Error Formulation Research Articles

MCE-BASED FACE RECOGNITION

This paper proposes a complete procedure for the extraction and recognition of human faces in complex scenes. The morphology-based face detection algorithm can locate multiple faces oriented in any direction. The recognition algorithm is based on the minimum classification error (MCE) criterion. In our work, the minimum classification error formulation is incorporated into a multilayer perceptron neural network. Experimental results show that our system is robust to noisy images and complex background.

Performance of a hybrid decision feedback equalizer structure for CAP-based DSL systems

We study the performance of a class of derision feedback equalizer (DFE) structures for high-speed digital transmission systems. We first present mathematical formulation of minimum mean-square error (MMSE) and the optimum tap coefficients for various finite-length phase-splitting equalizers over the loop in the presence of colored noise, such as near-end crosstalk (NEXT) and far-end crosstalk (FEXT). The performance of the equalizers is also analyzed in the presence of narrowband interference and the channel reflections introduced by bridged taps. The hybrid-type DFE (H-DFE) is presented as a practical equalizer structure for these applications. The results of analysis show that the H-DFE has advantages in the performance and/or in the implementation complexity as compared with the existing DFE structures. An additional advantage of the H-DFE is in the transmission systems that employ the precoding technique. The precoding for the H-DFE allows the system to track small changes in the channel.

Three-dimensional welding analysis using an adaptive mesh scheme

One major problem arising in finite element analysis of welding is the long computer times required for a complete three-dimensional analysis. An adaptive strategy for coupled thermo-mechanical analysis of welding is applied in order to reduce the computer time. The paper describes a generic posteriori error formulation that evaluates both the thermal and the mechanical error distribution. It is combined with a hierarchic remeshing strategy using a so-called graded element. The error indicator together with the known movement of the local heat source is used to predict areas of refinement. An increased accuracy is obtained with a reduced computational effort.

A composite adaptive output feedback tracking controller for robotic manipulators

This paper provides a solution to the composite adaptive output feedback tracking control problem for robotic manipulators. The proposed controller utilizes an update law that is a composite of a gradient update law driven by the link position tracking error and a least squares update law driven by the prediction error. In order to remove the controller's dependence on link velocity measurements, a linear filter and a new prediction error formulation are designed. The controller provides semi-global asymptotic link position tracking performance. Experimental results illustrate that the proposed controller provides improved link position tracking error transient performance and faster parameter estimate convergence in comparsion to the same controller using a gradient update law.

Filter design and comparison for two fast CWT algorithms

The continuous wavelet transform (CWT) is a powerful technique for signal analysis. Direct CWT computation by FFT requires O(N log/sub 2/ N) operations per scale, where N is the data length. The a trous algorithm and the Shensa (1992) algorithm are two fast methods to compute CWT recursively that require only O(N) operations per scale. Both of them can be described by the multiresolution analysis (MRA) structure but with different MRA filters. This paper proposes methods to design the MRA filters of the two algorithms to improve their accuracy on CWT computation. We begin with the formulation of the CWT computation error using the MRA structure. The MRA filters of the two algorithms are then designed to minimize the error. In either algorithm, both the lowpass and bandpass MRA filters can be optimized. The a trous algorithm has closed-form solutions for the two filters. The Shensa algorithm, on the other hand, has an analytic solution for the bandpass filter only. Finding the optimum lowpass filter requires a multidimensional numerical search. Simulation studies show that by using the proposed optimum filters, the Shensa algorithm, in general, outperforms the a trous algorithm.

Linear and Non-linear System Identification Using Separable Least-Squares

We demonstrate how the separable least-squares technique of Golub and Pereyra can be exploited in the identification of both linear and non-linear systems based on the prediction error formulation. The model classes to be considered here are the output error model and innovations model in the linear case and the Wiener system in the non-linear case. This technique together with a suitable choice of parametrisation allow us to solve, in the linear case, the associated optimisation problem using only np parameters instead of the usual n(m + p) + mp parameters when canonical forms are used, where n, m and p denote respectively the number of states, inputs and outputs, We also prove under certain assumptions that the separable optimisation method is numerically better conditioned than its non-separable counterpart. Successful operations of these identification algorithms are demonstrated by applying them to two sets of industrial data: an industrial dryer in the linear case and a high-purity distillation column in the non-linear case.

Error analysis of analytic coarse alignment methods

Two analytic coarse alignment methods and the associated error analyses are provided for strapdown inertial navigation systems. Although both methods are derived from the same measurements of the local gravity vector and Earth rate, their error formulations are not completely identical. By properly selecting the basis to compute a best estimate of transformation matrix, the drift misalignment angles of analytic alignment can be made to be equivalent to those which can be found by physical gyrocompassing.

