A generalization of the Friedlander Algorithm balancing of national accounts matrices

Owing to stochastic and systematic errors in test samples, the first estimates of national accounts items rarely satisfy all the well known definitional identities. Stone, Champernowne and Meade presented the initial argument for GLS balancing of such accounting matrices in 1942. The GLS principles were, however, rarely used in practical empirical work until Byron facilitated the computational process by applying the Conjugate Gradient Algorithm in 1978. This paper shows how a slight adjustment of another numerical process, the Friedlander Algorithm, generates an efficient and conceptually simple approach to the computation of a GLS-balanced set of accounts.     

Adaptive sliding mode control for a class of uncertain discrete-time systems using multi-rate output measurement

This article is concerned with the design of an adaptive sliding mode control (SMC) for a class of uncertain discrete-time systems using the multi-rate output measurement. The states of the discrete-time systems are assumed to be taken in the multi-rate output measurement by the contamination with measurement noise. The uncertainties are assumed not to satisfy the matching condition, and are expressed in a parameterised form. A least squares estimator (LSE) to take the estimates for the un-measurable states and the uncertainties is designed in a batch form by using the noisy multi-rate output measurement. The proposed adaptive SMC is designed by using the sliding surface expressed as the linear state function and the estimates obtained from the LSE. It is proved that the estimation errors converge to zero as time tends to infinite, and the states of the system are bounded under the action of the proposed adaptive SMC. The effectiveness of the proposed method is indicated through the simulation experiment in a simple system.     

Symmetric Laplace transform and its application to parametric identification of linear systems

Properties of bilateral symmetric integral transform, which possesses useful features for identification of linear systems, are investigated. Relationships for covariance functions of stochastic stationary processes of measurement errors and disturbances are determined. The optimal solution is proposed to the identification problem for linear multivariable system with measured state coordinates in the transformation parameter domain, with account for restricted bandwidth of dynamic processes in the system at hand. The problem is solved for unknown initial state of the system and complex measurement errors including correlated noise, constant errors and linear trends.     

Interval observer design for consistency checks of nonlinear continuous-time systems

This paper deals with fault detection for nonlinear continuous-time systems. A procedure based on interval analysis is proposed to build a guaranteed qLPV (quasi-Linear Parameter-Varying) approximation of the nonlinear model. The interval qLPV approximation makes it possible to derive two point observers which estimate respectively the lower and the upper bound of the state vector using cooperativity theory. A set guaranteed to contain the actual value of the residual is then designed. The modelling uncertainties and measurement errors are taken into account at the design stage. The proposed methodology is illustrated through numerical simulations.     

Modelling and forecasting noisy realized volatility

Several methods have recently been proposed in the ultra-high frequency financial literature to remove the effects of microstructure noise and to obtain consistent estimates of the integrated volatility (IV) as a measure of ex post daily volatility. Even bias-corrected and consistent realized volatility (RV) estimates of IV can contain residual microstructure noise and other measurement errors. Such noise is called “realized volatility error”. As such errors are ignored, we need to take account of them in estimating and forecasting IV. This paper investigates through Monte Carlo simulations the effects of RV errors on estimating and forecasting IV with RV data. It is found that: (i) neglecting RV errors can lead to serious bias in estimators; (ii) the effects of RV errors on one-step-ahead forecasts are minor when consistent estimators are used and when the number of intraday observations is large; (iii) even the partially corrected R² recently proposed in the literature should be fully corrected for evaluating forecasts. This paper proposes a full correction of R². An empirical example for S&P 500 data is used to demonstrate the techniques developed in this paper.     

