Mapping function (MF) converts the line-of-sight slant total electron content (STEC) into the vertical total electron content (VTEC), and vice versa. In an MF, an essential parameter is the ionospheric effective height. However, the inhomogeneous ionosphere makes this height vary spatially and temporally, meaning it is not a global constant. In the paper, we review several mapping functions and propose a mapping function that utilizes the ionospheric varying height (IVH). We investigate impacts of the IVH on mapping errors and on the ionospheric modeling, as well as on the satellite and receiver differential code biases (DCBs). Our analysis results indicate that the mapping errors using IVH are smaller than those from the fixed height of 450 km. The integral height achieves smaller mapping errors than using a fixed height of 450 km, an improvement of about 8% when compared with the fixed height of 450 km. And 35% smaller mapping errors were found using HmF2 at the lower latitude. Also, the effects of IVH on the satellite DCBs are about 0.1 ns, and larger impacts on the receiver DCBs at 1.0 ns.

P ³ -LINS, a navigation system tightly coupling PPP-GNSS/INS/LiDAR with the DRANSAC-RAIM and the DICP as its initialization procedure, is established for accurate and reliable positioning in urban environments. The position initialization of P ³ -LINS is completed by the static PPP with the DRANSAC-RAIM algorithm. The yaw is initialized through the proposed DICP algorithm which relies on the quadratic constraint least-squares problem built by Doppler speed, LiDAR-SLAM poses, and GNSS positions. After dealing with the initialization issue, the fusion framework of P ³ -LINS is constructed to handle the heterogeneous sensor data spatial-temporal consistency problem with the three phases EKF-based estimator. The experiments show the initialization of P ³ -LINS achieves decimeter-level positioning error in minutes when keeping static and tenths of a degree level yaw error after the vehicle moves a few seconds on the UrbanLoco. Moreover, P ³ -LINS outperforms the compared state-of-the-art methods in terms of positioning accuracy and reliability on both public datasets and self-collected datasets.

Differential Code Biases (DCBs) are much more relevant when GNSS data processing with code measurements is involved, such as in ionospheric sensing, positioning, and timing. The current approach to estimate DCBs is based on carrier-phase smoothed code observations together with ionospheric modeling. A limiting factor of the method is the effect of the leveling errors from the smoothing process on the DCB estimate. To reduce the leveling errors, a new DCB estimation method based on an Uncombined Precise Point Positioning (UPPP) model is proposed. A month's data from a global network in a high solar activity year from May 1 to 31, 2014 are processed to validate the method. The results show that most satellite DCB estimates are found to be more stable than when using the smoothed code method. The improvement can be up to about 0.22 ns. The stability and accuracy of the receiver DCB estimates is also enhanced. Copyright © 2017 Institute of Navigation