Marginal Models with Multiplicative Variance Components for Overdispersed Binomial Data

A marginal model for binomial data where the experimental units involving one or two random factors is presented. Two variance-covariance models are derived based on the multiplicative error formulation. The parameters of mean and variance components are estimated using quasi-likelihood and method of moments, respectively. The model is applied to analyzing multivariate overdispersed binomial data from a developmental toxicity experiment.

Linear and Non-Linear System Identification Using Separable Least-Squares

Abstract We demonstrate how the separable least-squares technique of Golub and Pereyra can be exploited in the identification of both linear and non-linear systems based on the prediction error formulation. The model classes to be considered here are the output error model and innovation model in the linear case and the Wiener system in the non-linear case. This technique together with a suitable choice of parameterization allow us to solve, in the linear case, the associated optimization problem using only np parameters instead of the usual n ( m + p ) + mp parameters when canonical forms are used, where n , m and p denote respectively the number of states, inputs and outputs. An example where the Wiener system identification algorithm is applied to real data obtained from a distillation column is given.

New schemes and theoretical analysis of the master-slave family of recursive identification algorithms

An analysis of the Master-Slave family of system identification algorithms is developed for the white noise input case. These methods try to avoid the biased parameter estimation problem of equation error methods in the presence of noisy data, while keeping the quadratic nature of the error variances to be minimized (a feature that is lost with the output error formulation). The Master-Slave techniques may be seen as off-line schemes that construct a sequence of equation error optimization problems, each one based on the solution to the previous one. Some conditions for the stationary points of the iteration are given. Examples are presented for plants with poles close to z = 1 where undesirable attractive convergent points arise. An alternative scheme based on interpolation conditions rather than minimizing error variances is proposed and shown to have a single stationary point corresponding to the plant parameters. Finally, a simplified structure and a lattice algorithm are presented for on-line implementation.

A general consistent equation-error algorithm for adaptive IIR filtering

This paper proposes a new adaptive IIR filtering algorithm based on equation error (EE) formulation. The algorithm allows for the compensation of the bias inherent to the equation error formulation. A study of the properties of the new algorithm shows that the asymptotic stability associated with the EE algorithm can be maintained. In addition, for sufficiently general conditions, the parameter estimates are consistent. Some methods recently proposed to remove the bias problem of the EE algorithm are particular cases of the general algorithm presented. Computer simulations are included to illustrate and compare the convergence properties of the proposed algorithm.

Accuracy of the general peaceman and Rachford alternating direction implicit method

In this paper, the truncation error of the general Peaceman and Rachford alternating direction implicit (ADI) method in a N-dimensional space was derived by using the Taylor-series-expansion approach. The formulation of this truncation error is TE= 2−N 2N 2 ∑ i=l N ∑ j=l N ∂ 4θ ∂η 2 iη 2 j δτ+O(δτ 2)+ ∑ i=l N O(δη 2 i which indicates that the method is second order accurate in both time and space for two dimensions but reduces to first order accuracy in time for higher dimensions. However the second order time accuracy is recovered when N → ∞. The worst case corresponding to the maximum value of (2-N) 2N 2 occurs at N = 4.

Architectures for block Toeplitz systems

In this paper efficient VLSI architectures of highly concurrent algorithms for the solution of block linear systems with Toeplitz or near-to-Toeplitz entries are presented. The main features of the proposed scheme are the use of scalar only operations, multiplications/divisions and additions, and the local communication which enables the development of wavefront array architecture. Both the mean squared error and the total squared error formulations are described and a variety of implementations are given.

Acoustic scattering from rigid shells of revolution using the generalized internal source density and SVD method

Acoustic harmonic nonaxisymmetric scattering from rigid shells of revolution is addressed using the generalized internal source density and SVD method. The development of the generalized ISD/SVD method, which entails the use of various internal multipole source distributions along the axis of the shell, will be presented. The approach is based on first expanding the incident pressure and associated velocity field into circumferential harmonics about the axis of the shell. Integral equations of the first kind are developed for the unknown source distributions. A least-mean-squared error formulation of the solution naturally leads to using the SVD method to determine the source distributions. The blocked surface pressure for each circumferential harmonic is then readily evaluated by simple quadrature methods and the associated far-field scattered pressures are shown to be simply related to the Fourier transforms of the source distributions. Numerical results for some selected problems are presented and some limitations of the method as a function of azimuthal wave number and shape of the shells are noted. These limitations are discussed and are readily interpreted in light of the above-noted Fourier transform relationship.

