According to the filtering formula deduced by the generalized least squares method and the fundamental principle of Helmert variance estimation, a new variance estimation formula with forecast residual vector is deduced.

For independent and heteroscedastic errors generated by increasing from the independent, identically distributed errors, according to the Bahadur-type linear representation of M-estimate of unknowns, this paper derives the Bahadur-type linear representation of the basic vector including the observational vector, the residual vector, the estimated vector of the unknowns and the adjusted observational vector.

For L_q-norm estimate with errors being normally distributed, the covariance matrices between the residual vector and the estimated vector of the unknown parameters, as well as the adjusted observational vector are not zero.

After a brief review of Sage adaptive filtering,the relations of analytical expressions and covariance matrices between the basic random vector,such as residual vector,innovation vector and correction vector of predicted state,are derived and discussed.

After a brief introduction of sage adaptive filtering, the shortcomings of covariance matrix adaptive estimation based on the residual vectors, innovation vectors and correction vectors of kinematic state are analyzed. Then, the improved method of sage adaptive filtering is proposed in this paper.

First of all, signal vector and signal matrix of Hilbert space are defined,and normalized residual vecrtors and partial correlation coefficient are described.

Except the parameter estimation (1), the other four items (2)~(5) all require that the variance-covariance matrix of the basic vector including the observations, the estimated parameters, the residuals and the adjustments of the observations are explicit and computable.

By contrast, BFDF method is of sim- ple structure, design the advantage such as being clear of the step, it is stupid and excellent that the incomplete difference vector quantity produced from BFDF has the stronger one to unknown introduction, to the carrying out device, the component and sensor trouble are all very sensitive, the vector quantity of incomplete difference has different directions to different troubles, the easy trou- ble is isolated.

By constructing a model of normal actuator,and comparing its analytic data with the output data of line displacement sensors,the actuator dispersion vectors are obtained,then the method of DTW is adopted to match the existent samples of fault for assuring and differentiating the fault.

For varions damage types,the displacement mode curvature mode and residual mode force vector were sensitive to damage ocation of the damage in a RCB,the absolute remaining difference vector(ARDV) enables to used to detect the local damages in a RCB.

This paper derives the complete Bahadur-type linear representation of the basic vector including the residual vector and the adjusted vector of the observations for the L1-norm estimation.

Two optimal adaptive factors are derived, one of which is deduced by requiring that the estimated covariance matrix of the predicted residual vector equals the corresponding theoretical one.

However with the exception of Gauss-Seidel iteration the residual vector ‖Axk-b‖ is of order ζ ‖A‖2 ‖A-1‖ ‖α‖ and hence the remaining three iterations arenot well-behaved.

In addition, through PCA we also obtained a time course of changes common to all wavelengths-the residual vector, corresponding to non-specific spectral changes due to preparation movement or mitochondrial swelling.

The scheme involves using the current residual vector to update the lower frequency limit during integration and to improve the accuracy of the converged solution.

The RNLAR is used to design primary residual vectors (PRV), which are highly sensitive to the faults and less sensitive to MPM and process disturbance, for sensor and actuator fault detection.

The PRVs are then transformed into a set of structured residual vectors (SRV) for fault isolation.

Considering different characteristics of the wave amplitude, a method of "non-identical weighted mean" is developed for computing the averaged observed residual and remaining residual vectors at each station.

The corresponding tangent stiffness matrices and residual vectors of the equations of motion are presented.

If? is the result of smoothingY in the least square sense, thenE can be split into two residual vectors:E=? - F - (? - Y).

In this paper, the Householder orthogonal transform algorithm is used to solve the problems of power system state estimation. The orthogonal transform is directly conducted for the weighted Jacobi matrix and the weighted residual vector of the measurement equations by using the Householder transform matrix. This algorithm reduces the condition number of using normal equation algorithm, raises the numerical stabillty of the solution, and is fit to solve the state estimation problem of a power systems which operates...

In this paper, the Householder orthogonal transform algorithm is used to solve the problems of power system state estimation. The orthogonal transform is directly conducted for the weighted Jacobi matrix and the weighted residual vector of the measurement equations by using the Householder transform matrix. This algorithm reduces the condition number of using normal equation algorithm, raises the numerical stabillty of the solution, and is fit to solve the state estimation problem of a power systems which operates under a morbid condition.

The controlled random search method is used for solving constrained nonlinear optimization problems.In this method several search points in parameter space are yielded to produce a centroid,instead of a single estimate,in order to get the solution more closely approching the global minimum of the sophisticated multivariate functions.Any norm of residuals can be used as objective function.No derivatives are employed and no initial guess is required.The method discussed converges rapidly and stea-dily.So far as...

The controlled random search method is used for solving constrained nonlinear optimization problems.In this method several search points in parameter space are yielded to produce a centroid,instead of a single estimate,in order to get the solution more closely approching the global minimum of the sophisticated multivariate functions.Any norm of residuals can be used as objective function.No derivatives are employed and no initial guess is required.The method discussed converges rapidly and stea-dily.So far as anti-disturbance capacity and convergence rate are ccncerned,the CRS method is muchbetter than Marquardt method and can be applied to interpretate magnetic and gravity anomalies genera-ted by a 2-D or 3-D body as well as to the inversion of density discontinuity interface data.

A new RLS lattice filter, which is based on the normalized sliding window covariance(NSWC)algorithm,is presented. And with the help of the filter, a novel fault detector is constructed. First of all, signal vector and signal matrix of Hilbert space are defined,and normalized residual vecrtors and partial correlation coefficient are described. Then,theequations of the filter algorithm are derived by use of the orthogonal projection approach invector space. By testing whiteness of the forward or backward prediction...

A new RLS lattice filter, which is based on the normalized sliding window covariance(NSWC)algorithm,is presented. And with the help of the filter, a novel fault detector is constructed. First of all, signal vector and signal matrix of Hilbert space are defined,and normalized residual vecrtors and partial correlation coefficient are described. Then,theequations of the filter algorithm are derived by use of the orthogonal projection approach invector space. By testing whiteness of the forward or backward prediction error, real timefault detection is carried out. Finally, simulation example is given to justify the effectivenessof this fault detection methodology. Simulation results show the fault detctor has many advantages such as the monitored system mathmatical model unnecessary, less computationand lower probability of wrongly alarming.