Abstract
The high noise of pseudorange and the ambiguity of carrier phase observation restrain the GNSS (Global Navigation Satellite System) application in military, industrial, and agricultural, to name a few. Thus, it is crucial for GNSS technology to integrate the pseudorange and carrier phase observations. However, the traditional method proposed by Hatch has obtained only a low convergence speed and precision. For higher convergence speed and precision of the smoothed pseudorange, aiming to improve positioning accuracy and expand the application of GNSS, we introduced a new method named MELS (Multi-Epochs Least-Squares) that considered the cross-correlation of the estimating parameters inspired by DELS (Double-Epochs Least-Square). In this study, the ionospheric delay was compensated, and so its impact was limited to the performance of the filters, and then exploited the various filters to integrate carrier phase observation and pseudorange. We compared the various types of Hatch’s filter and LS (Least-Square) methods using simulation datasets, which confirmed that the types of LS method provided a smaller residual error and a faster convergence speed than Hatch’s method under various precisions of raw pseudorange. The experimental results from the measured GNSS data showed that LS methods provided better performance than Hatch’s methods at E and U directions and a lower accuracy at N direction. Nevertheless, the types of LS method and Hatch’s methods improved about 12% and 9–10% at the 3D direction, respectively, which illustrated the accumulating improvement at the enhanced directions was more than the decreased direction, proving that the types of LS method resulted to better performance than the Hatch’s filters. Additionally, the curve of residual and precision based on various LS methods illustrated that the MELS only provided a millimeter accuracy difference compared with DELS, which was proved by the simulated and measured GNSS datasets.
Highlights
The GNSS (Global Navigation Satellite System) technology has been widely used for precision agriculture, time synchronization and delivery, and deformation monitoring, to name a few, the systems are still constructing and upgrading
The types of LS method and Hatch’s methods improved about 12% and 9–10% at the 3D direction, respectively, which illustrated the accumulating accuracy improvement at the E and U directions comparing LS method with Hatch’s methods was more than the decreased at the N direction, proving that the types of LS method could obtain a better performance than Hatch’s method
As we compared the different types of LS methods, the TELS method could provide a little better performance than DELS while the QELS could provide a little higher positioning accuracy than TELS, proving that the LS methods based on multi-epochs only provided a small difference with several millimeters corresponding to several percentage points, which is caused by the self-correlation of the constructed observation matrix
Summary
The GNSS (Global Navigation Satellite System) technology has been widely used for precision agriculture, time synchronization and delivery, and deformation monitoring, to name a few, the systems are still constructing and upgrading. Most of the scholars have demonstrated their methodology with an indirect method in lights of positioning results because it is hard to provide true pseudorange, and thereby Qian et al [24] simulated GNSS observations by adding diverse random error to the real satellite-to-receiver distance They obtained a higher precision smoothed pseudorange than Hatch’s smoother by employing the recursive LS, which is only used for an ionospheric removed GNSS. To counteract the influence of ionospheric delay and improve the precision of smoothed pseudorange, Chen [25] et al exploited a similar solution to the recursive LS [24] to integrate the pseudorange and TDCP (Time Difference Carrier Phase), which divided GNSS measurements into dispersion and non-dispersion term They exposed the merit according to the residual error and positioning accuracy, which lacked analyzing convergence speed and precision, and application scope. The effectiveness of the developed method was proved through the analysis of simulated dataset and field measurements and, was discussed the merit of the presented method and its contribution to body knowledge of the carrier phase smoothing pseudorange technology
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