An applicable algorithm for Total Kalman Filter (TKF) approach is proposed. Meanwhile, we extend it to the case in which we can consider arbitrary weight matrixes for the observation vector, the random design matrix a...
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An applicable algorithm for Total Kalman Filter (TKF) approach is proposed. Meanwhile, we extend it to the case in which we can consider arbitrary weight matrixes for the observation vector, the random design matrix and possible correlation between them. Also the updated dispersion matrix of the predicted unknown is given. This approach makes use of condition equations and straightforward variance propagation rules. It is applicable to data fusion within a dynamicerrors-in-variables (DEIV) model, which usually appears in the determination of the position and attitude of mobile sensors. Then, we apply for the first time the TKF algorithm and its extended version named WTKF to a DEIV model and compare the results. The results show the efficiency of the proposed WTKF algorithm. In particular in the case of large weights, WTKF shows approximately 25% improvement in contrast to TKF approach.
A linear multivariate measurement error model AX = B is considered. The errors in [A B] are row-wise finite dependent, and within each row, the errors may be correlated. Some of the columns may be observed without err...
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A linear multivariate measurement error model AX = B is considered. The errors in [A B] are row-wise finite dependent, and within each row, the errors may be correlated. Some of the columns may be observed without errors, and in addition the error covariance matrix may differ from row to row. The columns of the error matrix are united into two uncorrelated blocks, and in each block, the total covariance structure is supposed to be known up to a corresponding scalar factor. Moreover the row data are clustered into two groups, according to the behavior of the rows of true A matrix. The change point is unknown and estimated in the paper. After that, based on the method of corrected objective function, strongly consistent estimators of the scalar factors and X are constructed, as the numbers of rows in the clusters tend to infinity. Since Toeplitz/Hankel structure is allowed, the results are applicable to system identification, with a change point in the input data. (c) 2007 Elsevier B.V. All rights reserved.
The structured total least squares estimator, defined via a constrained optimization problem, is a generalization of the total least squares estimator when the data matrix and the applied correction satisfy given stru...
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The structured total least squares estimator, defined via a constrained optimization problem, is a generalization of the total least squares estimator when the data matrix and the applied correction satisfy given structural constraints. In the paper, an affine structure with additional assumptions is considered. In particular, Toeplitz and Hankel structured, noise free and unstructured blocks are allowed simultaneously in the augmented data matrix. An equivalent optimization problem is derived that has as decision variables only the estimated parameters. The cost function of the equivalent problem is used to prove consistency of the structured total least squares estimator. The results for the general affine structured multivariate model are illustrated by examples of special models. Modification of the results for block-Hankel/Toeplitz structures is also given. As a by-product of the analysis of the cost function, an iterative algorithm for the computation of the structured total least squares estimator is proposed. (c) 2004 Elsevier B.V. All rights reserved.
We establish the equivalence between the optimal least-squares state estimator for a linear time-invariant dynamic system with noise corrupted input and output, and an appropriately modi£ed Kalman £lter. The...
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We establish the equivalence between the optimal least-squares state estimator for a linear time-invariant dynamic system with noise corrupted input and output, and an appropriately modi£ed Kalman £lter. The approach used is algebraic and the result shows that the noisy input/output £ltering problem is not fundamentally different from the classical Kalman £ltering problem. The result is illustrated with a simulation example.
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