A two-step weighted least-squares method for joint estimation of source and sensor locations: A general framework

It is well known that the Two-step Weighted Least-Squares(TWLS) is a widely used method for source localization and sensor position refinement. For this reason, we propose a unified framework of the TWLS method for joint estimation of multiple disjoint sources and sensor locations in this paper. Unlike some existing works, the presented method is based on more general measurement model, and therefore it can be applied to many different localization scenarios.Besides, it does not have the initialization and local convergence problem. The closed-form expression for the covariance matrix of the proposed TWLS estimator is also derived by exploiting the first-order perturbation analysis. Moreover, the estimation accuracy of the TWLS method is shown analytically to achieve the Cramér-Rao Bound(CRB) before the threshold effect takes place. The theoretical analysis is also performed in a common mathematical framework, rather than aiming at some specific signal metrics. Finally, two numerical experiments are performed to support the theoretical development in this paper.

AN ASSESSMENT OF THE MESHLESS WEIGHTED LEAST-SQUARE METHOD

The meshless weighted least-square (MWLS) method was developed based on the weighted least-square method. The method possesses several advantages, such as high accuracy, high stability and high e?ciency. Moreover, the coe?cient matrix obtained is symmetric and semi- positive de?nite. In this paper, the method is further examined critically. The e?ects of several parameters on the results of MWLS are investigated systematically by using a cantilever beam and an in?nite plate with a central circular hole. The numerical results are compared with those obtained by using the collocation-based meshless method (CBMM) and Galerkin-based meshless method (GBMM). The investigated parameters include the type of approximations, the type of weight functions, the number of neighbors of an evaluation point, as well as the manner in which the neighbors of an evaluation point are determined. This study shows that the displacement accuracy and convergence rate obtained by MWLS is comparable to that of the GBMM while the stress accuracy and convergence rate yielded by MWLS is even higher than that of GBMM. Furthermore, MWLS is much more e?cient than GBMM. This study also shows that the instability of CBMM is mainly due to the neglect of the equi- librium residuals at boundary nodes. In MWLS, the residuals of all the governing equations are minimized in a weighted least-square sense.

Prediction of earth rotation parameters based on improved weighted least squares and autoregressive model

In this paper, an improved weighted least squares （WLS）, together with autoregressive （AR） model, is proposed to improve prediction accuracy of earth rotation parameters（ERP）. Four weighting schemes are developed and the optimal power e for determination of the weight elements is studied. The results show that the improved WLS-AR model can improve the ERP prediction accuracy effectively, and for different prediction intervals of ERP, different weight scheme should be chosen.

Design System of the Two-step Gear Reducer on Case-based Reasoning

The design of the two-step gear reducer is a tedious and time-consuming process. For the purpose of improving the efficiency and intelligence of design process, case-based reasoning（CBR） technology was applied to the design of the two-step gear reducer. Firstly, the current design method for the two-step gear reducer was analyzed and the principle of CBR was described. Secondly, according to the characteristics of the reducer, three key technologies of CBR were studied and the corresponding methods were provided, which are as follows： （a） an object-oriented knowledge representation method, （b） a retrieval method combining the nearest neighbor with the induction indexing, and （c） a case adaptation algorithm combining the revision based on rule with artificial revision. Also, for the purpose of improving the credibility of case retrieval, a new method for determining the weights of characteristics and a similarity formula were presented, which is a combinatorial weighting method with the analytic hierarchy process（AHP） and roughness set theory. Lastly, according to the above analytic results, a design system of the two-step gear reducer on CBR was developed by VC＋＋, UG and Access 2003. A new method for the design of the two-step gear reducer is provided in this study. If the foregoing developed system is applied to design the two-step gear reducer, design efficiency is improved, which enables the designer to release from the tedious design process of the gear reducer so as to put more efforts on innovative design. The study result fully reflects the feasibility and validity of CBR technology in the process of the design of the mechanical parts.

Defect detection on button surfaces with the weighted least-squares model

Defect detection assurance on production lines machine-vision-based surface is important in quality This paper presents a fast defect detection method using the weighted least-squares model. We assume that an inspection image can be regarded as a combination of a defect-free template image and a residual image. The defect-free template image is generated from training samples adaptively, and the residual image is the result of the subtraction between each inspection image and corresponding defect-free template image. In the weighted least-squares model, the residual error near the edge is suppressed to reduce the false alarms caused by spatial misalignment. Experiment results on different types of buttons show that the proposed method is robust to illumination vibration and rotation deviation and produces results that are better than those of two other methods.

