Inertial Navigation Research Articles

Online Calibration of Inertial Sensors Based on Error Backpropagation

Global satellite navigation systems (GNSSs) are the most-used technology for the localization of vehicles in the outdoor environment, but in the case of a densely built-up area or during passage through a tunnel, the satellite signal is not available or has poor quality. Inertial navigation systems (INSs) allow localization dead reckoning, but they have an integration error that grows over time. Inexpensive inertial measurement units (IMUs) are subject to thermal-dependent error and must be calibrated almost continuously. This article proposes a novel method of online (continuous) calibration of inertial sensors with the aid of the data from the GNSS receiver during the vehicle’s route. We performed data fusion using an extended Kalman filter (EKF) and calibrated the input sensors through error backpropagation. The algorithm thus calibrates the INS sensors while the GNSS receiver signal is good, and after a GNSS failure, for example in tunnels, the position is predicted only by low-cost inertial sensors. Such an approach significantly improved the localization precision in comparison with offline calibrated inertial localization with the same sensors.

Development of a Mobile Application for Musculoskeletal Rehabilitation Based on Computer Vision and Inertial Navigation Technologies

Monitoring the process of musculoskeletal rehabilitation is of great importance for ensuring a person’s health after suffering from illnesses, especially during the outpatient period when medical supervision is absent. The aim of this study is to create an accessible tool (a mobile application) that allows for the monitoring of the execution of musculoskeletal rehabilitation exercises. To achieve this goal, the architecture of a mobile application has been developed, along with its functioning algorithm, and the methods for processing information from two tracking systems (inertial navigation and computer vision) have been examined to assess the quality of performed exercises. During the experimental research, procedures for processing data from mobile inertial navigation sensors were refined, a solution to the classification task of musculoskeletal rehabilitation exercises was explored (with an accuracy of 93–100%), and prototyping of the mobile application was carried out. The results obtained can be used for evaluating outpatient rehabilitation and as a basis for more complex and functional mobile systems for musculoskeletal rehabilitation.

A Novel Approach for Kalman Filter Tuning for Direct and Indirect Inertial Navigation System/Global Navigation Satellite System Integration.

This work presents an innovative approach for tuning the Kalman filter in INS/GNSS integration, combining states from the inertial navigation system (INS) and data from the Global Navigation Satellite System (GNSS) to enhance navigation accuracy. The INS uses measurements from accelerometers and gyroscopes, which are subject to uncertainties in scale factor, misalignment, non-orthogonality, and bias, as well as temporal, thermal, and vibration variations. The GNSS receiver faces challenges such as multipath, temporary signal loss, and susceptibility to high-frequency noise. The novel approach for Kalman filter tuning involves previously performing Monte Carlo simulations using ideal data from a predetermined trajectory, applying the inertial sensor error model. For the indirect filter, errors from inertial sensors are used, while, for the direct filter, navigation errors in position, velocity, and attitude are also considered to obtain the process noise covariance matrix Q. This methodology is tested and validated with real data from Castro Leite Consultoria's commercial platforms, PINA-F and PINA-M. The results demonstrate the efficiency and consistency of the estimation technique, highlighting its applicability in real scenarios.

STGRL: SNN based two-stage geomagnetic road localization method

Abstract Geomagnetic navigation is a widely used positioning method capable of correcting the cumulative errors of odometers and inertial navigation systems, thereby ensuring long-distance positioning for vehicles in GPS-denied environments. However, common geomagnetic road navigation algorithms are susceptible to measurement noise, which hinder improvements in positioning efficiency and accuracy. To address this issue, this paper proposes a Siamese Neural Network (SNN) based two-stage geomagnetic road localization method. First, attitude angle information is combined with geomagnetic scalar and vector value to establish geomagnetic reference database to increase the feature dimensions of geomagnetic matching. Then, we use the Random Forest algorithm to perform a coarse matching of the data sequence to determine the current road, balancing the increased computational load resulting from the addition of feature dimensions. Finally, to further reduce the impact of random noise, this paper employs the SNN algorithm based on Transformer Encoder for fine matching of the data sequence. Experiments show that compared to existing methods, the average absolute positioning error of our algorithm has been reduced from 32.36 m to 4.07 m, and the increase in computational load is kept within an acceptable range.

