Inertial Navigation Research Articles

A robust integrated navigation optimization method for USV in signal occlusion environment

Unmanned surface vehicles (USV) can use global navigation satellite systems (GNSS) and inertial navigation systems (INS) for combined positioning and navigation. However, buildings such as port facilities and bridges blocking GNSS signals will increase the error in the discriminator output in the GNSS vector tracking loop and reduce positioning accuracy. Meanwhile, due to the cumulative error in the inertial navigation system, the credibility of the navigation results when the signal is blocked is further reduced. In this regard, this study proposes a robust integrated navigation optimization method. Specifically, the RTS smoothing optimized Kalman filter is used to constrain the carrier phase error and code phase error output by the discriminator, which can dynamically adjust the gain of the vector tracking loop, thereby improving the signal tracking capability. Simultaneously, the prediction results of the gated recurrent unit (GRU) network optimized based on the attention mechanism are combined with the inertial navigation system to improve navigation accuracy. Furthermore, an adaptive Kalman filter is utilized as the integrated navigation filter. The actual path of the carrier refers to the navigation solution of the existing receiver. In the open environment, the proposed optimization method reduces horizontal positioning error and speed error by 44.7% and 37.1% respectively compared with existing methods. Simultaneously, it can effectively improve the robustness of positioning in signal obstruction environments. The proposed integrated navigation method provides new possibilities for optimizing USV navigation solutions.

Evaluation of Traffic Sign Occlusion Rate Based on a 3D Point Cloud Space

The effectiveness of road signs is hindered by obstructions, such as vegetation, mutual obstruction of signs, or the road alignment itself. The traditional evaluation of road sign recognition effectiveness is conducted through in-vehicle field surveys. However, this method has several drawbacks, including discontinuous identification, unclear positioning, incomplete coverage, and being time-consuming. Consequently, it is unable to effectively assess the recognition status of road signs at any arbitrary point within the road space. Therefore, this study employed laser scanning to construct a point-surface model, which was based on a point cloud algorithm and SLAM (Simultaneous Localization and Mapping), integrated LiDAR and inertial navigation system data, and optimized the point model after processing steps such as denoising, resampling, and three-dimensional model construction. Furthermore, a method for assessing the highway sign occlusion rate based on the picking algorithm was proposed. The algorithm was applied to an actual road environment, and the occlusion by other items was simulated. The results demonstrated the effectiveness of the method. This new method provides support for the fast and accurate calculation of road sign occlusion rates, which is of great importance for ensuring the safe traveling of vehicles.

An improved Multi-State Constraint Kalman Filter for Visual-Inertial Odometry

Fast pose estimation (PE) plays a vital role for agile autonomous robots in successfully carrying out their tasks. While Global Navigation Satellite Systems (GNSS) such as Global Positioning System (GPS) have been traditionally used along with Inertial Navigation Systems (INS) for PE, their viability is compromised in indoor and urban environments due to their low update rates and inadequate signal coverage. Visual-Inertial Odometry (VIO) is gaining popularity as a practical alternative to GNSS/INS systems in GNSS-denied environments. Among various VIO-based methods, the Multi-State Constraint Kalman Filter (MSCKF) has garnered significant attention due to its robustness, speed and accuracy. Nevertheless, high computational cost of image processing is still challenging for real-time implementation on resource-constrained vehicles. In this paper, an enhanced version of the MSCKF is proposed. The proposed approach differs from the original MSCKF in the feature marginalization and state pruning steps of the algorithm. This new design results in a faster algorithm with comparable accuracy. We validate the proposed algorithm using both an open-source dataset and real-world experiments. It is demonstrated that the proposed Fast-MSCKF (referred to as FMSCKF) is approximately six times faster and at least 20% more accurate in final position estimation compared to the standard MSCKF.