A novel adaptive image zooming scheme via weighted least-squares estimation

A critical issue in image interpolation is preserving edge detail and texture information in images when zooming. In this paper, we propose a novel adaptive image zooming algorithm using weighted least-square estimation that can achieve arbitrary integer-ratio zoom （WLS-AIZ） For a given zooming ratio n, every pixel in a low-resolution （LR） image is associated with an n x n block of high-resolution （HR） pixels in the HR image. In WLS-AIZ, the LR image is interpolated using the bilinear method in advance. Model parameters of every n×n block are worked out through weighted least-square estimation. Subsequently, each pixel in the n × n block is substituted by a combination of its eight neighboring HR pixels using estimated parameters. Finally, a refinement strategy is adopted to obtain the ultimate HR pixel values. The proposed algorithm has significant adaptability to local image structure. Extensive experiments comparing WLS-AIZ with other state of the art image zooming methods demonstrate the superiority of WLS-AIZ. In terms of peak signal to noise ratio （PSNR）, structural similarity index （SSIM） and feature similarity index （FSIM）, WLS-AIZ produces better results than all other image integer-ratio zoom algorithms.

加权总体最小二乘在铁路曲线正矢拟合的应用

针对铁路线路正矢数据特征,考虑自变量、因变量同时存在误差的情况,提出EIV(Error-in-Variables)模型下的加权总体最小二乘法(WTLS)进行曲线拟合。通过分析拟合点贡献的不等确定度以及修正设计矩阵A的列向量分别引入权阵P y、P x、P0,并给出选权迭代算法。经实例证明,WTLS比传统的LS、TLS方法具有更高的拟合精度。

WLS filter for reducing atmospheric effects in spaceborne SAR tomography

A new approach was presented to eliminate the atmosphere-induced phase error utilizing only the single look complex(SLC) synthetic aperture radar(SAR) image set. This method exploited the space-invariance characteristic of phase error components contained in image pixels and estimates the phase error using the weighted least-squares(WLS) filter. Actually, this sort of method can be classified as autofocus algorithm which was generally applied in airborne SAR 2-D imaging to compensate the phase error introduced by airplane's nonideal motion. Real data processing, which is relevant to Honda center and Angel stadium of Anaheim test-sites and acquired by Envisat-ASAR during the period from June 2004 to October 2007, was carried out to evaluate this WLS estimation algorithm. Experimental results show that the phase error estimated from WLS filter is very accurate and the focusing quality along NSR dimension is improved prominently via phase correction, which verifies the practicability of this new method.

The improved element-free Galerkin method for three-dimensional transient heat conduction problems

With the improved moving least-squares (IMLS) approximation, an orthogonal function system with a weight function is used as the basis function. The combination of the element-free Galerkin (EFG) method and the IMLS approximation leads to the development of the improved element-free Galerkin (IEFG) method. In this paper, the IEFG method is applied to study the partial differential equations that control the heat flow in three-dimensional space. With the IEFG technique, the Galerkin weak form is employed to develop the discretized system equations, and the penalty method is applied to impose the essential boundary conditions. The traditional difference method for two-point boundary value problems is selected for the time discretization. As the transient heat conduction equations and the boundary and initial conditions are time dependent, the scaling parameter, number of nodes and time step length are considered in a convergence study.

Moving target localization in distributed MIMO radar with transmitter and receiver location uncertainties

In this paper, the problem of moving target localization from Bistatic Range(BR) and Bistatic Range Rate(BRR) measurements in a Multiple-Input Multiple-Output(MIMO) radar system having widely separated antennas is investigated. We consider a practically motivated scenario,where the accurate knowledge of transmitter and receiver locations is not known and only the nominal values are available for processing. With the transmitter and receiver location uncertainties,which are usually neglected in MIMO radar systems by prior studies, taken into account in the measurement model, we develop a novel algebraic solution to reduce the estimation error for moving target localization. The proposed algorithm is based on the pseudolinear set of equations and two-step weighted least squares estimation. The Cramer-Rao Lower Bound(CRLB) is derived in the presence of transmitter and receiver location uncertainties. Theoretical accuracy analysis demonstrates that the proposed solution attains the CRLB, and numerical examples show that the proposed solution achieves significant performance improvement over the existing algorithms.

