Because the real input acceleration cannot be obtained during the error model identification of inertial navigation platform, both the input and output data contain noises. In this case, the conventional regression mo...Because the real input acceleration cannot be obtained during the error model identification of inertial navigation platform, both the input and output data contain noises. In this case, the conventional regression model and the least squares （LS） method will result in bias. Based on the models of inertial navigation platform error and observation error, the errors-in-variables （EV） model and the total least squares （TLS） method axe proposed to identify the error model of the inertial navigation platform. The estimation precision is improved and the result is better than the conventional regression model based LS method. The simulation results illustrate the effectiveness of the proposed method.展开更多
Weighted total least squares(WTLS)have been regarded as the standard tool for the errors-in-variables(EIV)model in which all the elements in the observation vector and the coefficient matrix are contaminated with rand...Weighted total least squares(WTLS)have been regarded as the standard tool for the errors-in-variables(EIV)model in which all the elements in the observation vector and the coefficient matrix are contaminated with random errors.However,in many geodetic applications,some elements are error-free and some random observations appear repeatedly in different positions in the augmented coefficient matrix.It is called the linear structured EIV(LSEIV)model.Two kinds of methods are proposed for the LSEIV model from functional and stochastic modifications.On the one hand,the functional part of the LSEIV model is modified into the errors-in-observations(EIO)model.On the other hand,the stochastic model is modified by applying the Moore-Penrose inverse of the cofactor matrix.The algorithms are derived through the Lagrange multipliers method and linear approximation.The estimation principles and iterative formula of the parameters are proven to be consistent.The first-order approximate variance-covariance matrix(VCM)of the parameters is also derived.A numerical example is given to compare the performances of our proposed three algorithms with the STLS approach.Afterwards,the least squares(LS),total least squares(TLS)and linear structured weighted total least squares(LSWTLS)solutions are compared and the accuracy evaluation formula is proven to be feasible and effective.Finally,the LSWTLS is applied to the field of deformation analysis,which yields a better result than the traditional LS and TLS estimations.展开更多
This paper based on the essay [1], studies in case that replicated observations are available in some experimental points., the parameters estimation of one dimensional linear errors-in-variables (EV) models. Asymptot...This paper based on the essay [1], studies in case that replicated observations are available in some experimental points., the parameters estimation of one dimensional linear errors-in-variables (EV) models. Asymptotic normality is established.展开更多
In case that replicated observations are available in someexperimental points, the parameters estimation of one-dimensional linear errors-in-variables (EV) models was studied. Weak and strong consistency was proved un...In case that replicated observations are available in someexperimental points, the parameters estimation of one-dimensional linear errors-in-variables (EV) models was studied. Weak and strong consistency was proved under mild conditions.展开更多
The input uk and output yk of the multivariate ARMAX system A（x）yk = B（z）uk ＋ C（z）wk are observed with noises： uk^ob△=uk ＋ εk^u and yk^ob △=yk＋ εk^y, where εk^u and εk^y denote the observation noises. ...The input uk and output yk of the multivariate ARMAX system A（x）yk = B（z）uk ＋ C（z）wk are observed with noises： uk^ob△=uk ＋ εk^u and yk^ob △=yk＋ εk^y, where εk^u and εk^y denote the observation noises. Such kind of systems are called errors-in-variables （EIV） systems. In the paper, recursive algorithms based on observations are proposed for estimating coefficients of A（z）, B（z）, C（z）, and the covariance matrix Rw of wk without requiring higher than the second order statistics. The algorithms are convenient for computation and are proved to converge to the system coefficients under reasonable conditions. An illustrative example is provided, and the simulation results are shown to be consistent with the theoretical analysis.展开更多
This paper proposes a novel method to quantify the error of a nominal normalized right graph symbol （NRGS） for an errors- in-variables （EIV） system corrupted with bounded noise. Following an identification framewo...This paper proposes a novel method to quantify the error of a nominal normalized right graph symbol （NRGS） for an errors- in-variables （EIV） system corrupted with bounded noise. Following an identification framework for estimation of a perturbation model set, a worst-case v-gap error bound for the estimated nominal NRGS can be first determined from a priori and a posteriori information on the underlying EIV system. Then, an NRGS perturbation model set can be derived from a close relation between the v-gap metric of two models and H∞-norm of their NRGSs＇ difference. The obtained NRGS perturbation model set paves the way for robust controller design using an H∞ loop-shaping method because it is a standard form of the well-known NCF （normalized coprime factor） perturbation model set. Finally, a numerical simulation is used to demonstrate the effectiveness of the proposed identification method.展开更多
