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An improved regularization method for estimating near real-time systematic errors suitable for medium-long GPS baseline solutions


It is well known that the key problem associated with network-based real-time kinematic (RTK) positioning is the estimation of systematic errors of GPS observations, such as residual ionospheric delays, tropospheric delays, and orbit errors, particularly for medium-long baselines. Existing methods dealing with these systematic errors are either not applicable for making estimations in real-time or require additional observations in the computation. In both cases, the result is a difficulty in performing rapid positioning. We have developed a new strategy for estimating the systematic errors for near real-time applications. In this approach, only two epochs of observations are used each time to estimate the parameters. In order to overcome severe ill-conditioned problems of the normal equation, the Tikhonov regularization method is used. We suggest that the regularized matrix be constructed by combining the a priori information of the known coordinates of the reference stations, followed by the determination of the corresponding regularized parameter. A series of systematic errors estimation can be obtained using a session of GPS observations, and the new process can assist in resolving the integer ambiguities of medium-long baselines and in constructing the virtual observations for the virtual reference station. A number of tests using three medium- to long-range baselines (from tens of kilometers to longer than 1000 kilometers) are used to validate the new approach. Test results indicate that the coordinates of three baseline lengths derived are in the order of several centimeters after the systematical errors are successfully removed. Our results demonstrate that the proposed method can effectively estimate systematic errors in the near real-time for medium-long GPS baseline solutions.


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Correspondence to Xiaowen Luo.

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Luo, X., Ou, J., Yuan, Y. et al. An improved regularization method for estimating near real-time systematic errors suitable for medium-long GPS baseline solutions. Earth Planet Sp 60, 793–800 (2008).

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Key words

  • Medium-long baselines
  • systematic errors
  • GPS network RTK positioning
  • ill-conditioned equation
  • Tikhonov regularization