Linear Parameter Estimation Research Articles

Design and Implementation of On-Line Self-Tuning Control for PEM Fuel Cells

This paper presents the modelling and real time implementation of PEM (polymer electrolyte membrane) fuel cell flow control. Flow control presents a critical performance requirement to achieving dynamic power responses for electric vehicle motor demands. However a fuel cell’s complex structure and reactant requirements traditionally result in an unsatisfactory response to such dynamic loading instances. This in turn causes brief power losses associated with driving patterns such as acceleration and hill climbing. To improve the fuel cell’s dynamic response to such drive cycles, this paper presents new methodology for system identification and controller design. The fuel cell is modelled initially with established linear model and parameter estimation methods. The approach is then expanded to an on-line system identification LabVIEW programme to account for the non-linear and time varying characteristics. Based upon this identification process, a novel LabVIEW self-tuning PID controller is implemented in real time to control the response. The self-tuning controller continuously re-calculates the critical gain and period, and then adjusts the controller actions accordingly. Conclusions are then summarised from the results and future ongoing work is discussed briefly.

Measurement of Passive $R$, $L$, and $C$ Components Under Nonsinusoidal Conditions: The Solution of Some Case Studies

This paper deals with the measurement of the R, L, and C parameters of passive components in nonsinusoidal conditions. Since these components usually work with voltage and current waveforms that are different from sinusoidal ones, nonsinusoidal characterization has to be made. The importance of nonsinusoidal characterization of passive components is highlighted through the analysis of two case studies: (1) the influence of distorted waveforms on the line impedance stabilizer network (LISN) passive component behaviors and (2) the influence of voltage and current harmonics on hybrid filter responses. In this paper, the authors propose and describe a measurement method based on linear system identification and model parameter estimation techniques. Then, the two case studies are analyzed and described with the help of some test results.

Prediction of spatial soil property information from ancillary sensor data using ordinary linear regression: Model derivations, residual assumptions and model validation tests

Geospatial measurements of ancillary sensor data, such as bulk soil electrical conductivity or remotely sensed imagery data, are commonly used to characterize spatial variation in soil or crop properties. Geostatistical techniques like kriging with external drift or regression kriging are often used to calibrate geospatial sensor data to specific soil or crop properties. More traditional statistical methods such as ordinary linear regression models are also commonly used. Unfortunately, some soil scientists see these as competing and unrelated modeling approaches and are unaware of their relationship. In this article we review the connection between the ordinary linear regression model and the more comprehensive geostatistical mixed linear model and describe when and under what conditions ordinary linear regression models represent valid spatial prediction models. The formulas for the ordinary linear regression model parameter estimates and best linear unbiased predictions are derived from the geostatistical mixed linear model under two different residual error assumptions; i.e., strictly uncorrelated (SU) residuals and effectively uncorrelated (EU) residuals. The theoretically optimal (best linear unbiased) and computable (linear unbiased) predictions and variance estimates derived under the EU error assumption are examined in detail. Statistical tests for detecting spatial correlation in LR model residuals are also reviewed, in addition to three LR model validation tests derived from classical linear modeling theory. Two case studies are presented that highlight and demonstrate the various parameter estimation, response variable prediction and model validation techniques discussed in this article.

Optimal Adaptive Control—Contradiction in Terms or a Matter of Choosing the Right Cost Functional?

Approaching the problem of optimal adaptive control as ldquooptimal control made adaptive,rdquo namely, as a certainty equivalence combination of linear quadratic optimal control and standard parameter estimation, fails on two counts: numerical (as it requires a solution to a Riccati equation at each time step) and conceptual (as the combination actually does not possess any optimality property). In this note, we present a particular form of optimality achievable in Lyapunov-based adaptive control. State and control are subject to positive definite penalties, whereas the parameter estimation error is penalized through an exponential of its square, which means that no attempt is made to enforce the parameter convergence, but the estimation transients are penalized simultaneously with the state and control transients. The form of optimality we reveal here is different from our work in [Z. H. Li and M. Krstic, ldquoOptimal design of adaptive tracking controllers for nonlinear systems,rdquo <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Automatica</i> , vol. 33, pp. 1459-1473, 1997] where only the terminal value of the parameter error was penalized. We present our optimality concept on a partial differential equation (PDE) example-boundary control of a particular parabolic PDE with an unknown reaction coefficient. Two technical ideas are central to the developments in the note: a nonquadratic Lyapunov function and a normalization in the Lyapunov-based update law. The optimal adaptive control problem is fundamentally nonlinear and we explore this aspect through several examples that highlight the interplay between the non-quadratic cost and value functions.