Convergence of Self-Tuning Regulators Under Conditional Heteroscedastic Noises with Unknown High-Frequency Gain

In the classical theory of self-tuning regulators, it always requires that the conditional variances of the systems noises are bounded. However, such a requirement may not be satisfied when modeling many practical systems, and one significant example is the well-known ARCH(autoregressive conditional heteroscedasticity) model in econometrics. The aim of this paper is to consider self-tuning regulators of linear stochastic systems with both unknown parameters and conditional heteroscedastic noises, where the adaptive controller will be designed based on both the weighted least-squares algorithm and the certainty equivalence principle. The authors will show that under some natural conditions on the system structure and the noises with unbounded conditional variances, the closed-loop adaptive control system will be globally stable and the tracking error will be asymptotically optimal.Thus, this paper provides a significant extension of the classical theory on self-tuning regulators with expanded applicability.

High Precision Vertical Deflection Over China Marginal Sea and Global Sea Derived from Multi-Satellite Altimeter

On the basis of gravity field model （EIGEN_CG01C）, together with multi-altimeter data, the improved deflection of the vertical gridded in 2＇×2＇ in China marginal sea and gridded in 5＇×5＇ in the global sea was determined by using the weighted method of along-track least squares, and the accuracy is better than 1.2^# in China marginal sea. As for the quality of the deflection of the vertical, it meets the challenge for the gravity field of high resolution and accuracy, it shows that, compared with the shipboard gravimetry in the sea, the accuracy of the gravity anomalies computed with the marine deflection of the vertical by inverse Vening-Meinesz formula is 7.75 m.s ^-2.

Discrete Time Optimal Adaptive Control for Linear Stochastic Systems

The least-squares （LS） algorithm has been used for system modeling for a long time. Without any excitation conditions, only the convergence rate of the common LS algorithm can be obtained. This paper analyzed the weighted least-squares （WLS） algorithm and described the good properties of the WLS algorithm. The WLS algorithm was then used for adaptive control of linear stochastic systems to show that the linear closed-loop system was globally stable and that the system identification was consistent. Compared to the past optimal adaptive controller, this controller does not impose restricted conditions on the coefficients of the system, such as knowing the first coefficient before the controller. Without any persistent excitation conditions, the analysis shows that, with the regulation of the adaptive control, the closed-loop system was globally stable and the adaptive controller converged to the one-step-ahead optimal controller in some sense.

Statistical distribution based detector response function of a Si(PIN) detector for K_α and K_β X-ray

A semi-empirical detector response function （DRF） model of Si （PIN） detector is proposed to fit element Kα and Kβ X-ray spectra, which is based on statistical distribution analytic （SDA） method. The model for each single peak contains a step function, a Gaussian function and an exponential tail function. Parameters in the model are obtained by weighted nonlinear least-squares fitting method. In the application, six kinds of elements＇ characteristic X-ray spectra are obtained by Si （PIN） detector, and fitted out by the established DRF model. Reduced chi-square values are at the interval of 1.11-1.25. Other applications of the method are also discussed.

Convergence Results of Landweber Iterations for Linear Systems

The Landweber scheme is a method for algebraic image reconstructions. The convergence behavior of the Landweber scheme is of both theoretical and practical importance. Using the diagonalization of matrix, we derive a neat iterative representation formula for the Landweber schemes and consequently establish the convergence conditions of Landweber iteration. This work refines our previous convergence results on the Landweber scheme.

Edgeworth Expansion in Partial Linear Models

In this paper, under some fairly general conditions, a first-order Edgeworth expansion for the standardized statistic of βin partial linear models is given, then a non-residual type of consistent estimation for the error variance is constructed, and finally an Edgeworth expansion for the corresponding studentized version is presented.

Numerical Analysis of Crack-Tip Fields using a Meshless Method in Linear Elastic Materials

In this paper,the Discrete Least Squares Meshless(DLSM)method is developed to determine crack-tip fields.In DLSM,the problem domain and its boundary are discretized by unrelated field nodes used to introduce the shape functions by the moving least-squares(MLS)interpolant.This method aims to minimize the sum of squared residuals of the governing differential equations at any nodal point.Since high-continuity shape functions are used,some necessary treatments,including the visibility criterion,diffraction,and transparency approaches,are employed in the DLSM to introduce strong discontinuities such as cracks.The stress extrapolation and J-integral methods are used to calculate stress intensity factors.Three classic numerical examples using three approaches to defining discontinuities in the irregular distribution of nodal points are considered to investigate the effectiveness of the DLSM method.The numerical tests indicated that the proposed method effectively employed the approaches to defining discontinuities to deal with discontinuous boundaries.It was also demonstrated that the diffraction approach obtained higher accuracy than the other techniques.