## 5 Conclusions  
This study investigated GNSS/odometer integration with TDCP-designed EKF by utilizing vehicular motion constraint and robust regression for an automotive-grade receiver in an urban environment. The findings show that the phase-smoothing technique improved the state estimation and smoothed out some multipath effects after the TDCP updated the EKF state, but was subject to cycle-slip and NLOS reception. The degradation was apparent during the stationary motion. After the odometer-based aiding (method A) intervened, the aided constraints based on the resultant velocity and zero-assumption velocity of the lateral significantly enhanced the performance, when the state  
Figure 13: CDF for the different GNSS solutions; (**a**) horizontal position error; and (**b**) vertical position error. (The scope of the \(x\)-axis is limited within \(15\,\mathrm{m}\) for better viewing.)estimation reverted to the unsmoothed level due to a cycle slip. Moreover, the additional aiding from method A, including the zero-velocity constraint and the position-fix design, effectively averted the contamination of abnormal signals when the vehicle was stationary. However, the results show that method A had limited effectiveness in the lateral direction and presented a risk of fixing the position at an unsatisfactory level. When robust regression (method B) was added, the combination of method A and method B not only improved the accuracy in the lateral direction and the stationary condition, but also apparently enhanced the contribution of the odometer-aided FDE and DR, which effectively avoided erroneous outputs from the degradation of state estimation and performed seamless positioning, with adequate performance over a short period during a GNSS outage.  
The experimental results show that the GNSS/odometer integration with the proposed methods can satisfy the demand of guiding a vehicle on designated roads with a single-frequency SPP mode in an urban area, without INS aiding. However, the performance of the proposed methods significantly depends on the empirical coefficients by the tuning process, including (21)-(23). An adequate setting for general cases is a time-consuming process. The auxiliary mechanism can include machine learning approaches, such as the random forest algorithm, for improving this situation in the future. Moreover, to mitigate the limitations of the proposed odometer-aided FDE and DR during a heading-change motion, such as a turning maneuver, the aid of z-channel gyro is considerable, and must be investigated in the future.  
Conceptualization, K.-W.C. and Y.-H.L.; methodology, Y.-H.L.; validation, Y.-H.L.; formal analysis, Y.-H.L., L.-T.H., and F.-Y.C.; data curation, Y.-H.L.; writing--original draft preparation, Y.-H.L.; writing--review and editing, K.-W.C., L.-T.H., and F.-Y.C.; visualization, Y.-H.L.; supervision, K.-W.C. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Ministry of Interior under the grant number 109 CCL013C.  
The authors would like to acknowledge the financial support and the project under the Ministry of Interior (MOI). The authors thank the journal editor and anonymous reviewers for their constructive comments on this paper.  
The authors declare no conflict of interest.