Autonomous ground vehicle gravity anomaly measurement and dynamic error compensation

Abstract To address the issue that dynamic gravity anomaly measurement is overly dependent on GNSS and can’t be measured autonomously at this stage, this paper proposes an autonomous ground vehicle dynamic gravity anomaly measurement method based on a strapdown inertial navigation system (SINS), odometer (OD), barometer and platform gravimeter. The SINS/OD /barometer integrated navigation solution delivers high-precision navigation parameters, completes the calculation of correction terms, and performs the autonomous dynamic gravity anomaly measurement combined with the primary measurement results of the platform gravimeter. Numerical calculations provide the requirements for the application of the proposed method, and the cut-off frequency for extracting gravity anomalies is 0.02 Hz, as determined by power spectral density analysis. In order to further improve the measurement accuracy and account for dynamic errors caused by vehicle maneuvering, a long-short-term memory (LSTM) model of recurrent neural network (RNN) is introduced. A series of experiments under multiple circumstances with repeated lines were conducted in Tianjin, China, and the static measurements along the line were taken using CG-5 to provide true values of gravity anomalies. The results demonstrate that the autonomous measurement scheme can achieve accuracy comparable to GNSS-assisted, and that dynamic error compensation algorithm based on LSTM improves the dynamic gravity measurements accuracy significantly without sacrificing the spatial resolution of gravity anomalies.

Inertial Navigation Employing a Common-Frame Error Model

This paper examines an extension of previous common-frame theory in the state-error definition for inertial navigation systems (INS). In previous work, only body-frame errors were considered in relation to quantities such as biases from strapdown gyros. Reference-frame errors found in quantities such as the translational velocity have not been considered previously. The work here derives the full INS equations where an alternative vector state-error is defined using common coordinates over all vector-error realizations, thereby providing a true-to-life representation of the actual errors. The INS is analyzed through a stationary linear analysis to show that the fundamental frequencies are unchanged; however, there are now more coupling terms within the state matrix. The performance of the INS filter is then analyzed using a simulation.

Tight integration of real-time GNSS PPP and INS: Ionosphere-free combined vs uncombined models

The GNSS Precise Point Positioning (PPP) model is usually established in either an ionospheric-free (IF) combined form or an uncombined (UC) form. These formulations can be equivalent in theory but their applications in practice could still perform differently when integrated with external sensors. In this study, we compared the positioning performance of the two PPP models tightly coupled with the Inertial Navigation System (INS) using a high-grade inertial measurement unit (IMU) in real vehicle navigation tests. The ambiguity resolution (AR) was also exploited in the two PPP models after applying the observable specific biases (OSB) to the GNSS raw code and phase measurements. According to the results, under good satellite observability the UC PPP/INS tightly-coupled integration (TCI) significantly outperforms the IF PPP/INS TCI. The UC TCI model with AR could achieve a positioning accuracy of 4.6 and 3.0 cm in the horizontal and vertical directions, which are improved by 37 % and 63 % respectively relative to the IF TCI model. However, in the case of frequent GNSS signal interruptions or poor satellite observation condition, the IF TCI model shows a superior reliability than the UC TCI. Nevertheless, when the ionospheric parameters are properly constrained in the UC TCI model, substantial improvements in terms of convergence and accuracy are obtained. The UC PPP augmented with external precise ionospheric information would greatly increase the cost, and users may select the appropriate PPP model with INS TCI in real applications in accordance with the demanded accuracy level and measuring conditions.

A damping method of grid strapdown inertial navigation system for polar region

Abstract The conventional north-pointing inertial navigation system (INS) always points to the geographic north. However, when the system crosses the pole in the polar region, the geographic north quickly changes with 180 degrees, and the rate of change of the geographic north direction will be infinite. Secondly, when the latitude approaches to 90 degrees, which will lead to singularities in math for the angular velocity caused by vehicle motion. With its special definition and mechanization, the grid coordinate system can solve the above problems. Nevertheless, the error analysis of the grid strapdown INS shows that there are Schuler periodic and Foucault periodic oscillations, which badly degrade the accuracy of the strap-down INS. To address the problem, the external horizontal damping technology is adopted in this paper, wherein the external velocity is provided by the Doppler velocity log (DVL). Finally, the feasibility and the effectiveness of the external damping technology were verified by simulation.