Angular Bloch oscillations and their applications

Abstract To advance inertial navigation, we present the scheme for a compact quantum sensor which is based on the quantum phenomenon of the angular Bloch oscillations and measuring exclusively the angular acceleration of slow external rotation. We study the dynamics of ultra-cold atoms confined in a toroidal trap with a ring-lattice along the azimuth angle, realized with the superposition of two copropagating Laguerre–Gaussian beams. In the presence of external rotation with a small angular acceleration, or a prescribed linear chirp between the two beams, the measured angular momentum of the trapped atoms exhibits a specific periodic behaviour in time, which we call as the angular Bloch oscillations. This quantum phenomenon is shown to be a key element of fruitful applications for (i) an efficient transfer of quantized angular momentum from the light to the atoms by controlling the chirp, and (ii) the direct determination of the angular acceleration of external rotation by measuring the Bloch period.

Experimental assessment of IMU data processing techniques for a backpack mobile laser scanning system

Abstract. Positioning techniques are fundamental in many automation tasks with several applications. In GNSS-denied environments like in dense forests, other alternatives are required, such as inertial and visual navigation. However, Inertial Measurement Units (IMUs) data, mainly those from microelectromechanical-system (MEMS), are noisy, which affects the orientation estimation. MEMS IMUs have been employed in mobile laser scanning systems due to their compact design and low-cost solutions for short-term navigation. In this paper, we have compared three IMU processing techniques freely available: MAH (Mahony et al., 2009), MAD (Madgwick et al., 2011) and DCM (Hyyti and Visala, 2015). These techniques implemented different approaches to estimate the attitude. They were experimentally assessed with data from a backpack mobile laser scanning system, which is composed of an OS0-128 Ouster LiDAR equipped with an internal IMU. We have used data from a 5-second trajectory segment aiming to evaluate the attitude and position estimation for a local path. The results showed that the DCM algorithm maintained a consistent velocity for 5 seconds, achieving a positional error of 1.4 m, 0.06 m, and 1.05 m along the X-, Y- and Z-axis, respectively. In contrast, MAD and MAH showed a position error over 20 m, 7 m and 3 m along the X-, Y- and Z-axis, respectively, which was affected by the velocity drift.

Evaluating Alternative Registration Planes in Imageless, Computer-Assisted Navigation Systems for Direct Anterior Total Hip Arthroplasty.

(1) Background: Imageless computer navigation systems have the potential to improve the accuracy of acetabular cup position in total hip arthroplasty (THA). Popular imageless navigation methods include locating the patient in a three-dimensional space (registration method) while using a baseline to angle the acetabular cup (reference plane). This study aims to compare the accuracy of different methods for determining postoperative acetabular cup positioning in THA via the direct anterior approach. (2) Methods: Fifty-one participants were recruited. Optical and inertial sensor imageless navigation systems were used simultaneously with three combinations of registration methods and reference planes: the anterior pelvic plane (APP), the anterior superior iliac spine (ASIS) and the table tilt (TT) method. Postoperative acetabular cup position, inclination, and anteversion were assessed using CT scans. (3) Results: For inclination, the mean absolute error (MAE) was lower using the TT method (2.4° ± 1.7°) compared to the ASIS (2.8° ± 1.7°, p = 0.17) and APP method (3.7° ± 2.1°, p < 0.001). For anteversion, the MAE was significantly lower for the TT method (2.4° ± 1.8°) in contrast to the ASIS (3.9° ± 3.2°, p = 0.005) and APP method (9.1° ± 6.2°, p < 0.001). (4) Conclusion: A functional reference plane is superior to an anatomic reference plane to accurately measure intraoperative acetabular cup inclination and anteversion in THA using inertial imageless navigation systems.

Research on intelligent cutting control technology of transverse moving machine for large cross-section roadheader