Discriminative training of dynamic programming based speech recognizers

A new minimum recognition error formulation and a generalized probabilistic descent (GPD) algorithm are analyzed and used to accomplish discriminative training of a conventional dynamic-programming-based speech recognizer. The objective of discriminative training here is to directly minimize the recognition error rate. To achieve this, a formulation that allows controlled approximation of the exact error rate and renders optimization possible is used. The GPD method is implemented in a dynamic-time-warping (DTW)-based system. A linear discriminant function on the DTW distortion sequence is used to replace the conventional average DTW path distance. A series of speaker-independent recognition experiments using the highly confusible English E-set as the vocabulary showed a recognition rate of 84.4% compared to approximately 60% for traditional template training via clustering. The experimental results verified that the algorithm converges to a solution that achieves minimum error rate. >

A Method for Error Quantification in the FIR Model

The paper presents a method for quantifying modelling error of an FIR model whose parameters are estimated by using the least squares method. This method is also applicable to a model whose transfer function is expressed by a linear polynomial of the parameters.First, we introduce the method proposed by G.C. Goodwin et al. The method assumes that the unmodelled dynamics of the system is expressed by realizations of random variables which have independent distributions with exponentially decaying variance. But the formulation of the modelling error is modified in this paper as Goodwin's formulation is rather difficult to understand.Second, we point out that Goodwin's approximation is of a rough and unpractical nature, and also that the modelling error obtained by the method is not frequency-dependent. Hence, we propose a revised method where an assumption in Goodwin's method is modified to a more reasonable one. We also propose a parameter estimation algorithm which needs much less computation time with little loss of accuracy of estimation.Finally, we show, through several numerical simulations, that the mean-squared error estimated by the revised method is much closer to the real modelling error than that obtained by Goodwin's method.

Residual error formulation and adaptive minimization for representing nonstationary signals using mixed transforms

A technique is proposed for signal representation using superimposed partial sets of different transforms which are, in general, nonorthogonal to each other. The method is developed to maximize the signal-to-noise ratio (SNR) of the reconstructed signal for a given total number of transform coefficients. First, the residual error, which is the difference between the original signal and the reconstructed signal, is properly formulated. Then, two gradient techniques, in conjunction with an optimization strategy, are developed to minimize the residual error. Sample results using this approach for representing synthetic signals and speech signals employing mixed Fourier/Walsh and Fourier/Haar transforms are given to illustrate the efficiency and accuracy of the proposed method. >

Nonorthogonal signal decomposition.

To gain physical interpretations and insights from observed phenomena, it is often desirable to decompose a given function, i.e., the observed signal, into a set of nonorthogonal functions. This paper describes a signal processing algorithm based on the minimization of the mean-square error formulation of the decomposition analysis. The computation scheme is derived from a recursive gradient descent method to approach the correct answer for a set of over-determined simultaneous equations. The traditional matrix inversion technique is usually not workable for numerical operation because the matrices are often ill-conditioned. This suggested approach not only alleviates the computation problem, but also can more easily be implemented in a parallel architecture computer or a neural-like network. The signal received from a synthetic circular array [N. Yen, IEEE/JOE, Jan. 1992, pp. 40–47] is used, as a practical example, to illustrate that a composite signal can be reduced to a combination of the corresponding signals from various directions. Comparison of the results obtained by this algorithm with the traditional beamforming method supports the use of this new signal processing technique.

Moment-based estimation and testing of stochastic frontier models

This paper assesses the implications of relaxing some of the distributional assumptions that characterize most composed error formulations of frontier cost and production function models appearing in the literature. Generalized method of moments (GMM) estimation procedures are presented that enable various degrees of distributional flexibility that are typically difficult to attain in likelihood-based approaches to estimation of frontier models. Moment-based specification tests that are specially suited for frontier models are also described. Some properties of the estimators and tests are illustrated via cost functions estimated using three microdata samples of electric utility behavior.

Predictive Transform, Part I: Signal Coding and Modeling

The formulation of linear minimum mean square error (MSE) predictive transform (PT) coding is extended to the case where the encoded signal is generated by a controlled source and the predictive section of the coder has a nonlinear structure. The extended formulation is appealing for two fundamental reasons. First, it generally yields higher data compression than that achievable with linear minimum MSE PT coding. Secondly, the decoder of the PT coder is a whitening PT model of the source whose output we wish to encode and control. Hence the PT decoder is ideally suited for integration with control techniques that require a whitening model for the controlled source such as linear quadratic gaussian (LQG) control.