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《Acta Geodaetica Et Cartographic Sinica》 2002-S1
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Adaptive Filtering with Constraint for GPS Positioning

HU Cong wei ,LIU Da jie, YAO Lian bi (Department of Surveying and Geo informatics,Tongji University,Shanghai 200092,China)  
This paper has introduced the adaptive Kalman filtering with constraint. The recursive algorithm with constraint has been deduced without eliminating some of state parameters and it shows that only a small modification is needed for the prediction calculation compared with the conventional recursive filtering algorithm. The adaptive filtering with fading memory algorithm will be presented and demonstrates that it can be used almost in the same way as in the conventional filtering. It is assumed in conventional Kalman filtering that a priori statistical information about dynamic noise and observation noise are determined beforehand and they will maintain unchanged during the process of filtering. When such assumption is unreasonable or is changed, i.e. the sudden change of the state of the dynamic system, the filtering system will become unstable or diverging. In this case, the conventional Kalman filtering can not meet with the expected purpose and the adaptive filtering has to be adopted. For the filtering with constraint condition the same problem will also exist. There are many kinds of adaptive filtering algorithms. From a numeric test of DGPS with a fixed distance as a constraint condition, it has been showed that filtering divergence will also be caused by the acceleration of the moving object and can be overcome with adaptive method. Compared with conventional filtering, the accuracy improvement in north and east are about 10% and 0% respectively with constraint , and 26% and 13% respectively with constraint adaptive filtering. The accuracy improvement depends on the type and number of constraint condition. Both indicate that the constraint condition will contribute to the accuracy improvement of the filtering. As a result ,this method can be applied in the GPS navigation and attitude determination with Kalman filtering by utilizing constraint information such as DR data ,fixed distance among the antennas and some other constraint.
【Fund】: 中国科学院动力大地测量学开放研究实验室资助项目 (L98 0 2 )
【CateGory Index】: P228.4
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