With the continuous development of the coal mine industry in our country, the cross-section of the roadway is getting larger and larger. The widely used EBZ series roadheader cannot complete the roadway cutting operation with a large cross-section at one time, so it usually needs to move the equipment left and right to complete all its cutting tasks. This paper studies the intelligent control technology of large cross-section roadway cutting, which mainly solves the positioning and attitude determination technology of roadheader in the large cross-section, and offers an accurate shape-cutting control technology and a path planning technology using a lateral moving machine. This paper proposes to combine the signals of laser sensor and fiber-optic inertial navigation system to form a combined positioning and attitude determination system, so as to make use of the advantages and avoid the disadvantages of their respective systems, and improve the accuracy of roadheader positioning and attitude determination. A swing kinematics model of the cutting arm is established, based on which the precise motion control of the first roadway section cutting and the second roadway section cutting can be realized. A key parameter calculation model of roadheader lateral moving machine is put forward to calculate the operation parameters for roadheader lateral moving machine path planning. Finally, the experimental research on intelligent cutting control technology of large cross-section roadheader is carried out in 12307 intelligent heading face of Wangjialing Coal Mine. The results show that the positioning error of the combined positioning and attitude determination system proposed in this paper is between 50-90 mm in the X-axis direction and between 25-45 mm in the Y-axis direction. The average attitude measurement error of heading angle is between 0.5 and 1.5°. This makes the technology appropriate for engineering use. The studied cutting control system achieves a cutting error of 25-50 mm for the first section, and a cutting error of 40-90 mm for the complete section. The complete section cutting error meets the ±100 mm cutting error requirement required in engineering. The intelligent cutting control technology of the lateral moving machine of the large-section tunnel boring machine studied in this paper can realize accurate cutting of the large-section tunnel of 5.6 meters. The research results of this paper provide a reference for the intelligent construction of heading faces.

Quantum sensing of acceleration and rotation by interfering magnetically launched atoms.

Accurate and stable measurement of inertial quantities is essential in geophysics, geodesy, fundamental physics, and inertial navigation. Here, we present an architecture for a compact cold-atom accelerometer-gyroscope based on a magnetically launched atom interferometer. Characterizing the launching technique, we demonstrate 700-parts per million gyroscope scale factor stability over 1 day, while acceleration and rotation rate bias stabilities of 7 × 10-7 meters per second squared and 4 × 10-7 radians per second are reached after 2 days of integration of the cold-atom sensor. Hybridizing it with a classical accelerometer and gyroscope, we correct their drift and bias to achieve respective 100-fold and 3-fold increase on the stability of the hybridized sensor compared to the classical ones. Compared to a state-of-the-art atomic gyroscope, the simplicity and scalability of our launching technique make this architecture easily extendable to a compact full six-axis inertial measurement unit, providing a pathway toward autonomous positioning and orientation using cold-atom sensors.

The Improved Inertial Navigation Algorithm for Low-cost MEMS Sensors

Abstract This paper proposes an improved low-cost inertial guidance solution algorithm to address the issue of insufficient solution accuracy of traditional low-cost device inertial guidance algorithms. The influence of the Earth’s rotation is introduced into the attitude update of the traditional low-cost inertial guidance algorithm, thereby improving the navigation and positioning capability of the carrier. The results of the simulation demonstrate that the proposed algorithm outperforms the traditional algorithm in terms of attitude angle error, with a reduction of four orders of magnitude. Furthermore, the northward and skyward velocity errors are reduced by one order of magnitude, while the eastward velocity dispersion is effectively suppressed. The positioning accuracy is improved by 66%. These findings provide valuable insights that can inform the development of low-cost MEMS navigation engineering applications.

Digital Compensation Technology for Enhancing the Attitude Demodulation Precision of Laser Inertial Navigation System

Digital Compensation Technology for Enhancing the Attitude Demodulation Precision of Laser Inertial Navigation System

A rapid and accurate transfer alignment method using inertial instrument measurement information

The rapidity and precision of transfer alignment impacts the response speed and working precision of inertial navigation system (INS) directly, and flexural deformation is a critical constraint on transfer alignment performance. However, transfer alignment performance of the traditional modeling estimation method is easily degraded by the effect of model mismatch. Therefore, a rapid and accurate transfer alignment method using inertial instrument measurements is proposed in this paper. The relative attitude of main/sub INSs is roughly estimated by angular velocity measurements. Then, a novel transfer alignment filter model is established by relative attitude error model, and measurements of inertial instrument are used to construct angular increment matching and specific force matching quantities. This approach improves both the rapidity and precision of sub INS’s alignment. The performance validation results indicate that compared with traditional methods, the proposed method can improve alignment accuracy by more than 70% and significantly shorten alignment time, thus realizing rapid and accurate alignment.

