| Summary: | 碩士 === 國立海洋大學 === 導航與通訊系碩士班 === 91 === The Kalman filter is a popular estimation tool and can be applied to GPS Navigation design. Although the Kalman filter is the optimal filter but it has some assumptions and limits in use.
The Kalman filtering process contains the state equation and measurement equation. The process and measurement errors are assumed to be zero mean Gaussian white noise and independent each other in the derivation of Kalman filtering. In practice, the pseudorange error is not white. In order to obtain the better accuracy, the non-white noise model will be employed. Under the real error environment, Navigation accuracy based on the conventional Kalman filter can be severely degraded. To resolve the problem, two methods are proposed: (1) decorrelation process [3], (2) singular value decomposition (SVD) based Kalman filter [1][2].
It is assumed that the GPS error can be modeled as a first-order Morkov process [4]. Now we use the two methods to solve the problem. First, decorrelation process, we use preset (estimated) value to reduce the effect of the non-white noise and it would be white noise. The Kalman filter work well after decorrelation. Second, singular value decomposition (SVD) based Kalman filter. The algorithm has a good numerical stability and can handle the problem without any addition transformations.
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