Estimators are presented for the coefficients of the polynomial errors-in-variables (EV) model when replicated observations are taken at some experimental points. These estimators are shown to be strongly consistent u...Estimators are presented for the coefficients of the polynomial errors-in-variables (EV) model when replicated observations are taken at some experimental points. These estimators are shown to be strongly consistent under mild conditions.展开更多
This paper studies the parameter estimation of one dimensional linear errors-in-variables(EV) models in the case that replicated observations are available in some experimental points.Asymptotic normality is establis...This paper studies the parameter estimation of one dimensional linear errors-in-variables(EV) models in the case that replicated observations are available in some experimental points.Asymptotic normality is established under mild conditions, and the parameters entering the asymptotic variance are consistently estimated to render the result useable in construction of large-sample confidence regions.展开更多
A functional model named EIO(Errors-In-Observations) is proposed for general TLS(total least-squares)adjustment. The EIO model only considers the correction of the observation vector, but doesn't consider to corre...A functional model named EIO(Errors-In-Observations) is proposed for general TLS(total least-squares)adjustment. The EIO model only considers the correction of the observation vector, but doesn't consider to correct all elements in the design matrix as the EIV(Errors-In-Variables) model does, furthermore, the dimension of cofactor matrix is much smaller. Iterative algorithms for the parameter estimation and their precise covariance matrix are derived rigorously, and the computation steps are also presented. The proposed approach considers the correction of the observations in the coefficient matrix, and ensures their agreements in every matrix elements. Parameters and corrections can be solved at the same time.An approximate solution and a precise solution of the covariance matrix can be achieved by corresponding algorithms. Applications of EIO model and the proposed algorithms are demonstrated with several examples. The results and comparative studies show that the proposed EIO model and algorithms are feasible and reliable for general adjustment problems.展开更多
While the random errors are a function of Gaussian random variables that are stationary and long dependent, we investigate a partially linear errors-in-variables（EV） model by the wavelet method. Under general condit...While the random errors are a function of Gaussian random variables that are stationary and long dependent, we investigate a partially linear errors-in-variables（EV） model by the wavelet method. Under general conditions, we obtain asymptotic representation of the parametric estimator, and asymptotic distributions and weak convergence rates of the parametric and nonparametric estimators. At last, the validity of the wavelet method is illuminated by a simulation example and a real example.展开更多
When a regression model is applied as an approximation of underlying model of data, the model checking is important and relevant. In this paper, we investigate the lack-of-fit test for a polynomial errorin-variables m...When a regression model is applied as an approximation of underlying model of data, the model checking is important and relevant. In this paper, we investigate the lack-of-fit test for a polynomial errorin-variables model. As the ordinary residuals are biased when there exist measurement errors in covariables, we correct them and then construct a residual-based test of score type. The constructed test is asymptotically chi-squared under null hypotheses. Simulation study shows that the test can maintain the signi.cance level well. The choice of weight functions involved in the test statistic and the related power study are also investigated. The application to two examples is illustrated. The approach can be readily extended to handle more general models.展开更多
This paper proposes an L-two-optimal identification approach to cope with errors-in-variables model （EIVM） identification. With normalized coprime factor model （NCFM） representations, L-two-optimal approximate mod...This paper proposes an L-two-optimal identification approach to cope with errors-in-variables model （EIVM） identification. With normalized coprime factor model （NCFM） representations, L-two-optimal approximate models are derived from the framework of an EIVM according to the kernel and image representations of related signals. Based on the optimal approximate models, the v-gap metric is employed as a minimization criterion to optimize the parameters of a system model, and thus the resulting optimization problem can be solved by linear matrix inequalities （LMIs）. In terms of the optimized system model, the noise model （NM） can be readily obtained by right multiplication of an inner. Compared with other EIVM identification methods, the proposed one has a wider scope of applications because the statistical properties of disturbing noises are not demanded. It is also capable of giving identifiabiUty. Finally, a numerical simulation is used to verify the effectiveness of the proposed method.展开更多
In this paper, we consider the partially nonlinear errors-in-variables models when the non- parametric component is measured with additive error. The profile nonlinear least squares estimator of unknown parameter and ...In this paper, we consider the partially nonlinear errors-in-variables models when the non- parametric component is measured with additive error. The profile nonlinear least squares estimator of unknown parameter and the estimator of nonparametric component are constructed, and their asymptotic properties are derived under general assumptions. Finite sample performances of the proposed statistical inference procedures are illustrated by Monte Carlo simulation studies.展开更多
基金supported by the National Security Major Basic Research Project of China (973-61334).