Orientation of inertialess spheroidal particles in turbulent channel flow with spanwise rotation

The orientation dynamics of inertialess prolate and oblate spheroidal particles in a directly simulated spanwise-rotating turbulent channel flow has been investigated by means of an Eulerian–Lagrangian point-particle approach. The channel rotation and the particle shape were parameterized using a rotation number Ro and the aspect ratio λ, respectively. Eleven particle shapes 0.05 ≤ λ ≤ 20 and four rotation rates 0 ≤ Ro ≤ 10 have been examined. The spheroidal particles retained their almost isotropic orientation in the core region of the channel, despite the significant mean shear rate set up by the Coriolis force. Irrespective of channel rotation rate Ro, rod-like spheroids tend to align in the streamwise direction, while disk-like particles are oriented in the wall-normal direction. These trends were accentuated with increasing departure from sphericity λ = 1. The changeover from the isotropic orientation mode in the centre to the highly anisotropic near-wall orientation mode commenced further away from the suction-side wall with increasing Ro, whereas the particle orientations on the pressure side of the rotating channel remained essentially unaffected by Ro. We observed that the alignments of the fluid rotation vector with the Lagrangian stretching direction were similarly unaffected by the imposed system rotation, except that the de-alignment set in deeper into the core at high Ro. This contrasts with the well-known substantial impact of system rotation on the velocity and vorticity fields. Similarly, slender rods and flatter disks were aligned with the Lagrangian stretching and compression directions, respectively, for all Ro considered, except in the vicinity of the walls. The typical near-wall de-alignment extended considerably further away from the suction-side wall at high Ro. We conjecture that this phenomenon reflects a change in the relative importance of mean shear and small-scale turbulence caused by the Coriolis force. Preferential particle alignment with Lagrangian stretching and compression directions are known from isotropic and anisotropic turbulence in inertial reference systems. The present results demonstrate the validity of this principle also in a non-inertial system.

A Novel Robust Position Integration Optimization-Based Alignment Method for In-Flight Coarse Alignment.

In-flight alignment is a critical milestone for inertial navigation system/global navigation satellite system (INS/GNSS) applications in unmanned aerial vehicles (UAVs). The traditional position integration formula for in-flight coarse alignment requires the GNSS velocity data to be valid throughout the alignment period, which greatly limits the engineering applicability of the method. In this paper, a new robust position integration optimization-based alignment (OBA) method for in-flight coarse alignment is presented to solve the problem of in-flight alignment under a prolonged ineffective GNSS. In this methodology, to achieve a higher alignment accuracy in case the GNSS is not effective throughout the alignment period, the integration of GNSS velocity into the local-level navigation frame is replaced by the GNSS position in the Earth-centered, Earth-fixed frame, which avoids the need for complete GNSS velocity data. The simulation and flight test results show that the new robust position integration method proposed in this paper achieves higher stability and robustness than the conventional position integration OBA method and can achieve an alignment accuracy of 0.2° even when the GNSS is partially time-invalidated. Thus, this greatly extends the application of the OBA method for in-flight alignment.

Application and Prospect of Strapdown Inertial Navigation System in Coal Mining Equipment.

In recent years, with the rapid construction of a safe, clean, efficient and sustainable modern energy system, the intelligence of coal mining has become the inevitable direction of the development of the coal mining industry. The intelligence of coal mining system and equipment is the core of intelligent mining, and the positioning technology of mining equipment is the key to underground intelligent mining. The strapdown inertial navigation system can make up for the shortcomings of traditional GPS positioning systems and laser positioning because of its strong anti-interference, high precision and real-time monitoring, and ability to carry out real-time dynamic positioning of mining equipment in underground coal mines. This paper briefly introduces the basic principle of the strapdown inertial navigation system, analyzes the application of the existing strapdown inertial navigation system in mining equipment, and lists and analyzes the research status of the improvement strategy of the inertial navigation system, such as zero speed correction and integrated navigation technology. Finally, by analyzing the application and future development trend of inertial navigation systems in mining equipment, this paper provides more data and method support for the positioning of mining equipment in the future.

Positioning Systems for Unmanned Underwater Vehicles: A Comprehensive Review

Positioning systems are integral to Unmanned Underwater Vehicle (UUV) operation, enabling precise navigation and control in complex underwater environments. This paper comprehensively reviews the key technologies employed for UUV positioning, including acoustic systems, inertial navigation, Doppler velocity logs, and GPS when near the surface. These systems are essential for seabed mapping, marine infrastructure inspection, and search and rescue operations. The review highlights recent technological advancements and examines the integration of these systems to enhance accuracy and operational efficiency. It also addresses ongoing challenges, such as communication constraints, environmental variability, and discrepancies between theoretical models and field applications. Future trends in positioning system development are discussed, with a focus on improving reliability and performance in diverse underwater conditions to support the expanding capabilities of UUVs across scientific, commercial, and rescue missions.