基于残差修正法的无线传感器网络定位技术

测距定位是无线传感器网络节点定位中一种常见的方法。然而距离测量往往容易出现错误,导致潜在的大量非高斯误差的测量数据,最终会导致不精确的定位结果。通过分析非线性最小平方残差定位时,测距误差与残差的分布关系,一种坏测距误差的误差估计方法在本文中被提出。采用估计出的测距误差,修正了非线性最小平方残差值,提高了定位精度。仿真实验表明,该算法能有效估计出坏测距误差,并改进了定位效果。     

Blind maximum likelihood identification of Hammerstein systems

This paper is about the identification of discrete-time Hammerstein systems from output measurements only (blind identification). Assuming that the unobserved input is white Gaussian noise, that the static nonlinearity is invertible, and that the output is observed without errors, a Gaussian maximum likelihood estimator is constructed. Its asymptotic properties are analyzed and the Cramér–Rao lower bound is calculated. In practice, the latter can be computed accurately without using the strong law of large numbers. A two-step procedure is described that allows to find high quality initial estimates to start up the iterative Gauss–Newton based optimization scheme. The paper includes the illustration of the method on a simulation example. A theoretical analysis demonstrates that additive output measurement noise introduces a bias that is proportional to the variance of that additive, unmodeled noise source. The simulations support this result, and show that this bias is insignificant beyond a certain Signal-to-Noise Ratio (40 dB in the example).     

Class point: an approach for the size estimation of object-oriented systems

In this paper, we present an FP-like approach, named class point, which was conceived to estimate the size of object-oriented products. In particular, two measures are proposed, which are theoretically validated showing that they satisfy well-known properties necessary for size measures. An initial, empirical validation is also performed, meant to assess the usefulness and effectiveness of the proposed measures to predict the development effort of object-oriented systems. Moreover, a comparative analysis is carried out, taking into account several other size measures.     

Multimodal Data fusion for SRGPS antenna motion error reduction

Antenna motion is a primary fault that degrades the integrity of shipboard relative GPS (SRGPS) systems, so we must investigate how to monitor and mitigate its impacts. Previous work proposed a single-baseline mode, but it had obvious problems, such as large motion errors, error measurement difficulties, and poor reliability. To solve these issues, we propose a multiple reference station architecture that deploys more than one reference station at different positions on ship. The observations are first translated to the ship reference point, and then integrated into a comprehensive measurement that accounts for the overall antenna motion errors. We consider two integrating methods: direct and weighted average methods. The direct average method is simple and intuitive, but the weighted average method more effectively reduced the overall antenna motion error by using the reciprocal standard deviation of historical measurements as weighting factors. All the antennas are mounted on the same ship body, so their correlations should also be considered when determining weighting factors. We used the ranking scores of the antennas derived using a graph-learning algorithm and fused them with the standard deviations to create new weighting factors. Finally, our experimental results demonstrated that the weighting factors based on the standard deviations and ranking scores reduced the overall antenna-motion error variance and improved the system integrity.

     

Tensor: A program to extract hyperfine tensors from single crystal EPR and ENDOR data

A program to determine hyperfine tensors from EPR or ENDOR single crystal data is described. The variation of hyperfine interaction upon rotating the crystal with respect to the static field is studied by a least-squares algorithm which affords various weighting methods. These take into account the fact that the model equations are not linear in the variables, so that equal measurement errors affect the calculation to different extents. An iterative procedure is available which accounts for experimental uncertainty in both dependent and independent variables. Fitting parameters are then cast into a matrix form of tensors. These are diagonalized by a Householder transform followed by application of Sturm bisection algorithm. This procedure is very accurate and matrix inversion is not needed. Extensive error analysis is performed and error propagation is followed throughout the calculation. The standard error of tensor eigenvalues and eigenvectors is estimated. TENSOR features a friendly menu-guided user interface, a data editor, a file manager and routines for printing and plotting.     

Convergence of fixed‐point iteration for the identification of Hammerstein and Wiener systems

Convergence property of the iterative algorithm for Hammerstein or Wiener systems is generally hard to establish because of the existence the unmeasurable internal variables in such systems. In this paper, a fixed‐point iteration is introduced to identifying both Hammerstein and Wiener systems with a unified algorithm. This newly proposed estimation algorithm gives consistent estimates under arbitrary nonzero initial conditions. In addition, the errors of the estimates are established as functions of the noise variance, and thus how the noise affects the quality of parameter estimates for a finite number of data points is made clear. Copyright © 2012 John Wiley & Sons, Ltd.     

