies as a way to enhance the SNR. Numerical evaluations, using both simulated and real NQR data, indicate a significant gain in probability of accurate detection as compared to a current state-of-the-art approach.
The problem of estimating the parameters in continuous-time autoregressive moving average (ARMA) processes from discrete-time data is considered. Both direct and indirect methods are studied, and similarities and differences are discussed. A general discussion of the inherent difficulties of the problem is given together with a comprehensive study on how the choice of the sampling interval influences the estimation result. A special focus is given to how the Cramer-Rao lower bound depends on the sampling interval.
In this paper, we investigate the nonparametric estimation of the frequency dependent complex modulus of a viscoelastic material. The strains due to flexural wave propagation in a bar specimen are registered at different cross sections. The time domain data is transformed into frequency domain using discrete Fourier transform and a nonlinear least squares algorithm is then employed to estimate the complex modulus at each frequency. Inherent numerical problems due to associated ill-conditioned matrices are treated with special care. An analysis of the quality of the nonlinear least squares estimate is also carried out. The validity of the theoretical results are confirmed by numerical studies and experimental tests
A subset of long-range dependent FARIMA processes is considered. A method for estimating the parameter that describes the long-range dependency of such a process is suggested. The method is based on an asymptotic expression for the covariance function of the process and gives a closed form solution by means of a weighted linear least squares estimate. The variance of the estimate given by themethod is analyzed and, at the same time, the optimal choice of the weighting is expressed. A numerical illustration of the method and the material in the paper is provided
Fractional Gaussian noise, given as the increment of fractional Brownian motion, is a stationary Gaussian process characterized by the Hurst parameter. In the paper, moments based estimators of the Hurst parameter are presented and analyzed with respect to asymptotic variance
The problem of estimating the parameters in stochastic continuous-time signals, represented as continuous-time autoregressive moving average (ARMA) processes, from discrete-time data is considered. The proposed solution is to fit the covariance function of the process, parameterized by the unknown parameters, to sample covariances. It is shown that the method is consistent, and an expression for the approximate covariance matrix of the estimated parameter vector is derived. The derived variances are compared with empirical variances from a Monte Carlo simulation, and with the Cramer-Rao bound. It turns out that the variances are close to the Cramer-Rao bound for certain choices of the sampling interval and the number of covariance elements used in the criterion function.
A new approach for electric power consumption forecasting that consists of using subspace identification techniques is presented in the paper. The new and powerful subspace identification techniques are introduced to the members of the power system engineering community who are not familiar with them, and it is shown that they can be an important tool in this area of electrical engineering. The usefulness of the techniques is illustrated on real data, and the identified models give reliable 24-h ahead predictions.
The parameters in a general Gaussian process, including the parameters in an additive Gaussian noise process, are estimated based on zero crossing data for the total process and arbitrarily filtered versions thereof. A nonlinear weighted least squares estimate is considered and an analysis of the asymptotic covariance matrix of the estimated parameter vector is made. The proposed estimator and the use of zero crossing data are suitable when information of a process is sent from wireless sensors to a node center for further processing due to an efficient use of available bandwidth.
A computationally efficient estimator of continuous-time autoregressive (AR) process parameters from irregularly sampled data affected by discrete-time white measurement noise is presented. It is described how an instrumental variable approach can be used for estimating the AR process parameters with high accuracy. Possible estimators of the incremental variance of the driving continuous-time white noise source and of the variance of the discrete-time white measurement noise are also discussed.
Two sampling strategies are used for solving an errors-in-variables problem where the system as well as the white measurement noises are of a continuous-time nature. The sampling strategies are integrated sampling, and lowpass filtering followed by instantaneous sampling. Covariance relations are derived and systems of equations are formed for the data obtained from the two sampling strategies, and parameter estimators based on these relations and equations are proposed.