Autonomous Positioning for Mobile Vehicles Based on Visual‐Inertial Fusion in Challenging Dark Roadway Scenes

ABSTRACTAccurate positioning for autonomous driven underground mining vehicles (UMVs) and coal mine robots (CMRs) is indeed one of the cores in the intelligentization of coal mining. Completely different from positioning on the ground and in parking scenes, there will be great difficulties in realizing the accurate active positioning for UMVs shuttled in dark and narrow roadways. We propose an effective visual and inertial fusion positioning method for autonomous CMRs and roadheaders in challenging roadway scenarios based on the odometer‐aided inertial navigation system and visual pose estimation system. Velocity information of the odometer is adapted to restrain the error accumulation of inertial positioning based on a Kalman filter. The hybrid visual feature detection algorithm is put forward to improve the accuracy and robustness of visual observation information in a dark environment. Autonomous experiments for CMRs and roadheaders are separately performed in the narrow roadway and dark passageway to demonstrate the applicability of our localization method. The proposed approach outperforms the subsystems and existing methods in accuracy and has outstanding stability.

Invariant Extended Kalman Filtering for Pedestrian Deep-Inertial Odometry

Abstract. Indoor localization for pedestrians, which relies solely on inertial odometry, has been a topic of great interest. Its significance lies in its ability to provide positioning solutions independently, without the need for external data. Although traditional strap-down inertial navigation shows rapid drift, the introduction of pedestrian dead reckoning (PDR), and artificial intelligence (AI) has enhanced the applicability of inertial odometry for indoor localization. However, inertial odometry continues to be affected by drift, inherent to the nature of dead reckoning. This implies that even a slight error at a given moment can lead to a significant decrease in accuracy after continuous integration operations. In this paper, we propose a novel approach aimed at enhancing the positioning accuracy of inertial odometry. Firstly, we derive a learning-based forward speed using inertial measurements from a smartphone. Unlike mainstream methods where the learned speed is directly used to determine the position, we use the forward speed combined with non-holonomic constraint (NHC) as a measurement to update the state predicted within a strap-down inertial navigation framework. Secondly, we employ an invariant extended Kalman filter (IEKF)-based state estimation to facilitate fusion to cope with the nonlinearity arising from the system and measurement model. Experimental tests are carried out in different scenarios using an iPhone 12, and traditional methods, including PDR, robust neural inertial navigation (RONIN), and the EKF-based method, are compared. The results suggest that the method we propose surpasses these traditional methods in performance.

Global integrated navigation position correction algorithm and virtual polar region technology based on normal vector

To achieve the inherent uniformity of all-earth navigation for autonomous underwater vehicles (AUV), a global integrated navigation position correction algorithm based on the normal vector (n-vector) is proposed. First, a four-element vector comprising the non-singular n-vector and height represents the carrier’s position in the Earth-centered Earth-fixed (ECEF) frame. The integrated navigation systems are designed with the strapdown inertial navigation system (SINS), Doppler velocity log (DVL), and other equipment. Secondly, the reverse navigation algorithm in the ECEF mechanization is derived, and the results of forward and reverse navigation are fused to correct the AUV’s underwater position. Additionally, a virtual polar region technology based on the ECEF attitude, velocity, and height invariant method (E-AVHIM) is proposed to convert the actual test data obtained at low and middle latitudes into high latitudes for more convincing polar region algorithm verification. Simulations and lake trial demonstrated the excellence and efficiency of the proposed algorithm.

Simulation of Launch Pad Atomization for Military Weapon System

This study aims to optimize three critical parameters (inclination angle, hook lifting, and sparking) for a missile launching system by combining precise mathematical methods, IoT concepts, and advanced sensor technologies. The system uses an Inertial Navigation System (INS) in conjunction with gyro and proximity sensors to ensure accurate target interception by carefully determining the optimal launch angle. The Internet of Things concept is integrated effortlessly, with a clever coordinating WiFi networking, weight estimation, and sensor data processing for real-time cloud data flow. Security protocols protect the integrity of the data, and a reliable power supply system guarantees reliable operation. The project incorporates both Hot Start and Cold Start functionalities, enabling dependable launches and prompt adaptations to dynamic changes. Flexible igniting mechanisms such as Chemical, Electrical, and Electro-Chemical systems are available, and reliable and secure missile launches are prioritized with safety features like Spark Damping Inner Tube Coating and Moisture-Resistant igniting. All things considered, this project prioritizes security, dependability, and adaptability while addressing critical elements required for a sophisticated and efficient missile launching system.