# A general weighted total Kalman filter algorithm with numerical evaluation

@article{Mahboub2016AGW, title={A general weighted total Kalman filter algorithm with numerical evaluation}, author={Vahid Mahboub and Mohammad Saadatseresht and Alireza Azmoudeh Ardalan}, journal={Studia Geophysica et Geodaetica}, year={2016}, volume={61}, pages={19-34} }

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 dynamic errors-in-variables (DEIV… Expand

#### 13 Citations

A robust total Kalman filter algorithm with numerical evaluation

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The RTKF improves the precision of a pseudorange differential positioning compared with KF and robust Kalman filter (RKF) algorithms regardless the observation model has outliers or not in this empirical example. Expand

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Abstract. Here we present a review on a new family of Kalman filter algorithms which recently developed for integrated navigation. In particular it is useful for vision based navigation due to the… Expand

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An unscented total Kalman filter (UTKF) estimator with nonlinear dynamic errors-in-variables (DEIV) model is derived based on correlational inference and is a Jacobian matrix free alternative to the existing TKF estimators. Expand

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- Acta Geodaetica et Geophysica
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In this paper, a nonlinear dynamic errors-in-variables (DEIV) model which considers all of the random errors in both system equations and observation equations is presented. The nonlinear DEIV model… Expand

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A constrained integrated total Kalman filter algorithm is developed. It considers a quadratic constraint which may appear in some problems of integrated direct geo-referencing in particular when INS… Expand

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- Acta Geodaetica et Geophysica
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We noticed that if INS data is used as system equations of a Kalman filter algorithm for integrated direct geo-referencing, one encounters with a dynamic errors-in-variables (DEIV) model. Although… Expand

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A constrained extended Kalman filter (CEKF) based on least-squares variance component estimation (LS-VCE) is generally developed by condition equations since the proper prediction of dispersion… Expand

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A robust Kalman filter algorithm is proposed to solve nonlinear errors-in-variables dynamic problems in the presence of outliers and can consider the neglected random unknowns of the functional model of the dynamic problem which gives an added advantage over the previous Kalman filters. Expand

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Three constrained extended Kalman filters (CEKF) are developed by making use of condition equations which equations allows one to predict directly the residuals of all variables to deal with problems which encounter with raw GPS data. Expand

An iterated reweighting total least squares algorithm formulated by standard least-squares theory

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If both the coefficient matrix and the observation vector are affected by noise, a total least-squares algorithm should be applied to obtain the solution. However, if they are also contaminated by… Expand

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