Automated extrinsic calibration of solid-state frame LiDAR sensors with non-overlapping field of view for monitoring indoor stockpile storage facilities

Several industrial and commercial bulk material management applications rely on accurate, current stockpile volume estimation. Proximal imaging and LiDAR sensing modalities can be used to derive stockpile volume estimates in outdoor and indoor storage facilities. Among available imaging and LiDAR sensing modalities, the latter is more advantageous for indoor storage facilities due to its ability to capture scans under poor lighting conditions. Evaluating volumes from such sensing modalities requires the pose (i.e., position and orientation) parameters of the used sensors relative to a common reference frame. For outdoor facilities, a Global Navigation Satellite System (GNSS) combined with an Inertial Navigation System (INS) can be used to derive the sensors’ pose relative to a global reference frame. For indoor facilities, GNSS signal outages will not allow for such capability. Prior research has developed strategies for establishing the sensor position and orientation for stockpile volume estimation while relying on multi-beam spinning LiDAR units. These approaches are feasible due to the large range and Field of View (FOV) of such systems that can capture the internal surfaces of indoor storage facilities.The mechanical movement of multi-beam spinning LiDAR units together with the harsh conditions within indoor facilities (e.g., excessive humidity, wide range of temperature variation, dust, and corrosive environment in deicing salt storage facilities) limit the use of such systems. With the increasing availability of solid-state LiDAR units, there is an interest in exploring their potential for stockpile volume estimation. Despite their higher robustness to harsh conditions, solid-state LiDAR units have shorter distance measurement range and limited FOV when compared with multi-beam spinning LiDAR. This research presents a strategy for the extrinsic calibration (i.e., estimating the relative pose parameters) of installed solid-state LiDAR units inside stockpile storage facilities. The extrinsic calibration is made possible using deployed spherical targets and a complete, reference scan of the facility from another LiDAR sensing modality. The proposed research introduces strategies for: 1) automated extraction of the spherical targets; 2) automated matching of these targets in the solid-state LiDAR and reference scans using invariant relationships among them; and 3) coarse-to-fine estimation of the calibration parameters. Experimental results in several facilities have shown the feasibility of using the proposed methodology to conduct the extrinsic calibration and volume evaluation with an error percentage less than 3.5% even with occlusion percentages reaching up to 50%.

Startup drift compensation of RLG based on monotone constrained RBF neural network

Serious startup drift of the Ring Laser Gyroscope (RLG) is observed during cold startup process, which will dramatically degrade the performances of the corresponding Inertial Navigation System (INS). In this paper, correlation analysis method, which analyzes the relationship between the startup drift of the RLG and the temperature change, is used to determine the significant temperature-related terms during gyroscope startup. Based on the significant temperature-related terms and the startup time length, a startup drift compensation model for RLG based on monotonicity-constrained Radial Basis Function (RBF) neural network is proposed and validated. Compared with the raw RLG data without compensation, the standard deviation of the RLG output with the proposed constrained RBF network model is decreased by more than 46%, and the peak-to-peak value is decreased by more than 35%. Compared with the traditional multiple regression model, the standard deviation and peak-to-peak value of the RLG output are decreased by more than 10% and 6%, respectively. Compared with the common RBF network model, the standard deviation and peak-to-peak value of the RLG output are decreased by more than 8% and 3%, respectively. Navigation experiments also validate the effectiveness of the compensation model.