Self-calibration and mirror center offset elimination of a multi-beam laser tracking system

New methods for the self-calibration of a laser tracking coordinate measuring machine are reported in this paper. Proper calibration of a laser tracking system is essential prior to using such a device for coordinate measuring. The task is nontrivial in the absence of other measurement systems of comparable accuracy. One has to rely on a self-calibration strategy. Two calibration methods, one based on a four-tracker system and the other based on three trackers combined with precision planes to constrain the target motion, are proposed. Iterative optimization algorithms are developed. A basic assumption for these calibration methods is that there is no tracking mirror center offset. Error analysis presented in this paper reveals that measurement errors due to mirror center offsets are significant. Therefore before calibrating the laser tracking system, the mirrors must be adjusted so that the laser beams hit the mirror centers. The adjustment is a tedious manual task. In the FAU laser tracking machine, an adjustment procedure which employs a four quadrant detector has been devised for the elimination of tracking mirror center offsets. Simulation and experimental results are presented to demonstrate the effectiveness of the suggested methods.     

Systematic geometric rigid body error identification of 5-axis milling machines

A 5-axis milling machine has 39 independent geometric error components when the machine tool is considered as a set of five rigid bodies. The identification of the deterministic component of the systematic error is very important. It permits one to improve the accuracy close to the repeatability of the machine tool. This paper gives a new way to identify and compensate all the systematic angular errors separately and then use them further to identify the systematic translational error.Identification based on a new mathematical method and a stable numerical solution method is proposed. The model explains from first principles why some error components have no effect in a first order model. The identification of the total angular systematic errors can be done independently from the translation errors. However, the total translation error depends on the angular errors and the translation errors of each machine tool slide. The main problems solved are to find enough linear independent equations and avoid numerical instability in the computation. It is important to separate numerical problems and linear dependence. The very complex equations are first analyzed in symbolic form to eliminate the linear dependencies. The total of linear independent components in the model is reduced from 30 to 26 for the position dependent errors and from 9 to 3 for the position independent components. Secondly, the large system of linear equations is broken down in many smaller systems. The model is tested first with simulated errors modeled as cubic polynomials. An artifact-based identification is proposed and implemented based on drilling holes in various locations and orientations. New ways to measure the volumetric error directly are proposed. Direct measurement of the total volumetric error requires considerably less measurement than measuring all 6 components of each machine slide especially in the case of a 5-axis machine.     

Design of an adaptive fuzzy sliding mode control for uncertain discrete-time nonlinear systems based on noisy measurements

This paper presents the design of an adaptive fuzzy sliding mode control (AFSMC) for uncertain discrete-time nonlinear dynamic systems. The dynamic systems are described by a discrete-time state equation with nonlinear uncertainties, and the uncertainties include the modelling errors and the external disturbances to be unknown but nonlinear with the bounded properties. The states are measured by the restriction of measurement sensors and the contamination with independent measurement noises. The nonlinear uncertainties are approximated by using the fuzzy IF-THEN rules based on the universal approximation theorem, and the approximation error is compensated by adding an adaptive complementary term to the proposed AFSMC. The fuzzy inference approach based on the extended single input rule modules is proposed to reduce the number of the fuzzy IF-THEN rules. The estimates for the un-measurable states and the adjustable parameters are obtained by using the weighted least squares estimator and its simplified one. It is proved that under some conditions the estimation errors will remain in the vicinity of zero as time increases, and the states are ultimately bounded subject to the proposed AFSMC. The effectiveness of the proposed method is indicated through the simulation experiment of a simple numerical system.     

基于移动长基线和误差修正算法的多UUV协同导航

在移动长基线（MLBL）定位结构中,虽可利用基于水声传播延迟（TOF）原理获取的量测信息和贝叶斯滤波器（如扩展卡尔曼滤波（EKF））提高低自定位能力无人水下航行器（UUV）的定位精度,但较高的测量误差会降低这种提高的幅度.根据水声通信的特点提出了一种相关性假设并构建了误差修正算法（ECA）,在设定条件下利用误差间的相关性减小量测误差,从而实现量测的粗估计.仿真结果表明,先粗估计量测值再结合贝叶斯滤波器,可显著提高配备低精度自定位传感器的UUV的定位精度.     

