Enhancing Pure Inertial Navigation Accuracy through a Redundant High-Precision Accelerometer-Based Method Utilizing Neural Networks.

The pure inertial navigation system, crucial for autonomous navigation in GPS-denied environments, faces challenges of error accumulation over time, impacting its effectiveness for prolonged missions. Traditional methods to enhance accuracy have focused on improving instrumentation and algorithms but face limitations due to complexity and costs. This study introduces a novel device-level redundant inertial navigation framework using high-precision accelerometers combined with a neural network-based method to refine navigation accuracy. Experimental validation confirms that this integration significantly boosts navigational precision, outperforming conventional system-level redundancy approaches. The proposed method utilizes the advanced capabilities of high-precision accelerometers and deep learning to achieve superior predictive accuracy and error reduction. This research paves the way for the future integration of cutting-edge technologies like high-precision optomechanical and atom interferometer accelerometers, offering new directions for advanced inertial navigation systems and enhancing their application scope in challenging environments.

Research on Inertial Navigation and Environmental Correction Indoor Ultra-Wideband Ranging and Positioning Methods.

In contrast to outdoor environments, indoor positioning encounters signal propagation disruptions due to the presence of buildings, resulting in reduced accuracy and, at times, the inability to determine a location accurately. This research, leveraging the robust penetrative capabilities of Ultra-Wideband (UWB) signals in non-line-of-sight (NLOS) scenarios, introduces a methodology for refining ranging outcomes through a combination of inertial navigation and environmental adjustments to achieve high-precision spatial positioning. This approach systematically enhances the correction of signal propagation errors through walls. Initially, it digitalizes the spatial setting, preserving the error correction parameters. Subsequently, it employs inertial navigation to estimate spatial coordinates and delineate signal propagation pathways to achieve precise ranging results. It iteratively hones the positioning outcomes for enhanced precision. Empirical findings demonstrate that within NLOS conditions, compared to standalone UWB positioning and IMU/UWB fusion positioning using the ESKF algorithm, this positioning technique significantly enhances planar positioning accuracy while achieving a marginal elevation accuracy improvement, albeit with some residual deviations from actual values. Furthermore, this positioning methodology effectively rectifies results in NOLS settings, paving the way for a novel approach to optimize indoor positioning through UWB technology.

Experimental Research on Shipborne SINS Rapid Mooring Alignment with Variance-Constraint Kalman Filter and GNSS Position Updates.

Analytical coarse alignment and Kalman filter fine alignment based on zero-velocity are typically used to obtain initial attitude for inertial navigation systems (SINS) on a static base. However, in the shipboard mooring state, the static observation condition is corrupted. This paper presents a rapid alignment method for SINS on swaying bases. The proposed method begins with a coarse alignment technique in the inertial frame to obtain an initial rough attitude. Subsequently, a Kalman filter with position updates is employed to estimate the remaining misalignment error. To enhance the filter estimation performance, an appropriate lower boundary is set to the target states' variances according to a carefully designed relative convergence index. The variance-constraint Kalman filter (VCKF) approach is proposed in this paper, and the shipborne experiments validate its effectiveness. The results demonstrate that the VCKF approach significantly reduces the time requirement for fine alignment to achieve the same accuracy on a swaying base, from 90 min in the classic Kalman filter to 30 min. Additionally, the parameter estimation performance in the Kalman filter is also improved, particularly in situations where unpredicted external interference is involved during fine alignment.

Abnormal Pavement Condition Detection with Vehicle Posture Data Considering Speed Variations.

Pavement condition monitoring is an important task in road asset management and efficient abnormal pavement condition detection is critical for timely conservation management decisions. The present work introduces a mobile pavement condition monitoring approach utilizing low-cost sensor technology and machine-learning-based methodologies. Specifically, an on-board unit (OBU) embedded with an inertial measurement unit (IMU) and global positioning system (GPS) is applied to collect vehicle posture data in real time. Through a comprehensive analysis of both time domain and frequency domain data features for both normal and abnormal pavement conditions, feature engineering is conducted to identify how the most important features affect abnormal pavement condition recognition. Six machine learning models are then developed to identify different types of pavement conditions. The performance of different algorithms and the significance of different features are then analyzed. Moreover, the influence of vehicle speed on pavement condition assessment is further examined and classification models for different speed intervals are developed. The results indicate that the random forest (RF) model that considers vehicle speed achieves the best performance in pavement condition monitoring. The outcomes of the present work would contribute to cost-effective pavement condition monitoring and provide an important reference for pavement maintenance sectors.