Dual Kalman Filter Based on a Single Direction under Colored Measurement Noise for INS-Based Integrated Human Localization

For inertial-based integrated pedestrian navigation, the navigation environment might affect the positioning accuracy in different directions. Meanwhile, complex filtering algorithms can reduce computational efficiency. Therefore, one dual Kalman filter (KF) based on a single direction under a colored measurement noise (CMN) scheme is developed herein to improve the robustness and operational efficiency. The proposed method involves designing a data fusion model for the KF that integrates data from an inertial navigation system (INS) and ultrawideband (UWB). Subsequently, the INS/UWB integrated model-based KF under CMN (cKF) will be derived. Then, two sub-cKFs are proposed to fuse the data in the east and north directions, respectively. The empirical findings highlight the superior performance of the proposed approach over the KF for position estimation accuracy and runtime reduction, demonstrating its effectiveness.

Atom interferometry at arbitrary orientations and rotation rates

The exquisite precision of atom interferometers has sparked the interest of a large community for uses ranging from fundamental physics to geodesy and inertial navigation. However, their implementation for onboard applications is still limited, not least because rotation and acceleration are intertwined in a single phase shift, which makes the extraction of a useful signal more challenging. Moreover, the spatial separation of the wave packets due to rotations leads to a loss of signal. We present an atom interferometer operating over a large range of random angles, rotation rates and accelerations. A model of the expected phase shift allows us to untangle the rotation and acceleration signals. We also implement a real-time compensation system using fiber-optic gyroscopes and a rotating reference mirror to maintain the full contrast of the interferometer. We demonstrate a single-shot sensitivity to acceleration of 24 μg for rotation rates reaching 14° s−1.

A dynamic object removing 3D reconstruction system based on multi-sensor fusion

Abstract Currently, one of the key technologies for autonomous navigation of unmanned mobile robots is SLAM, which faces many challenges in practical applications. These challenges include a lack of texture, deterioration in sensor performance, and interference from moving objects in dynamic outdoor environments, all of which have an impact on the mapping system. To address these issues, this paper proposes a framework for lidar, vision camera, and inertial navigation data, resulting in fusion and dynamic object removing. The system consists of three sub-modules: the Lidar-Inertial Module (LIM), the Visual-Inertial Module (VIM), and the Dynamic-Object-Removing Module (DORM). LIM and VIM assist each other, with lidar point clouds providing three-dimensional information for the global voxel map and the camera providing pixel-level color information. At the same time, the DORM performs synchronous dynamic object detection to remove dynamic objects from the global map. The system constructs a multi-sensor factor graph using the state and observation models, and the optimal solution is obtained using least squares. Furthermore, this paper employs triangle descriptors and bundle adjustment methods for loop closure detection in order to reduce accumulated errors and maintain consistency. Experimental results demonstrate that the system can perform clean state estimation, dynamic removing and scene reconstruction in a variety of complex scenarios.

A Low-Cost Redundant Attitude System for Small Satellites, Based on Strap-Down Inertial Techniques and Gyro Sensors Linear Clustering

The significant technological changes related to the manufacturing of the miniaturized sensors produced a higher impact at the level of the detection units equipping the strap-down inertial navigation systems (INSs). Together with miniaturization, many more advantages are brought by these technologies, related to low costs, low necessary energy, high robustness and high potential for adapting the design solutions. However, reducing the dimensions and weight of the sensors is reflected by a decrease in their performance in terms of sensitivity, noise and the possibility of controlling sensitive elements. On the other hand, there is a permanent increase in the need to have in-space applications of miniaturized systems with a high degree of redundancy and to equip miniaturized satellites, miniaturized space robots or space rovers. The paper proposes a new methodology to increase the quality of the signals received from the miniaturized inertial measurement units (IMUs), but also to increase the degree of redundancy, by using low-cost sensors arranged in redundant linear configurations. The presentation is focused on the development of an attitude system based on strap-down inertial techniques which uses a redundant IMU equipped with three linear clusters of miniaturized gyros. For each of the three clusters, a data fusion mechanism based on the maximal ratio combining method is applied. This fusion mechanism reduces the noise power and bias of the signal delivered to the navigation processor. Shown are the theory, software modeling and experimentation results for the attitude algorithm, for the data fusion method, and for the integrated system.

