Single-frequency GPS/BeiDou navigation satellite system (BDS) real-time kinematic (RTK) and inertial navigation system (INS) integration has wide range of application prospects due to the global deployment of GPS along with the rapid development of BDS. The instantaneous single-frequency ambiguity resolution will be significantly improved by the combined GPS/BDS and INS configuration. Owing to road conditions and an inertial measurement unit (IMU) on the carrier not being rigidly mounted, biased measurements in the IMU will occasionally emerge, leading to biased INS predictions. However, bias or inaccuracy from INS-predicted position can prevent the successful resolution of the whole set of ambiguities. This paper proposes the use of a positional polynomial fitting (PPF) constraint to compensate for the epochs with abnormal INS predictions. The aid from PPF is provided at two levels, i.e., at the ambiguity resolution (AR) level and at the solution level. In order to further increase the availability of ambiguity-fixed positioning solutions, a partial ambiguity resolution (PAR) strategy is introduced when full ambiguity resolution (FAR) fails. A field vehicular experiment was performed to show the validity of the proposed PPF-aided method by comparing different schemes regarding different INS-aided satellite system configurations, different AR strategies, and whether the PPF-aided method was adopted. The results show that the most attractive scheme is to combine the PAR with the PPF-aided dual-constellation and INS integration.

To address the challenges of GNSS signal blockages and severe multipath effects in complex urban environments, this paper proposes a tightly coupled precise point positioning (PPP)/inertial navigation system (INS) integration method based on an adaptive robust Kalman filter (ARKF) for smartphones. The proposed method integrates a robust estimation module based on the IGG-III weight function and an adaptive factor derived from vehicle dynamic intensity and geometric precision indicators, to mitigate observation outliers and dynamic model errors. To evaluate the positioning performance of this algorithm, two typical vehicle experiments based on the GNSS and inertial measurement unit (IMU) chipsets of the Xiaomi Mi 8, as well as an external H30 IMU, were conducted. Experimental results show that in the urban expressway environment, the horizontal root mean square (RMS) error of the loosely coupled PPP/INS solution was reduced by 74.17% compared with the conventional PPP solution, while the maximum horizontal positioning error of the tightly coupled PPP/INS solution was reduced by 44.82% compared with the loosely coupled PPP/INS solution. In the complex urban road and tunnel environments, the proposed ARKF-based tightly coupled PPP/INS method achieved a 36.79% reduction in horizontal RMS error compared with the tightly coupled PPP/INS solution based on the standard extended Kalman filter (EKF) and demonstrated more robust positioning performance in the tunnel.