Design of a Multi-Position Alignment Scheme.

The current new type of inertial navigation system, including rotating inertial navigation systems and three-autonomy inertial navigation systems, has been increasingly widely applied. Benefited by the rotating mechanisms of these inertial navigation systems, alignment accuracy can be significantly enhanced by implementing IMU (Inertial Measurement Unit) rotation during the alignment process. The principle of suppressing initial alignment errors using rotational modulation technology was investigated, and the impact of various component error terms on alignment accuracy of IMU during rotation was analyzed. A corresponding error suppression scheme was designed to overcome the shortcoming of the significant scale factor error of fiber optic gyroscopes, and the research content of this paper is validated through corresponding simulations and experiments. The results indicate that the designed alignment scheme can effectively suppress the gyro scale factor error introduced by angular motion and improve alignment accuracy.

Testing and Analysis of Selected Navigation Parameters of the GNSS/INS System for USV Path Localization during Inland Hydrographic Surveys.

One of the main methods of the path localization of moving objects is positioning using Global Navigation Satellite Systems (GNSSs) in cooperation with Inertial Navigation Systems (INSs). Its basic task is to provide high availability, in particular in areas with limited access to satellite signals such as forests, tunnels or urban areas. The aim of the article is to carry out the testing and analysis of selected navigation parameters (3D position coordinates (Northing, Easting, and height) and Euler angles (pitch and roll)) of the GNSS/INS system for Unmanned Surface Vehicle (USV) path localization during inland hydrographic surveys. The research used the Ellipse-D GNSS/INS system working in the Real Time Kinematic (RTK) mode in order to determine the position of the "HydroDron" Autonomous Surface Vehicle (ASV). Measurements were conducted on four representative routes with a parallel and spiral arrangement of sounding profiles on Lake Klodno (Poland). Based on the obtained research results, position accuracy measures of the "HydroDron" USV were determined using the Ellipse-D GNSS/INS system. Additionally, it was determined whether USV path localization using a GNSS/INS system working in the RTK mode meets the positioning requirements for inland hydrographic surveys. Research has shown that the Ellipse-D system operating in the RTK mode can be successfully used to position vessels when carrying out inland hydrographic surveys in all International Hydrographic Organization (IHO) Orders (Exclusive, Special, 1a/1b and 2) even when it does not work 100% correctly, e.g., loss of RTK corrections for an extended period of time. In an area with limited coverage of the mobile network operator (30-40% of the time the receiver operated in the differential mode), the positioning accuracy of the "HydroDron" USV using the Ellipse-D GNSS/INS system working in the RTK mode was from 0.877 m to 0.941 m for the R95(2D) measure, depending on the route travelled. Moreover, research has shown that if the Ellipse-D system performed GNSS/INS measurements using the RTK method, the pitch and roll error values amounted to approx. 0.06°, which is almost identical to that recommended by the device manufacturer. However, when working in the differential mode, the pitch and roll error values increased from 0.06° to just over 0.2°.

Seamless Fusion: Multi-Modal Localization for First Responders in Challenging Environments.