文摘Because the real input acceleration cannot be obtained during the error model identification of inertial navigation platform, both the input and output data contain noises. In this case, the conventional regression model and the least squares （LS） method will result in bias. Based on the models of inertial navigation platform error and observation error, the errors-in-variables （EV） model and the total least squares （TLS） method axe proposed to identify the error model of the inertial navigation platform. The estimation precision is improved and the result is better than the conventional regression model based LS method. The simulation results illustrate the effectiveness of the proposed method.
基金the financial support of the National Natural Science Foundation of China(Grant No.42074016,42104025,42274057and 41704007)Hunan Provincial Natural Science Foundation of China(Grant No.2021JJ30244)Scientific Research Fund of Hunan Provincial Education Department(Grant No.22B0496)。
文摘Weighted total least squares(WTLS)have been regarded as the standard tool for the errors-in-variables(EIV)model in which all the elements in the observation vector and the coefficient matrix are contaminated with random errors.However,in many geodetic applications,some elements are error-free and some random observations appear repeatedly in different positions in the augmented coefficient matrix.It is called the linear structured EIV(LSEIV)model.Two kinds of methods are proposed for the LSEIV model from functional and stochastic modifications.On the one hand,the functional part of the LSEIV model is modified into the errors-in-observations(EIO)model.On the other hand,the stochastic model is modified by applying the Moore-Penrose inverse of the cofactor matrix.The algorithms are derived through the Lagrange multipliers method and linear approximation.The estimation principles and iterative formula of the parameters are proven to be consistent.The first-order approximate variance-covariance matrix(VCM)of the parameters is also derived.A numerical example is given to compare the performances of our proposed three algorithms with the STLS approach.Afterwards,the least squares(LS),total least squares(TLS)and linear structured weighted total least squares(LSWTLS)solutions are compared and the accuracy evaluation formula is proven to be feasible and effective.Finally,the LSWTLS is applied to the field of deformation analysis,which yields a better result than the traditional LS and TLS estimations.
基金the National Natural Science Foundation of China (Grant No. 19631040)
文摘This paper based on the essay [1], studies in case that replicated observations are available in some experimental points., the parameters estimation of one dimensional linear errors-in-variables (EV) models. Asymptotic normality is established.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 19631040) .
文摘In case that replicated observations are available in someexperimental points, the parameters estimation of one-dimensional linear errors-in-variables (EV) models was studied. Weak and strong consistency was proved under mild conditions.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 60821091, 60874001)the National Laboratory of Space Intelligent Control
文摘The input uk and output yk of the multivariate ARMAX system A（x）yk = B（z）uk ＋ C（z）wk are observed with noises： uk^ob△=uk ＋ εk^u and yk^ob △=yk＋ εk^y, where εk^u and εk^y denote the observation noises. Such kind of systems are called errors-in-variables （EIV） systems. In the paper, recursive algorithms based on observations are proposed for estimating coefficients of A（z）, B（z）, C（z）, and the covariance matrix Rw of wk without requiring higher than the second order statistics. The algorithms are convenient for computation and are proved to converge to the system coefficients under reasonable conditions. An illustrative example is provided, and the simulation results are shown to be consistent with the theoretical analysis.
基金supported in part by the National Natural Science Foundation of China(Nos.61203119,61304153)the Key Program of Tianjin Natural Science Foundation,China(No.14JCZDJC36300)the Tianjin University of Technology and Education funded project(No.RC14-48)
文摘This paper proposes a novel method to quantify the error of a nominal normalized right graph symbol （NRGS） for an errors- in-variables （EIV） system corrupted with bounded noise. Following an identification framework for estimation of a perturbation model set, a worst-case v-gap error bound for the estimated nominal NRGS can be first determined from a priori and a posteriori information on the underlying EIV system. Then, an NRGS perturbation model set can be derived from a close relation between the v-gap metric of two models and H∞-norm of their NRGSs＇ difference. The obtained NRGS perturbation model set paves the way for robust controller design using an H∞ loop-shaping method because it is a standard form of the well-known NCF （normalized coprime factor） perturbation model set. Finally, a numerical simulation is used to demonstrate the effectiveness of the proposed identification method.
基金This work was supported by the National Natural Science Foundation of China (Grant No.19631040).