Bootstrap mean squared error of a small-area EBLUP

Concerning the estimation of linear parameters in small areas, a nested-error regression model is assumed for the values of the target variable in the units of a finite population. Then, a bootstrap procedure is proposed for estimating the mean squared error (MSE) of the EBLUP under the finite population setup. The consistency of the bootstrap procedure is studied, and a simulation experiment is carried out in order to compare the performance of two different bootstrap estimators with the approximation given by Prasad and Rao [Prasad, N.G.N. and Rao, J.N.K., 1990, The estimation of the mean squared error of small-area estimators. Journal of the American Statistical Association, 85, 163–171.]. In the numerical results, one of the bootstrap estimators shows a better bias behavior than the Prasad–Rao approximation for some of the small areas and not much worse in any case. Further, it shows less MSE in situations of moderate heteroscedasticity and under mispecification of the error distribution as normal when the true distribution is logistic or Gumbel. The proposed bootstrap method can be applied to more general types of parameters (linear of not) and predictors.

Functional response of the lady beetle Harmonia axyridis (Pallas) (Coleoptera: Coccinellidae) on the aphid Myzus persicae (Sulzer) (Homoptera: Aphididae)

The functional responses of each instar larva and adult of the coccinellid Harmonia axyridis to adults of the green peach aphid Myzus persicae were estimated under laboratory conditions. Linear parameter estimates from a logistic model of the proportion of M. persicae consumed by H. axyridis were negative at all development stages. Although a realistic estimate for the handling time of first instar larvae could not be produced, functional response curves of fitting the data with a random predator equation exhibited a Type II curve in most development stages. Fourth instar larva had the highest attack rate and shortest prey handling time. The implications of these results are discussed with more effective stages of H. axyridis in the context of biological control.

A blind separation method of overlapped multi-components based on time varying AR model

A method utilizing single channel recordings to blindly separate the multicomponents overlapped in time and frequency domains is proposed in this paper. Based on the time varying AR model, the instantaneous frequency and amplitude of each signal component are estimated respectively, thus the signal component separation is achieved. By using prolate spheroidal sequence as basis functions to expand the time varying parameters of the AR model, the method turns the problem of linear time varying parameters estimation to a linear time invariant parameter estimation problem, then the parameters are estimated by a recursive algorithm. The computation of this method is simple, and no prior knowledge of the signals is needed. Simulation results demonstrate validity and excellent performance of this method.

A priori weighting for parameter estimation

We propose a new approach to weighting initial parameter misfits in a least squares optimization problem for linear parameter estimation. Parameter misfit weights are found by solving an optimization problem which ensures the penalty function has the properties of a χ 2 random variable with n degrees of freedom, where n is the number of data. This approach differs from others in that weights found by the proposed algorithm vary along a diagonal matrix rather than remain constant. In addition, it is assumed that data and parameters are random, but not necessarily normally distributed. The proposed algorithm successfully solved three benchmark problems, one with discontinuous solutions. Solutions from a more idealized discontinuous problem show that the algorithm can successfully weight initial parameter misfits even though the two-norm typically smoothes solutions. For all test problems sample solutions show that results from the proposed algorithm can be better than those found using the L-curve and generalized cross-validation. In the cases where the parameter estimates are not as accurate, their corresponding standard deviations or error bounds correctly identify their uncertainty.

Determination of source parameters of strong earthquakes of Kamchatka, the Kurile Islands, and Japan from aftershock sequences

Aftershock sequences of some strong earthquakes of Kamchatka, the Kurile Islands, and Japan are examined. Such source parameters as the length L, along-dip width W, motion on fault D, and stress drop Δσ are determined from the aftershock sequences considered. The values of these parameters were obtained by the formal estimation of linear source parameters (lower bound estimates) and visually (upper bound estimates). The correlation dependences of the obtained parameters on the surface wave (MS) and seismic moment (MW) magnitudes are calculated.

Mining information from binary black hole mergers: A comparison of estimation methods for complex exponentials in noise

The ringdown phase following a binary black hole merger is usually assumed to be well described by a linear superposition of complex exponentials (quasinormal modes). In the strong-field conditions typical of a binary black hole merger, nonlinear effects may produce mode coupling. Artificial mode coupling can also be induced by the black hole's rotation, if the radiation field is expanded in terms of spin-weighted spherical harmonics (rather than spin-weighted spheroidal harmonics). Observing deviations from the predictions of linear black hole perturbation theory requires optimal fitting techniques to extract ringdown parameters from numerical waveforms, which are inevitably affected by numerical error. So far, nonlinear least-squares fitting methods have been used as the standard workhorse to extract frequencies from ringdown waveforms. These methods are known not to be optimal for estimating parameters of complex exponentials. Furthermore, different fitting methods have different performance in the presence of noise. The main purpose of this paper is to introduce the gravitational wave community to modern variations of a linear parameter estimation technique first devised in 1795 by Prony: the Kumaresan-Tufts and matrix pencil methods. Using ``test'' damped sinusoidal signals in Gaussian white noise we illustrate the advantages of these methods, showing that they have variance and bias at least comparable to standard nonlinear least-squares techniques. Then we compare the performance of different methods on unequal-mass binary black hole merger waveforms. The methods we discuss should be useful both theoretically (to monitor errors and search for nonlinearities in numerical relativity simulations) and experimentally (for parameter estimation from ringdown signals after a gravitational wave detection).

