Global positioning system (GPS) has been widely used to estimate the absolute position of outdoor vehicles. Global positioning system and inertial measurement unit (IMU) can be integrated to deliver an enhanced effect over the individual system. GPS/IMU navigation solution that utilizes time-differenced carrier phase (TDCP) as observation can achieve high-precision positioning. The traditional TDCP-GPS/IMU navigation methods are compromised by the loss of constraints, especially when cycle slip occurs. This article proposes an optimal time difference-based TDCP-GPS/IMU navigation using graph optimization. Different from current methods, an optimal time difference strategy is designed to formulate integer-free constraints that span multiple epochs in a time window. Each satellite can be fully used to restrain the accumulation errors even though cycle slip happens. Then, the integer-free constraints are fused with relative constraints from IMU preintegration and TDCP between two successive epochs using graph optimization. Field tests are carried out to validate the performance of the proposed method. The results show that the proposed method can make the most of window length constraints to improve the positioning performance compared with traditional methods.

Multi-sensor integrated navigation systems based on factor graph are increasingly used on indoor robots, UAVs, and other vehicles. The output information of the equipped low-cost inertial measurement unit (IMU) is usually processed by IMU pre-integration techniques. As the accuracy of IMU increases, the traditional factor graph using the IMU pre-integration method need to be improved. This paper proposes a factor graph optimization algorithm for high-precision IMU based navigation system. An improved IMU pre-integration method is used in the algorithm to deal with the data from inertial sensors. Different from traditional methods, the effect of the curvature of the Earth’s surface on the IMU pre-integration method is taken into account. Meanwhile, the parameters affecting the accuracy of the IMU pre-integration method are corrected by the estimated navigation state of the carrier. Thus, a more accurate relative constraint is constructed. After that, this constraint and other measurement information are fused by the factor graph optimization algorithm. Finally, different simulation tests and field vehicle tests are carried out to validate the performance of the proposed method. The test results show that the proposed method can improve the carrier positioning accuracy by 20% to 90% when using high-precision inertial sensors under different conditions.

The errors of an inertial navigation system (INS) in response to gyros' errors can be effectively reduced by the rotation technique, which is a commonly used method to improve an INS's accuracy. A gyro's error consists of a deterministic contribution and a stochastic contribution. The compensation effects of gyros' deterministic errors are clear now, but the compensation effects of gyros' stochastic errors are as yet unknown. However, the compensation effects are always needed in a rotational inertial navigation system's (RINS) error analysis and optimization study. In this paper, the compensation effects of gyros' stochastic errors, which are modelled as a Gaussian white (GW) noise plus a first-order Markov process, are analysed and the specific formulae are derived. During the research, the responses of an INS's and a RINS's position error equations to gyros' stochastic errors are first analysed. Then the compensation effects of gyros' stochastic errors brought by the rotation technique are discussed by comparing the error propagation characteristics in an INS and a RINS. In order to verify the theory, a large number of simulations are carried out. The simulation results show a good consistency with the derived formulae, which can indicate the correctness of the theory.

GNSS/IMU/in-vehicle sensors navigation can provide accurate localization for land vehicles. Although the sensor fusion is often carried out by Kalman filter, graph optimization can obtain better state estimation. However, the graph optimization is still affected by the lack of rigorous IMU/in-vehicle sensors preintegration. In this paper, an improved preintegration method for GNSS/IMU/in-vehicle sensors navigation using graph optimization is proposed. Different from current methods, the preintegration that involves total error parameters of in-vehicle sensors is derived. The improved factors are subsequently fused with GNSS measurements and kinematic models using graph optimization, which can allow to yield a total parameters estimation. Thereby, more accurate relative constraints provided by the proposed method can improve the positioning accuracy compared with traditional preintegration methods. Meanwhile, the estimation accuracy of the proposed method for these error parameters can be superior to Kalman filter. The KITTI datasets and field tests are carried out to validate the competitive performance of the proposed method. Finally, the computational load of the proposed method is also discussed to verify its applicability for real-time operations.

At present, multiple unmanned aerial vehicles (UAVs) collaboration have attracted people’s more and more attention. The abundant relative distance information in UAV cooperative network can be employed to further improve UAV’s positioning accuracy. However, the traditional distance-based cooperative localization (CL) algorithm does not consider the performance of cooperative navigation information. Cooperative information with poor navigation performance will affect follower UAV’s state estimation accuracy. Thus, this paper proposes a weight factor graph CL method based on navigation performance evaluation. A novel navigation performance evaluation strategy based on Fisher information and relative entropy is proposed. The distance observations and cooperative nodes’ positions with higher estimation accuracy and contribution are selected to estimate follower UAV’s position. Considering the difference contributions of the selected cooperative information to follower UAV’s state estimation, we employ the information weight processing to achieve higher state estimation accuracy. Based on the selected cooperative information and weight coefficient, a multi-UAVs cooperative optimization graph model based on navigation performance is constructed. The global optimization cost function is constructed using relative distance constraints from the current time to historical time in the sliding window. The global optimal navigation solution of follower UAV is achieved using iterative weighted least squares method. Simulation and experiment results show that the proposed navigation performance evaluation strategy can effectively screen cooperative information with higher estimation accuracy and contribution for CL. Using the selected high-quality cooperative information, the system computational complexity is reduced without significantly affecting system positioning accuracy.

The presence of asynchronous absolute and relative measurements has posed a great challenge to the current multisensor positioning method in robotic systems. Although traditional factor graph methods possess a capability of plug-and-play, only a compromised performance can be obtained when dealing with an increasing number of asynchronous observations. In this article, a novel plug-and-play factor graph method for asynchronous absolute/relative measurements fusion in multisensor positioning is proposed. Different from traditional methods, a fixed-rate graph model is formed. The variable nodes in the graph are built at a fixed update rate to do the optimization, which is not affected by the arrival of measurements. Asynchronous absolute and relative measurements between two successive variable nodes are associated with corresponding variable nodes in the graph via the propagation of closed-form inertial measurement unit (IMU) preintegration. The simulations, datasets, and field tests are carried out to validate the proposed method. The results indicate that the closed-form IMU preintegration method has better dynamic adaptability in fusion system to formulate the association with asynchronous measurements. On this basis, the proposed method can integrate asynchronous measurements in a plug-and-play manner and achieve better performance compared to current methods. Meanwhile, the computational load can also be reduced.