In dynamic and unpredictable environments, the precise localization of first responders and rescuers is crucial for effective incident response. This paper introduces a novel approach leveraging three complementary localization modalities: visual-based, Galileo-based, and inertial-based. Each modality contributes uniquely to the final Fusion tool, facilitating seamless indoor and outdoor localization, offering a robust and accurate localization solution without reliance on pre-existing infrastructure, essential for maintaining responder safety and optimizing operational effectiveness. The visual-based localization method utilizes an RGB camera coupled with a modified implementation of the ORB-SLAM2 method, enabling operation with or without prior area scanning. The Galileo-based localization method employs a lightweight prototype equipped with a high-accuracy GNSS receiver board, tailored to meet the specific needs of first responders. The inertial-based localization method utilizes sensor fusion, primarily leveraging smartphone inertial measurement units, to predict and adjust first responders' positions incrementally, compensating for the GPS signal attenuation indoors. A comprehensive validation test involving various environmental conditions was carried out to demonstrate the efficacy of the proposed fused localization tool. Our results show that our proposed solution always provides a location regardless of the conditions (indoors, outdoors, etc.), with an overall mean error of 1.73 m.

A Fast Self-Calibration Method for Dual-Axis Rotational Inertial Navigation Systems Based on Invariant Errors.

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.

An Improved Initial Alignment Method Based on SE2(3)/EKF for SINS/GNSS Integrated Navigation System with Large Misalignment Angles.

This paper proposes an improved initial alignment method for a strap-down inertial navigation system/global navigation satellite system (SINS/GNSS) integrated navigation system with large misalignment angles. Its methodology is based on the three-dimensional special Euclidean group and extended Kalman filter (SE2(3)/EKF) and aims to overcome the challenges of achieving fast alignment under large misalignment angles using traditional methods. To accurately characterize the state errors of attitude, velocity, and position, these elements are constructed as elements of a Lie group. The nonlinear error on the Lie group can then be well quantified. Additionally, a group vector mixed error model is developed, taking into account the zero bias errors of gyroscopes and accelerometers. Using this new error definition, a GNSS-assisted SINS dynamic initial alignment algorithm is derived, which is based on the invariance of velocity and position measurements. Simulation experiments demonstrate that the alignment method based on SE2(3)/EKF can achieve a higher accuracy in various scenarios with large misalignment angles, while the attitude error can be rapidly reduced to a lower level.

[Research on Locating Device for the Entry Point of Intramedullary Nail Based on Inertial Navigation].

Objective: To introduce a locating device for the entry point of intramedullary nail based on the inertial navigation technology, which utilizes multi-dimensional angle information to assist in rapid and accurate positioning of the ideal direction of femoral anterograde intramedullary nails' entry point, and to verify its clinical value through clinical tests. Methods: After matching the locating module with the developing board, which are the two components of the locating device, they were placed on the skin surface of the proximal femur of the affected side. Anteroposterior fluoroscopy was performed. The developing angle corresponding to the ideal direction of entry point was selected based on the X-ray image, and then the yaw angle of the locating module was reset to zero. After resetting, the locating module was combined with the surgical instrument to guide the insertion angle of the guide wire. The ideal direction of entry point was accurately located based on the angle guidance. By setting up an experimental group and a control group for clinical surgical operations, the number of guide wire insertion times, surgical time, fluoroscopy frequency, and intraoperative blood loss with or without the locating device was recorded. Results: Compared to the control group, the experimental group showed significant improvement in the number of guide wire insertion times, surgical time, fluoroscopy frequency, and intraoperative blood loss, with a statistically significant difference (P<0.01). Conclusion: The locating device can assist doctors in quickly locating the entry point of intramedullary nail, effectively reducing the fluoroscopy frequency and surgical time by improving the success rate of the guide wire insertion with one shot, improving surgical efficiency, and possessing certain clinical value.

Gyro-Free Inertial Navigation Systems Based on Linear Opto-Mechanical Accelerometers.