Visual servoing for large camera displacements

The first aim of any visual-servoing strategy is to avoid features being lost from the field of view and that the desired location may not be reached. However, avoiding both these system failures turns out to be very difficult, especially when the initial and desired locations are distant. Moreover, the methods that succeed in presence of large camera displacements often produce a long translational trajectory that may not be allowed by the robot workspace and/or joint limits. In this paper, a new strategy for dealing with such problems is proposed, which consists of generating circular-like trajectories that may satisfy the task requirements more naturally than other solutions. Knowledge of geometrical models of the object or points depth is not required. It is shown that system failures are avoided for a calibrated camera. Moreover, necessary and sufficient conditions are provided for establishing tolerable errors on the estimates of the intrinsic and extrinsic parameters, in order to guarantee a robust field of view and robust local asymptotic stability. Several simulation results show that the translational trajectories obtained in presence of large displacements are significantly shorter than those produced by the existing methods, in cases of both correct and bad camera calibration. Very satisfactory results are achieved also in presence of small displacements.     

Design of a simplified adaptive fuzzy backstepping control for uncertain discrete-time nonlinear systems

This paper presents a simplified adaptive fuzzy backstepping control for uncertain discrete-time nonlinear systems. It is assumed that the systems are described by a discrete-time equation with nonlinear uncertainties to be viewed as the modelling errors and the unknown external disturbances, and the states are observed with measurement noises. To design the simplified adaptive fuzzy backstepping control, the modelling errors are approximated by using the fuzzy inference approach based on the extended single-input rule modules, and the estimates for the unmeasurable states and the adjustable parameters are derived by using the weighted and its simplified weighted least squares estimators. It is proved that the states are ultimately bounded, and the estimation errors remain in the vicinity of zero. The effectiveness of the proposed approach is indicated through the simulation experiment of a simple numerical system.     

Methods for obtaining reliable solutions to systems of linear algebraic equations

The general case of incompatible systems of linear algebraic equations with matrices of arbitrary rank is considered. The estimates for total errors are obtained for all the considered cases under conditions of approximate data. In solving systems by iterative methods, the conditions of completion of iterative processes that provide solutions with a prescribed accuracy are considered in detail. A special attention is given to the solution of incompatible systems with symmetric positive semidefinite matrices by the method of three-stage regularization in which an algorithm for choosing the regularization parameter is proposed that allows finding solutions with the required accuracy.     

Discrete-time adaptive sliding mode control for uncertain systems based on multi-rate output measurement

This article presents the design of a discrete-time adaptive sliding mode control (SMC) for uncertain systems using the noisy multi-rate output measurement. It is assumed that the dynamic systems are described by a discrete-time state equation with mismatched uncertainties. The proposed discrete-time adaptive SMC is composed of the equivalent and the nonlinear switching controls, and it is derived based on a new sliding surface. A new least squares estimator (LSE) to take the estimates for the un-measurable states and the uncertainties is designed without the information of the statistics for the measurement noises and the initial state. In the design of the proposed discrete-time adaptive SMC, the un-measurable states and the uncertainties are, respectively, replaced as their estimates obtained from the proposed LSE, and the sliding coefficient matrices are selected such that the states for the systems are ultimately bounded, and the effect of the external disturbances to give the states is reduced as small as possible. The effectiveness of the proposed method is indicated through the simulation experiment in a simple system.     

Reformulation of parameter identification with unknown-but-bounded errors

In this paper a new formulation of the problem of identification of discrete-time linear models in the case of Unknown-But-Bounded errors is proposed. The bounds of the error at each sampling time are specified over a measurement noise rather than over an equation error, which is mainly motivated by experimental considerations. The method is particularly suitable for ARMAX models, as it accounts for the presence of uncertainties in the autoregressive terms.It provides parameter uncertainty intervals using an off-line procedure. Simulations provide results that favourably compare with those of three classical identification methods (Simple-Least-Squares, Output-Error method, Maximum-Likelihood method) and those of the equation error based U.B.B. approach.