Vision-aided inertial navigation for planetary landing without feature extraction and matching

In this paper, a vision-aided inertial navigation method for planetary landing based on the direct method is proposed. This approach requires only a monocular camera and an inertial measurement unit (IMU) to be equipped on the lander. Unlike traditional feature-based visual-aided inertial navigation algorithms, which entail extracting and matching image features and thus incurring high computational costs, the proposed method utilizes the direct method that tracks any pixel with a sufficient intensity gradient. By jointly optimizing photometric and inertial errors, the proposed algorithm estimates the camera motion and sparse map of the scene. Simulation results demonstrate that the proposed method reduces computation by nearly 65 % compared to the feature point method, with a slight decrease in navigation accuracy.

Research on collaborative multi-UAV localization method based on combination navigation information

In challenging environments, unmanned aerial vehicle (UAV) systems often encounter unstable satellite signals and communication link interference. This paper proposes an integrated navigation method that integrates inertial navigation system (INS), global navigation satellite system (GNSS), and visual navigation system (VNS). Utilizing data from onboard sensors, this method merges relative navigation information from feature tracking of multiple UAVs with each UAV’s absolute navigation data. It includes specially designed transmission rules to reduce data exchange between UAVs. Each UAV uses an adaptive unscented Kalman filter (AUKF) method, which is enhanced into a collaborative AUKF (C-AUKF) using a message passing-based approach. Experiments in a simulated mission scenario revealed that the C-AUKF, in comparison to using extended Kalman filter (EKF), significantly improved flight test performance across the entire testing area, with a cumulative deviation of only 10.22 m, about 0.85% of the total flight distance. These results demonstrate that the proposed method not only meets accuracy requirements for position and velocity in integrated navigation but also significantly enhances multi-UAV navigation precision, particularly in scenarios with global positioning system (GPS) interference.

Research on the Construction Technology of INS Digital Prototype Based on Digital Twin

In response to the continuous advancement of digitalization and intelligence in equipment as mandated by the state, a digital twin-based inertial navigation digital prototype construction scheme has been designed. This scheme supports the realization of intelligent manufacturing, testing, evaluation, and operational assurance throughout the lifecycle of inertial navigation products. This paper decomposes the physical entities of the " three-autonomy " SINS and integrates component-level inertial navigation digital prototypes based on the principles of inertial navigation. The prototypes were integrated using heterogeneous models in simulation software. Pure navigation functionality verification was conducted on the prototypes. The results show that the errors in pure simulation of the inertial navigation digital prototypes constructed in this study are consistent with the physical navigation results of inertial navigation systems, providing a reference for the development of inertial navigation digital twin systems.

A hybrid information fusion method for SINS/GNSS integrated navigation system utilizing GRU-aided AKF during GNSS outages

Abstract To enhance the performance of integrated inertial navigation system (INS) and global navigation satellite system (GNSS) during GNSS outages, this paper proposed a fusion positioning method based on predictive observation information and adaptive filter parameter. Combined with an adaptive Kalman filter (AKF) and a Gated Recurrent Unit neural network (NN) that directly relates the inertial measurement unit (IMU) output sequence to the error estimation, the hybrid information fusion system can provide effective corrections to compensate for horizontal position errors under the constraints of complex and dynamic vehicle movement data during GNSS outages. Meanwhile, the designed adaptive parameter of the integrated navigation filter can adjust the credibility of the state prediction section when the GNSS is reconnected, ensuring the system can switch rapidly between the INS/GNSS and INS/NN integrated modes. The performance of the proposed information fusion method has been experimentally validated using IMU and GNSS data collected in a vehicle navigation test conducted on a stretch of expressway. The comparison results indicate that the proposed algorithm has error suppression capabilities under various experimental constraints and demonstrates a degree of extendibility and reusability.

An Adaptive Cooperative Localization Method for Heterogeneous Air-to-Ground Robots Based on Relative Distance Constraints in a Satellite-Denial Environment.