High-sensitivity uniaxial opto-mechanical accelerometers provide very accurate linear acceleration measurements. In addition, an array of at least six accelerometers allows the estimation of linear and angular accelerations and becomes a gyro-free inertial navigation system. In this paper, we analyze the performance of such systems considering opto-mechanical accelerometers with different sensitivities and bandwidths. In the six-accelerometer configuration adopted here, the angular acceleration is estimated using a linear combination of accelerometers' read-outs. The linear acceleration is estimated similarly but requires a correcting term that includes angular velocities. Accelerometers' colored noise from experimental data is used to derive, analytically and through simulations, the performance of the inertial sensor. Results for six accelerometers, separated by 0.5 m in a cube configuration show noise levels of 10-7 m s-2 and 10-5 m s-2 (in Allan deviation) for time scales of one second for the low-frequency (Hz) and high-frequency (kHz) opto-mechanical accelerometers, respectively. The Allan deviation for the angular velocity at one second is 10-5 rad s-1 and 5×10-4 rad s-1. Compared to other technologies such as MEMS-based inertial sensors and optical gyroscopes, the high-frequency opto-mechanical accelerometer exhibits better performance than tactical-grade MEMS for time scales shorter than 10 s. For angular velocity, it is only superior for time scales less than a few seconds. The linear acceleration of the low-frequency accelerometer outperforms the MEMS for time scales up to 300 s and for angular velocity only for a few seconds. Fiber optical gyroscopes are orders of magnitude better than the high- and low-frequency accelerometers in gyro-free configurations. However, when considering the theoretical thermal noise limit of the low-frequency opto-mechanical accelerometer, 5×10-11 m s-2, linear acceleration noise is orders of magnitude lower than MEMS navigation systems. Angular velocity precision is around 10-10 rad s-1 at one second and 5×10-7 rad s-1 at one hour, which is comparable to fiber optical gyroscopes. While experimental validation is yet not available, the results shown here indicate the potential of opto-mechanical accelerometers as gyro-free inertial navigation sensors, provided the fundamental noise limit of the accelerometer is reached, and technical limitations such as misalignments and initial conditions errors are well controlled.

A Combination Scheme of Pure Strapdown and Dual-Axis Rotation Inertial Navigation Systems.

Compared with the strapdown inertial navigation system (SINS), the rotation strapdown inertial navigation system (RSINS) can effectively improve the accuracy of navigation information, but rotational modulation also leads to an increase in the oscillation frequency of attitude errors. In this paper, a dual-inertial navigation scheme that combines the strapdown inertial navigation system and the dual-axis rotation inertial navigation system is proposed, which can effectively improve the attitude error accuracy in the horizontal direction by using the high-position information of the rotation inertial navigation system and the stability characteristics of the attitude error of the strapdown inertial navigation system. Firstly, the error characteristics of the strapdown inertial navigation system and the rotation strapdown inertial navigation system are analyzed, and then the combination scheme and Kalman filter are designed according to the error characteristics, and finally, the simulation experiment shows that the pitch angle error of the dual inertial navigation system is reduced by more than 35% and the roll angle error is reduced by more than 45% compared with the rotation strapdown inertial navigation system. Therefore, the combination scheme of double inertial navigation proposed in this paper can further reduce the attitude error of the rotation strapdown inertial navigation system, and at the same time, the two sets of inertial navigation systems can also enhance the reliability of ship navigation.

A Robust INS/USBL/DVL Integrated Navigation Algorithm Using Graph Optimization.

The Autonomous Underwater Vehicle (AUV) is usually equipped with multiple sensors, such as an inertial navigation system (INS), ultra-short baseline system (USBL), and Doppler velocity log (DVL), to achieve autonomous navigation. Multi-source information fusion is the key to realizing high-precision underwater navigation and positioning. To solve the problem, a fusion scheme based on factor graph optimization (FGO) is proposed. Due to multiple iterations and joint optimization of historical data, FGO could usually show a better performance than the traditional Kalman filter. In addition, considering that USBL and DVL are usually heavily influenced by the environment, outliers are often present. A robust integrated navigation algorithm based on a maximum correntropy criterion and FGO scheme is proposed. The proposed algorithm solves the problem of multi-sensor fusion and non-Gaussian noise. Numerical simulations and field tests demonstrate that the proposed FGO scheme shows a better performance and robustness than the traditional Kalman filter. Compared with the traditional Kalman filtering, the positioning accuracy is improved by 5.3%, 9.1%, and 5.1% in the east, north, and height directions. It can realize a more accurate navigation and positioning of underwater multi-sensors.