文摘Estimators are presented for the coefficients of the polynomial errors-in-variables (EV) model when replicated observations are taken at some experimental points. These estimators are shown to be strongly consistent under mild conditions.
基金Project supported by the National Natural Science Foundation of China (No. 19631040).
文摘This paper studies the parameter estimation of one dimensional linear errors-in-variables(EV) models in the case that replicated observations are available in some experimental points.Asymptotic normality is established under mild conditions, and the parameters entering the asymptotic variance are consistently estimated to render the result useable in construction of large-sample confidence regions.
基金supported by the Open Fund of Engineering laboratory of Spatial Information Technology of Highway Geological Disaster Early Warning in Hunan Province(Changsha University of Science & Technology, Grant No:KFJ150602)Hunan Province Science and Technology Program Funded Projects, China (Grant No:2015NK3035)
文摘A functional model named EIO(Errors-In-Observations) is proposed for general TLS(total least-squares)adjustment. The EIO model only considers the correction of the observation vector, but doesn't consider to correct all elements in the design matrix as the EIV(Errors-In-Variables) model does, furthermore, the dimension of cofactor matrix is much smaller. Iterative algorithms for the parameter estimation and their precise covariance matrix are derived rigorously, and the computation steps are also presented. The proposed approach considers the correction of the observations in the coefficient matrix, and ensures their agreements in every matrix elements. Parameters and corrections can be solved at the same time.An approximate solution and a precise solution of the covariance matrix can be achieved by corresponding algorithms. Applications of EIO model and the proposed algorithms are demonstrated with several examples. The results and comparative studies show that the proposed EIO model and algorithms are feasible and reliable for general adjustment problems.
基金Supported by the National Natural Science Foundation of China(No.11471105,11471223)Scientific Research Item of Education Office,Hubei(No.D20172501)
文摘While the random errors are a function of Gaussian random variables that are stationary and long dependent, we investigate a partially linear errors-in-variables（EV） model by the wavelet method. Under general conditions, we obtain asymptotic representation of the parametric estimator, and asymptotic distributions and weak convergence rates of the parametric and nonparametric estimators. At last, the validity of the wavelet method is illuminated by a simulation example and a real example.
基金a CRCG Grant of the University of Hong Kong and a RGC Grant of Hong Kong,HKSAR,ChinaNational Natural Science Foundation of China (No.10071009).
文摘When a regression model is applied as an approximation of underlying model of data, the model checking is important and relevant. In this paper, we investigate the lack-of-fit test for a polynomial errorin-variables model. As the ordinary residuals are biased when there exist measurement errors in covariables, we correct them and then construct a residual-based test of score type. The constructed test is asymptotically chi-squared under null hypotheses. Simulation study shows that the test can maintain the signi.cance level well. The choice of weight functions involved in the test statistic and the related power study are also investigated. The application to two examples is illustrated. The approach can be readily extended to handle more general models.
文摘This paper proposes an L-two-optimal identification approach to cope with errors-in-variables model （EIVM） identification. With normalized coprime factor model （NCFM） representations, L-two-optimal approximate models are derived from the framework of an EIVM according to the kernel and image representations of related signals. Based on the optimal approximate models, the v-gap metric is employed as a minimization criterion to optimize the parameters of a system model, and thus the resulting optimization problem can be solved by linear matrix inequalities （LMIs）. In terms of the optimized system model, the noise model （NM） can be readily obtained by right multiplication of an inner. Compared with other EIVM identification methods, the proposed one has a wider scope of applications because the statistical properties of disturbing noises are not demanded. It is also capable of giving identifiabiUty. Finally, a numerical simulation is used to verify the effectiveness of the proposed method.
基金Supported by National Natural Science Foundation of China(Grant Nos.11101014 and 11002005)the Beijing Natural Science Foundation(Grant No.1142002)+2 种基金the Doctoral Fund of Innovation of Beijing Universityof Technologythe Science and Technology Project of Beijing Municipal Education Commission(Grant No.KM201410005010)the Training Programme Foundation for the Beijing Municipal Excellent Talents(GrantNo.2013D005007000005)
文摘In this paper, we consider the partially nonlinear errors-in-variables models when the non- parametric component is measured with additive error. The profile nonlinear least squares estimator of unknown parameter and the estimator of nonparametric component are constructed, and their asymptotic properties are derived under general assumptions. Finite sample performances of the proposed statistical inference procedures are illustrated by Monte Carlo simulation studies.