Cooperative localization (CL) for air-to-ground robots in a satellite-denial environment has become a current research hotspot. The traditional distance-based heterogeneous multiple-robot CL method requires at least four unmanned aerial vehicles (UAVs) with known positions. When the number of known-position UAVs in a cluster collaborative network is insufficient, the traditional distance-based CL method has a certain inapplicability. A novel adaptive CL method for air-to-ground robots based on relative distance constraints is proposed in this paper. Based on a dynamically changing number of known-position UAVs in the cluster collaborative network, the adaptive fusion estimation threshold is set. When the number of known-position UAVs in the cluster cooperative network is large, the real-time dynamic topology characteristics of multiple robots' spatial geometric configurations are considered. The optimal spatial geometric configuration between UAVs and unmanned ground vehicles (UGVs) is utilized to achieve a high-precision CL solution for UGVs. Otherwise, in the event that the number of known-position UAVs in a cluster collaborative network is insufficient, distance observation constraint information between UAVs and UGVs is retained in real time. Position observation equations for UGVs' inertial navigation system (INS) have been constructed using inertial-based high-precision relative position constraints and relative distance constraints from historical to current times. The experimental results show that the proposed method achieves adaptive fusion estimation with a dynamically changing number of known-position UAVs in the cluster collaborative network, effectively verifying the effectiveness of the proposed method.

CORAL-Catamaran for Underwater Exploration: Development of a Multipurpose Unmanned Surface Vessel for Environmental Studies.

CORAL (Catamaran fOr UndeRwAter expLoration) is a compact, unmanned catamaran-type vehicle designed and developed to assist the scientific community in exploring marine areas such as inshore regions that are not easily accessible by traditional vessels. This vehicle can operate in different modalities: completely autonomous, semi-autonomous, or remotely assisted by the operator, thus accommodating various investigative scenarios. CORAL is characterized by compact dimensions, a very low draft and a total electric propulsion system. The vehicle is equipped with a single echo-sounder, a 450 kHz Side Scan Sonar, an Inertial Navigation System assisted by a GPS receiver and a pair of high-definition cameras for recording both above and below the water surface. Here, we present results from two investigations: the first conducted in the tourist harbour in Pozzuoli Gulf and the second in the Riomaggiore-Manarola marine area within the Cinque Terre territory (Italy). Both surveys yielded promising results regarding the potentiality of CORAL to collect fine-scale submarine elements such as anthropic objects, sedimentary features, and seagrass meadow spots. These capabilities characterize the CORAL system as a highly efficient investigation tool for depicting shallow bedforms, reconstructing coastal dynamics and erosion processes and monitoring the evolution of biological habitats.

An Invariant Filtering Method Based on Frame Transformed for Underwater INS/DVL/PS Navigation

Underwater vehicles heavily depend on the integration of inertial navigation with Doppler Velocity Log (DVL) for fusion-based localization. Given the constraints imposed by sensor costs, ensuring the optimization ability and robustness of fusion algorithms is of paramount importance. While filtering-based techniques such as Extended Kalman Filter (EKF) offer mature solutions to nonlinear problems, their reliance on linearization approximation may compromise final accuracy. Recently, Invariant EKF (IEKF) methods based on the concept of smooth manifolds have emerged to address this limitation. However, the optimization by matrix Lie groups must satisfy the “group affine” property to ensure state independence, which constrains the applicability of IEKF to high-precision positioning of underwater multi-sensor fusion. In this study, an alternative state-independent underwater fusion invariant filtering approach based on a two-frame group utilizing DVL, Inertial Measurement Unit (IMU), and Earth-Centered Earth-Fixed (ECEF) configuration is proposed. This methodology circumvents the necessity for group affine in the presence of biases. We account for inertial biases and DVL pole-arm effects, achieving convergence in an imperfect IEKF by either fixed observation or body observation information. Through simulations and real datasets that are time-synchronized, we demonstrate the effectiveness and robustness of the proposed algorithm.