Note on Coarse Alignment of Gyro-Free Inertial Navigation System.

In this note, the feasibility of initial alignment of a gyro-free inertial navigation system (GF-INS) is investigated. Initial roll and initial pitch are obtained using leveling of conventional INS since centripetal acceleration is very small. The equation for the initial heading cannot be used since the GF inertial measurement unit (IMU) cannot directly measure the Earth rate. A new equation is derived to obtain the initial heading from GF-IMU accelerometer outputs. Initial heading is expressed in the accelerometer outputs of two configurations, which satisfies a specific condition among 15 GF-IMU configurations presented in the literature. The initial heading error to arrangement and accelerometer error is quantitatively analyzed from the initial heading calculation equation of GF-INS and the initial heading error analysis of the general INS. The initial heading error is investigated when gyroscopes are used with GF-IMU. The results show that the initial heading error depends more on the performance of the gyroscope than that of the accelerometer, and the initial heading cannot be obtained within a practical error level by using only GF-IMU, even when an extremely accurate accelerometer is used. Therefore, aiding sensors have to be used in order to have a practical initial heading.

Simulation Optimization and Application of Shearer Strapdown Inertial Navigation System Modulation Scheme.

The operating attitude of a shearer based on a three-dimensional (3D) space scale is the necessary basic information for realizing intelligent mining. Aiming to address the problem of the insufficient perception accuracy of shearers, in this paper, the rotation model of the actual turning mechanism of the strapdown inertial navigation system (SINS) of shearers is established, and the error propagation characteristics of different single-axis rotation modulation schemes are revealed. Through theory and simulation, the optimal rotation modulation scheme is determined to be the improved four-position turn-stop modulation with a rotation of <360°. The experiment shows that the 24 h positioning error of this scheme is 3.7 nmile, and the heading angle changes by 0.06°, which proves that this scheme can effectively improve the attitude perception accuracy of the inertial navigation system (INS). The field application of the shearer operating attitude perception based on this scheme shows that the positioning error after error compensation is 17% of that before compensation, and the heading angle error is 75% of that before compensation, which verifies that this scheme can significantly improve the accuracy of shearer operating attitude perception in field applications. This scheme can achieve higher precision perception accuracy based on SINS and has broad application prospects in the field of high-precision pose perception of coal mining machines, roadheaders, and other equipment.

Analysis and Suppression of Nonlinear Error of Pendulous Integrating Gyroscopic Accelerometer at Instrument Level.

The error coefficients of the pendulous integrating gyroscopic accelerometer (PIGA) mainly include the bias, scale factor, and nonlinear error. Previous works have fully studied and suppressed the bias and scale factor of PIGAs. At present, the nonlinear error is the most critical factor restricting the measurement accuracy of PIGAs. To address this barrier, a study on the analysis and suppression of the nonlinear error of PIGAs at the instrument level was carried out. Firstly, the error model of a PIGA is established by kinematics and dynamics analyses. Then, nonlinear error is analyzed based on the established model. Finally, a suppression method for the nonlinear error is proposed based on the analysis results. The nonlinear error analysis found that (1) the nonlinear error includes a quadratic term error caused by unequal inertia and the inertia product, cross-coupling error is caused by lateral accelerations, and error is caused by unequal stiffness; (2) unequal inertia and the inertia product were the most critical factors resulting in nonlinear error. Based on the results in the nonlinear error analysis, the suppression method for error focuses on unequal inertia and the inertia product. The proposed method of analysis and suppression was validated experimentally as the quadratic term coefficient was reduced by an order of magnitude from 1.9 × 10-6/g0 to 1.91 × 10-7/g0.

Research on Algorithm of Airborne Dual-Antenna GNSS/MINS Integrated Navigation System.

