The error propagation of traditional strapdown inertial navigation system (SINS)/Doppler velocity log (DVL) is not autonomous because its error state model is trajectory-dependence. Recently, the invariant error defined on Lie group has raised much attention due to its trajectory-independent and autonomous error propagation. In this paper, the invariant error-based Kalman filter for SINS/DVL integration solution is investigated with main focus on its extension and comparison. The contributions of this study are threefold. First, the invariant error defined on matrix Lie group (group of double direct isometrics) are extended to model the non-group-affine traditional SINS mechanism and the group-affine transformed SINS mechanism, both of them are derived in Earth frame and augmented with the drift and bias of the inertial measurement units (IMUs). Then, the observation equations for different invariant error-based state models are derived for SINS/DVL application, theoretical analysis is performed and comprehensive evaluation are conducted under different maneuvering condition by lake field trial. Finally, the variational Bayesian approach is introduced into invariant error-based Kalman filter to inferring the inaccurate process noise covariance matrix (PNCM) and time-varying measurement noise covariant matrix (MNCM) from a practical perspective, experimental results demonstrate that it can improve the navigation accuracy significantly. This study is expected to facilitate the selection of appropriate invariant error to SINS/DVL application.

This paper investigates the strapdown inertial navigation system (SINS) initial alignment aided by Doppler velocity log (DVL). A linear Kalman filtering method is proposed using the theory of Lie group, which is immune to the initial misalignment. The dead-reckoning position based on the body velocity provided by DVL and attitude provided by SINS is used as measurement. The SINS calculated attitude, velocity, position and DVL dead-reckoning position are formulated together as the elements of Lie group SE ₃ (3). Since the dead-reckoning position is a type of left-invariant measurement, the corresponding linear error-state model is derived based on the left-invariant group error definition. Although the Lie group state model is not group affine, thesmall attitude error assumption does not introduce accuracy degeneracy in deriving the linear error-state model. This is the core reason why the derived linear error-state model is still applicable for cases with large initial misalignment. Experiments are conducted to verify the feasibility and effectiveness of the proposed methods. The test results show that the proposed method has higher accuracy and faster convergence speed as compared with the existing methods.

The SINS/USBL integrated navigation system has an important application in many underwater navigation situations. Accurate system-level installation parameter (SIP), including installation misalignment angle (IMA), lever arm and transponder position, is the prerequisite for reliable navigation. Traditional separation-based calibration methods which just calibrate the SIP partially are labor-intensive and inconvenient to a certain due to the requirement of pre-scheduled maneuvers, pre-located transponder and accurate prior knowledge. This work investigated the SIP calibration of SINS/USBL and proposed an improved random drift particle swarm optimization (RDPSO)-aided approach for identifying the SIPs of SINS/USBL. This methodology implemented a unified calibration for SIPs by minimizing the cost function and eliminated the additional requirements for separation-based calibration methods. Field comparative tests with other methods demonstrated that our approach is capable of effectively calibrating the SIP of SINS/USBL with higher calibration accuracy, better convergence stability and repeatability, and a more expeditious convergence rate, thereby leading to a good performance of the SINS/USBL integrated navigation system.

Accurate and robust localization using multi-modal sensors is crucial for autonomous driving applications. Although wheel encoder measurements can provide additional velocity information for visual-inertial odometry (VIO), the existing visual-inertial-wheel odometry (VIWO) still cannot avoid long-term drift caused by the low-precision attitude acquired by the gyroscope of a low-cost inertial measurement unit (IMU), especially in visually restricted scenes where the visual information cannot accurately correct for the IMU bias. In this work, leveraging the powerful data processing capability of deep learning, we propose a novel tightly coupled monocular visual-inertial-wheel odometry with neural gyroscope calibration (NGC) to obtain accurate, robust, and long-term localization for autonomous vehicles. First, to cure the drift of the gyroscope, we design a robust neural gyroscope calibration network for low-cost IMU gyroscope measurements (called NGC-Net). Following a carefully deduced mathematical calibration model, NGC-Net leverages the temporal convolutional network to extract different scale features from raw IMU measurements in the past and regress the gyroscope corrections to output the de-noised gyroscope. A series of experiments on public datasets show that our NGC-Net has better performance on gyroscope de-noising than learning methods and competes with state-of-the-art VIO methods. Moreover, based on the more accurate de-noised gyroscope, an effective strategy for combining the advantages of VIWO and NGC-Net outputs is proposed in a tightly coupled framework, which significantly improves the accuracy of the state-of-the-art VIO/VIWO methods. In long-term and large-scale urban environments, our RNGC-VIWO tracking system performs robustly, and experimental results demonstrate the superiority of our method in terms of robustness and accuracy.

The development of underwater high-precision navigation technology is of great significance for the application of autonomous underwater vehicles (AUVs). Traditional long baseline (LBL) positioning systems require pre-deployment and the calibration of multiple beacons, which consumes valuable time and manpower. In contrast, the range-only single-beacon (ROSB) positioning technology can help autonomous underwater vehicles (AUVs) obtain accurate position information by deploying only one beacon. This method greatly reduces the time and workload of deploying beacons, showing high application potential and cost ratio. Given the operational constraints of AUV open-ocean navigation with single-beacon weak observations and absence of valid a priori positioning data in calibration zones, a multi-sensor underwater virtual beacon localization framework was established, proposing a differential Chan–Gauss–Newton (DCGN) methodology for submerged vehicles. Based on inertial navigation, the method uses the distance measurement information from a single beacon and observations from multiple sensors, such as the Doppler velocity log (DVL) and pressure sensor, to obtain accurate position estimates by discriminating the initial position of multiple hypotheses. A simulation experiment and lake test show that the proposed method not only significantly improves the positioning accuracy and convergence speed, but also shows high reliability.

Underwater acoustic single-beacon positioning technology achieves localization by integrating vehicle motion with range measurements acquired from acoustic ranging devices, offering advantages such as system simplicity, flexible deployment, and high cost-effectiveness. However, its accuracy is limited by weak initial observability and degraded observation geometry. To address this, a sensor data correction and collaborative optimization framework is proposed. A hybrid outlier rejection strategy first suppresses acoustic multipath and sensor noise. To compensate for systematic sensor errors ignored in conventional Virtual Long Baseline methods, an affine transformation maps the true trajectory to the sensor-indicated one, reformulating error compensation as a correction to virtual beacon coordinates. To further mitigate the accuracy degradation caused by degenerated geometric configurations, this paper proposes a collaborative algorithm that integrates Chan initialization with affine transformation optimization. This approach formulates the positioning problem as an optimization task, simultaneously estimating the position information and affine transformation parameters through iterative refinement to achieve high-precision localization. The process begins with Chan’s algorithm, which provides an initial estimate from the virtual sensor array. This estimate is then refined under affine constraints to achieve high-precision localization. Experimental results show the method improves positioning accuracy by 36.30% compared to baseline algorithms, demonstrating significant performance enhancement.