Optical Flow 3D Segmentation and Interpretation: A Variational Method with Active Curve Evolution and Level Sets

This study investigates a variational, active curve evolution method for dense three-dimentional (3D) segmentation and interpretation of optical flow in an image sequence of a scene containing moving rigid objects viewed by a possibly moving camera. This method jointly performs 3D motion segmentation, 3D interpretation (recovery of 3D structure and motion), and optical flow estimation. The objective functional contains two data terms for each segmentation region, one based on the motion-only equation which relates the essential parameters of 3D rigid body motion to optical flow, and the other on the Horn and Schunck optical flow constraint. It also contains two regularization terms for each region, one for optical flow, the other for the region boundary. The necessary conditions for a minimum of the functional result in concurrent 3D-motion segmentation, by active curve evolution via level sets, and linear estimation of each region essential parameters and optical flow. Subsequently, the screw of 3D motion and regularized relative depth are recovered analytically for each region from the estimated essential parameters and optical flow. Examples are provided which verify the method and its implementation.

Camera Calibration of Stereo Photogrammetric System with One-Dimensional Optical Reference Bar

To carry out the precise measurement of large-scale complex workpieces, accurately calibration of the stereo photogrammetric system has becoming more and more important. This paper proposed a flexible and reliable camera calibration of stereo photogrammetric system based on quaternion with one-dimensional optical reference bar, which has three small collinear infrared LED marks and the lengths between these marks have been precisely calibration. By moving the optical reference bar at a number of locations/orientations over the measurement volume, we calibrate the stereo photogrammetric systems with the geometric constraint of the optical reference bar. The extrinsic parameters calibration process consists of linear parameters estimation based on quaternion and nonlinear refinement based on the maximum likelihood criterion. Firstly, we linear estimate the extrinsic parameters of the stereo photogrameetric systems based on quaternion. Then with the quaternion results as the initial values, we refine the extrinsic parameters through maximum likelihood criterion with the Levenberg-Marquardt Algorithm. In the calibration process, we can automatically control the light intensity and optimize the exposure time to get uniform intensity profile of the image points at different distance and obtain higher S/N ratio. The experiment result proves that the calibration method proposed is flexible, valid and obtains good results in the application.

Inference in Curved Exponential Family Models for Networks

Network data arise in a wide variety of applications. Although descriptive statistics for networks abound in the literature, the science of fitting statistical models to complex network data is still in its infancy. The models considered in this article are based on exponential families; therefore, we refer to them as exponential random graph models (ERGMs). Although ERGMs are easy to postulate, maximum likelihood estimation of parameters in these models is very difficult. In this article, we first review the method of maximum likelihood estimation using Markov chain Monte Carlo in the context of fitting linear ERGMs. We then extend this methodology to the situation where the model comes from a curved exponential family. The curved exponential family methodology is applied to new specifications of ERGMs, proposed in an earlier article, having nonlinear parameters to represent structural properties of networks such as transitivity and heterogeneity of degrees. We review the difficult topic of implementing likelihood ratio tests for these models, then apply all these model-fitting and testing techniques to the estimation of linear and nonlinear parameters for a collaboration network between partners in a New England law firm.

Power quality analysis based on fuzzy estimation algorithm: Voltage flicker measurements

This paper presents a method based on fuzzy linear estimation for voltage flicker measurements. The proposed algorithm uses the digitized samples of the voltage signal at the location where the power quality standards are implemented. The voltage signal is modeled as a fuzzy linear parameter estimation problem, where the coefficients are assumed to be fuzzy having certain middle and spread. A triangular membership is assumed. The linear programming based simplex method is used to solve the resulting linear optimization problem. Results for simulated examples are given in the text.

Estimating the matrix of root-mean-square errors of estimates of linear regression parameters for an arbitrary number of regressors and three inequality constraints

The problem of estimating linear regression parameters is considered with regard to three inequality constraints. Formulas are proposed for calculating a sample estimate for the matrix of root-mean-square error estimates of regression parameters and noise variance.