In view of the difficulties regarding that airborne navigation equipment relies on imports and the expensive domestic high-precision navigation equipment in the manufacturing field of Chinese navigable aircraft, a dual-antenna GNSS (global navigation satellite system)/MINS (micro-inertial navigation system) integrated navigation system was developed to implement high-precision and high-reliability airborne integrated navigation equipment. First, the state equation and measurement equation of the system were established based on the classical discrete Kalman filter principle. Second, according to the characteristics of the MEMS (micro-electric-mechanical system), the IMU (inertial measurement unit) is not sensitive to Earth rotation to realize self-alignment; the magnetometer, accelerometer and dual-antenna GNSS are utilized for reliable attitude initial alignment. Finally, flight status identification was implemented by the different satellite data, accelerometer and gyroscope parameters of the aircraft in different states. The test results shown that the RMS (root mean square) of the pitch angle and roll angle error of the testing system are less than 0.05° and the heading angle error RMS is less than 0.15° under the indoor static condition. A UAV flight test was carried out to test the navigation effect of the equipment upon aircraft take-off, climbing, turning, cruising and other states, and to verify the effectiveness of the system algorithm.

Research on Error Correction Technology in Underwater SINS/DVL Integrated Positioning and Navigation.

Underwater vehicles are key carriers for underwater inspection and operation tasks, and the successful implementation of these tasks depends on the positioning and navigation equipment with corresponding accuracy. In practice, multiple positioning and navigation devices are often combined to integrate the advantages of each equipment. Currently, the most common method for integrated navigation is combination of the Strapdown Inertial Navigation System (SINS) and Doppler Velocity Log (DVL). Various errors will occur when SINS and DVL are combined together, such as installation declination. In addition, DVL itself also has errors in the measurement of speed. These errors will affect the final accuracy of the combined positioning and navigation system. Therefore, error correction technology has great significance for underwater inspection and operation tasks. This paper takes the SINS/DVL integrated positioning and navigation system as the research object and deeply studies the DVL error correction technology in the integrated system.

ConGPS: A Smart Container Positioning System Using Inertial Sensor and Electronic Map with Infrequent GPS.

Real-time global positioning is important for container-based logistics. However, a challenge in real-time global positioning arises from the frequency of both global positioning system (GPS) calls and GPS-denied environments during transportation. This paper proposes a novel system named ConGPS that integrates both inertial sensor and electronic map data. ConGPS estimates the speed and heading direction of a moving container based on the inertial sensor data, the container trajectory, and the speed limit information provided by an electronic map. The directional information from magnetometers, coupled with map-matching algorithms, is employed to compute container trajectories and current positions. ConGPS significantly reduces the frequency of GPS calls required to maintain an accurate current position. To evaluate the accuracy of the system, 280 min of driving data, covering a distance of 360 km, are collected. The results demonstrate that ConGPS can maintain positioning accuracy within a GPS-call interval of 15 min, even if using low-cost inertial sensors in GPS-denied environments.

RIOT: Recursive Inertial Odometry Transformer for Localisation from Low-Cost IMU Measurements.

Inertial localisation is an important technique as it enables ego-motion estimation in conditions where external observers are unavailable. However, low-cost inertial sensors are inherently corrupted by bias and noise, which lead to unbound errors, making straight integration for position intractable. Traditional mathematical approaches are reliant on prior system knowledge, geometric theories and are constrained by predefined dynamics. Recent advances in deep learning, which benefit from ever-increasing volumes of data and computational power, allow for data-driven solutions that offer more comprehensive understanding. Existing deep inertial odometry solutions rely on estimating the latent states, such as velocity, or are dependent on fixed-sensor positions and periodic motion patterns. In this work, we propose taking the traditional state estimation recursive methodology and applying it in the deep learning domain. Our approach, which incorporates the true position priors in the training process, is trained on inertial measurements and ground truth displacement data, allowing recursion and learning both motion characteristics and systemic error bias and drift. We present two end-to-end frameworks for pose invariant deep inertial odometry that utilises self-attention to capture both spatial features and long-range dependencies in inertial data. We evaluate our approaches against a custom 2-layer Gated Recurrent Unit, trained in the same manner on the same data, and tested each approach on a number of different users, devices and activities. Each network had a sequence length weighted relative trajectory error mean ≤0.4594 m, highlighting the effectiveness of our learning process used in the development of the models.