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.

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.

The integration of global navigation satellite system (GNSS), inertial measurement unit (IMU) and odometer has been widely utilized in vehicular localization. Due to the advantage in accessing accurate state estimation, factor graph is commonly employed to achieve the integration of vehicular sensors. However, the fusion performance of traditional factor graph reduces when dealing with asynchronous and abnormal measurements, yielding compromised estimation results for localization and calibration. In this paper, an enhanced adaptable factor graph for simultaneous localization and calibration (SLAC) in GNSS/IMU/odometer integration is proposed. First, a novel factor graph framework for GNSS/IMU/odometer integration is designed. In view of the asynchronism among sensors, the variable nodes in factor graph are built according to odometer measurement. IMU pre-integration is then used to establish the relationship between asynchronous GNSS position and corresponding variable nodes to form residuals. To properly deal with the coupling noise in the proposed model, the expectation maximum (EM) algorithm is utilized to estimate the noise parameters based on the proposed model. Simulations and field tests are done to validate the proposed method. It shows that the proposed method has better estimation accuracy for localization and calibration compared with traditional methods. Meanwhile, the computational load of the proposed method is discussed.

To autonomous systems (ASs) equipped with single-frequency GNSS chipsets, it is hard to fully use the high-precision carrier phase to assist positioning as the inherent integer ambiguity cannot be reliably obtained using only single-frequency observations, especially in obstructed environments. Although the time difference can be done to eliminate the integer ambiguity to form accurate constraint in graph based fusion, cycle slip is not properly handled in current methods, leading to degraded performance. In this paper, a performance enhancement of tightly coupled GNSS/IMU integration based on factor graph with robust time-differenced carrier phase (TDCP) loop closure is proposed. Different from traditional methods, cycle slip detection is firstly performed, and the effect of cycle slip can be eliminated in the formation of loop closure, which can bring about better robustness. Doppler frequency shift is used to detect cycle slip and carrier phase measurements at corresponding epochs are then selected to build TDCP loop closure. The proposed robust TDCP loop closure is fused with pseudorange, Doppler frequency shift and IMU via factor graph, which can make the full use of the absolute and relative measurements to enhance the performance of tightly coupled GNSS/IMU integration. Simulation and field tests are conducted to validate the proposed method. The results show that the proposed method can improve the positioning performance with robust TDCP loop closure. Meanwhile, the computational load of proposed method is discussed.

In order to ensure that dual-axis rotational inertial navigation systems (RINSs) maintain a high level of accuracy over the long term, there is a demand for periodic calibration during their service life. Traditional calibration methods for inertial measurement units (IMUs) involve removing the IMU from the equipment, which is a laborious and time-consuming process. Reinstalling the IMU after calibration may introduce new installation errors. This paper focuses on dual-axis rotational inertial navigation systems and presents a system-level self-calibration method based on invariant errors, enabling high-precision automated calibration without the need for equipment disassembly. First, navigation parameter errors in the inertial frame are expressed as invariant errors. This allows the corresponding error models to estimate initial attitude even more rapidly and accurately in cases of extreme misalignment, eliminating the need for coarse alignment. Next, by utilizing the output of a gimbal mechanism, angular velocity constraint equations are established, and the backtracking navigation is introduced to reuse sensor data, thereby reducing the calibration time. Finally, a rotation scheme for the IMU is designed to ensure that all errors are observable. The observability of the system is analyzed based on a piecewise constant system method and singular value decomposition (SVD) observability analysis. The simulation and experimental results demonstrate that this method can effectively estimate IMU errors and installation errors related to the rotation axis within 12 min, and the estimated error is less than 4%. After using this method to compensate for the calibration error, the velocity and position accuracies of a RINS are significantly improved.

In previous navigation positioning methods, micro inertial measurement unit provides navigation information by measuring the linear acceleration and angular velocity of the quadrotors. However, low-cost micro inertial measurement unit often fails in harsh environments and produce large misalignment angles during initial alignment, reducing the navigation performance of quadrotors. Therefore, this article introduces the dynamics model of quadrotors, integrating the roll and pitch moment model, torque model, drag model, thrust model, XYZ-axis gyroscope, XYZ-axis accelerometer and global navigation satellite system to form a micro inertial measurement unit fault-tolerant federated Kalman filter based on analytical redundancy. Meanwhile, this article introduces Lie group manifold theory into the unscented Kalman filter to improve the attitude estimation accuracy under large misalignment angles and reduce the influence of attitude errors on velocity and position. The proposed federated unscented Kalman filter on Lie group manifold can accurately estimate navigation parameters when micro inertial measurement unit fails. Real flight experiment data were used for verification, showing that faults in the XYZ-axis gyroscope, XYZ-axis accelerometer and dynamics model of quadrotors can be detected and isolated. When there are no faults, the attitude, velocity and position accuracy of the quadrotor after introducing the dynamics model are increased by more than 5.5%, 3.1% and 10.7% respectively. The estimation accuracy of roll, pitch, and yaw increased by more than 88.1%, 68.9%, and 66.4% respectively under large misalignment angles.