The Unscented Kalman Filter (UKF) is a well-known nonlinear state estimation method. It shows superior performance at nonlinear estimation compared to the Extended Kalman Filter (EKF). This paper is devoted to an investigation between UKF and EKF with different feedback control modes in vehicle navigation. Theoretical formulation, simulation and field tests have been carried out to compare the performance of UKF and EKF. The simulation and test results demonstrate that the estimated state of a UKF relies on the measurements and is less sensitive to historical model information. The results also indicate that UKF has benefits for prototype model design due to avoidance of calculation of a Jacobian matrix. EKF, however, is more computationally efficient and more stable.

Factor graph optimization has been widely used for state estimation in robotic SLAM community. Extensive algorithms have been proposed for camera/LiDAR/INS based SLAM. However, GNSS positioning based on factor graph optimization is limited, which prevents the introduction of high precise GNSS to robotic SLAM community. The current implementations are focused on pseudorange or RTK based positioning. PPP with ambiguity resolution (AR) is the state-of-the-art positioning technique for the past decade. Therefore, the PPP AR based on factor graph optimization is proposed, in which the pseudorange and carrier phases factors are constructed from the error equations of raw observations, while the ambiguity resolution factor is built from the ambiguity resolution. Results from 80 MGEX stations show that the average accuracy of static PPP is improved from 1.25, 0.61 and 2.29 cm to 0.81, 0.5 and 2.1 cm, corresponding to improvements of 35.1%, 18.7% and 8.7% in east, north, and up directions, respectively. As for kinematic PPP, the average accuracy is improved from 2.62, 2.21 and 5.8 cm to 1.64, 1.74 and 5.37 cm, corresponding to improvements of 37.5%, 21.6% and 7.4% in east, north, and up directions, respectively. The kinematic PPP was also verified with real-world data collected from a moving vehicle. After the first ambiguity fixing, the accuracy of PPP is improved from 3.7, 2.1 and 10.1 cm to 1.6, 2.0 and 9.0 cm for east, north and up component, respectively, corresponding to improvements of 32%, 5% and 11%. The above results confirm the efficiency of the proposed algorithm.

BeiDou Global Navigation Satellite System (BDS-3) provides a regional Precise Point Positioning (PPP) service, called PPP-B2b, for users in China and surrounding areas through B2b signal transmitted from its three geostationary earth orbit (GEO) satellites. The information broadcasted by the B2b signal include satellite orbit corrections, satellite clock offset corrections, and differential code bias (DCB) corrections of BDS-3 satellites. In this study, the accuracies of PPP-B2b corrections along with real-time PPP performance are comprehensively evaluated referenced to precise orbit and clock products from GFZ and the precise DCB products from CAS. The result indicates that the accuracy of the BDS-3 broadcast orbit is similar to that of the PPP-B2b real-time orbit. The PPP-B2b clock offset correction improved the satellite clock offset precision of the BDS-3 broadcast ephemeris. The Signal-in-Space Range Error (SISRE) of broadcast ephemeris and PPP-B2b are calculated, which are 0.536 and 1.24 m, respectively. The large SISRE value of PPP-B2b is caused by the satellite-specified systematic bias to IGS final products. The positioning performance evaluation of real-time PPP with B2b service is carried out and compared with the real-time product provided by Wuhan University (WHU) based on the eight IGS MGEX stations in China and surrounding countries. The positioning accuracy of static positioning mode with PPP-B2b service achieved centimeter-level accuracy in the selected station, and that of kinematic positioning mode achieved decimeter-level accuracy. The availability rate of PPP-B2b corrections in the surrounding area of China, however, degrades from 88.76% to 60.91% in the selected stations. The accuracy of the PPP solution using PPP-B2b correction is better than that of using WHU real-time product within China. The positioning performance of stations located at the boundary of the PPP-B2b service area, however, is affected by the number of PPP-B2b available satellites. The positioning accuracy in kinematic positioning mode is worse than that of using WHU real-time precise product.

The global navigation satellite system (GNSS) and inertial navigation system (INS) integrated navigation system have been widely used in Intelligent Transportation Systems (ITSs). However, the positioning error of integrated navigation systems is rapidly divergent when GNSS outages occur. Motion constraint and back propagation (BP) neural networks can provide additional knowledge to solve this issue. However, the predictions of a neural network have outliers and motion constraint is difficult to adapt according to the motion states of vehicles and boats. Therefore, this paper fused a BP neural network with motion constraints, and proposed a motion-constrained GNSS/INS integrated navigation method based on a BP neural network (MC-BP method). The pseudo-measurement of the GNSS was predicted using a fitting model trained by the BP neural network. At the same time, the prediction outliers were detected and corrected using motion constraint. To assess the performance of the proposed method, simulated and real data experiments were conducted with a vehicle on land and a boat offshore. A classical GNSS/INS integration algorithm, a motion-constrained GNSS/INS algorithm, and the proposed method were compared through data processing. Compared with the classical GNSS/INS integration algorithm and the motion-constrained GNSS/INS algorithm, the positioning accuracies of the proposed method were improved by 90% and 64%, respectively, in the vehicle land experiment. Similar performances were found in the offshore boat experiment. Using the proposed MC-BP method, improved meter-level-positioning results can be achieved with the GNSS/INS integration algorithm when GNSS outages occur.

Global Navigation Satellite Systems (GNSS) integrated with Inertial Navigation System (INS) have been widely applied in many Intelligent Transport Systems. At present, integrating GNSS, MEMS, on-board controller area network sensors and vehicle motion constraint information is the most practical and low-cost vehicle multi-fusion navigation scheme when GNSS outages. It is especially true when using three-dimensional velocity from nonholonomic constraints (NHC) and odometer (OD). However, the GNSS/INS/OD/NHC integration has the problem of the inaccuracy lateral velocity constraint parameters. To overcome this problem, a BP neural network based GNSS/INS/OD/NHC adaptive integrated navigation method considering the vehicle motion state is proposed in this paper. The relationship between the forward velocity, the heading angular velocity and the lateral velocity is analyzed and considered when the NHC lateral velocity constraint modeling is established by using the BP neural network. To assess the performance of this method, three sets of real land vehicle data are tested with intentionally GNSS signal interruption at different vehicle states. The performances of classic INS/NHC model, INS/OD/NHC integration and the proposed method are compared respectively. Experimental results show: The mean error and RMSE of the lateral velocity predicted by the proposed method is 0.007m/s and 0.049m/s. The mean 3D RMSE of the positioning errors and the velocity errors of the proposed method is 1.515m and 0.182m/s respectively, which are improved by 54.86% and 44.85% compared with that of the classic INS/OD/NHC integration.