Codebook driven short-term predictor parameter estimation for speech enhancement

In this paper, we present a new technique for the estimation of short-term linear predictive parameters of speech and noise from noisy data and their subsequent use in waveform enhancement schemes. The method exploits a priori information about speech and noise spectral shapes stored in trained codebooks, parameterized as linear predictive coefficients. The method also uses information about noise statistics estimated from the noisy observation. Maximum-likelihood estimates of the speech and noise short-term predictor parameters are obtained by searching for the combination of codebook entries that optimizes the likelihood. The estimation involves the computation of the excitation variances of the speech and noise auto-regressive models on a frame-by-frame basis, using the a priori information and the noisy observation. The high computational complexity resulting from a full search of the joint speech and noise codebooks is avoided through an iterative optimization procedure. We introduce a classified noise codebook scheme that uses different noise codebooks for different noise types. Experimental results show that the use of a priori information and the calculation of the instantaneous speech and noise excitation variances on a frame-by-frame basis result in good performance in both stationary and nonstationary noise conditions.

Accruals, Accounting-Based Valuation Models, and the Prediction of Equity Values

This study uses out-of-sample equity value estimates to determine whether earnings disaggregation, imposing linear information valuation model (LIM) structure and separate industry estimation of valuation model parameters aid in predicting contemporaneous equity values. We consider three levels of earnings disaggregation: aggregate earnings, cashflow and total accruals and cash flow and four major components of accruals. For pooled estimations, imposing the LIM structure results in significantly smaller prediction errors; for by-industry estimations, it does not. However, by-industry prediction errors are substantially smaller, suggesting that the by-industry estimations are better specified. Mean squared and absolute prediction errors are smallest when earnings are disaggregated into cash flow and major accrual components; median prediction errors are smallest when earnings are disaggregated into cash flow and total accruals. These findings suggest that (1) if concern is with errors in the tails of the equity value prediction error distribution, then earnings should be disaggregated into cash flow and the major accrual components; otherwise earnings should be disaggregated only into cash flow and total accruals; (2) imposing the LIM structure neither increases nor decreases prediction errors, which supports the efficacy of drawing inferences from valuation equations based on residual income models that do not impose the structure implied by the model; (3) valuation of abnormal earnings, accruals, accrual components, equity book value, and other information varies significantly across industries.

Fast error whitening algorithms for system identification and control with noisy data

Linear system identification with noisy input/output is a critical problem in signal processing and control. Conventional techniques based on the mean squared-error (MSE) criterion can at best provide a biased parameter estimate of the unknown system being modeled. Recently, we proposed a new criterion called the error whitening criterion (EWC) to solve the problem of linear parameter estimation in the presence of additive white noise. Accordingly, the central idea is to partially whiten the error signal beyond a predetermined correlation lag. In the first-half of the paper, we will derive a fast Quasi-Newton type recursive algorithm to compute the optimal EWC solution in an online manner. The algorithm has O( N 2) complexity where, N represents the length of the parameter vector to be estimated. One of the primary limitations of EWC is the assumption that the input noise must be white. In the second-half of this paper, we will introduce a modified cost function that overcomes this assumption and allows the noise in the input to be colored. The analysis of this modified cost function is then presented followed by a sample-by-sample stochastic gradient algorithm to optimally compute the analytical solution. Finally, we will show the experimental results with EWC as well as the modified criterion in system identification and controller design problems.

On the Convergence of the Generalized Linear Least Squares Algorithm

This paper considers the issue of parameter estimation for biomedical applications using nonuniformly sampled data. The generalized linear least squares (GLLS) algorithm, first introduced by Feng and Ho (1993), is used in the medical imaging community for removal of bias when the data defining the model are correlated. GLLS provides an efficient iterative linear algorithm for the solution of the non linear parameter estimation problem. This paper presents a theoretical discussion of GLLS and introduces use of both Gauss Newton and an alternating Gauss Newton for solution of the parameter estimation problem in nonlinear form. Numerical examples are presented to contrast the algorithms and emphasize aspects of the theoretical discussion.

On the Identification of Wiener Systems Having Saturation-like Functions with Positive Slopes

The aim of the given paper is the development of an approach for parametric identification of Wiener systems with piecewise linear nonlinearities, i.e., when the linear part with unknown parameters is followed by a saturation-like function with unknown slopes. It is shown here that by a simple data reordering and by a following data partition the problem of identification of a nonlinear Wiener system could be reduced to a linear parametric estimation problem. Afterwards, estimates of the unknown parameters of linear regression models are calculated by processing respective particles of input-output data. A technique based on ordinary least squares (LS) is proposed here for the estimation of parameters of linear and nonlinear parts of the Wiener system, including the unknown threshold of piecewise nonlinearity, too. The results of numerical simulation and identification obtained by processing observations of input-output signals of a discrete-time Wiener system with a piecewise nonlinearity by computer are given.