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 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 this paper, a drag model-aided fault-tolerant state estimation method is presented for quadrotors. Firstly, the drag model accuracy was improved by modeling an angular rate related item and an angular acceleration related item, which are related with flight maneuver. Then the drag model, light detection and ranging (LIDAR), and inertial measurement unit (IMU) were fused based on the Federal Kalman filter frame. In the filter, the LIDAR estimation fault was detected and isolated, and the disturbance to the drag model was estimated and compensated. Some experiments were carried out, showing that the velocity and position estimation were improved compared with the traditional LIDAR/IMU fusion scheme.