Decimeter-Level Accuracy for Smartphone Real-Time Kinematic Positioning Implementing a Robust Kalman Filter Approach and Inertial Navigation System Infusion in Complex Urban Environments.

New smartphones provide real-time access to GNSS pseudorange, Doppler, or carrier-phase measurement data at 1 Hz. Simultaneously, they can receive corrections broadcast by GNSS reference stations to perform real-time kinematic (RTK) positioning. This study aims at the real-time positioning capabilities of smartphones using raw GNSS measurements as a conventional method and proposes an improvement to the positioning through the integration of Inertial Navigation System (INS) measurements. A U-Blox GNSS receiver, model ZED-F9R, was used as a benchmark for comparison. We propose an enhanced ambiguity resolution algorithm that integrates the traditional LAMBDA method with an adaptive thresholding mechanism based on real-time quality metrics. The RTK/INS fusion method integrates RTK and INS measurements using an extended Kalman filter (EKF), where the state vector x includes the position, velocity, orientation, and their respective biases. The innovation here is the inclusion of a real-time weighting scheme that adjusts the contribution of the RTK and INS measurements based on their current estimated accuracy. Also, we use the tightly coupled (TC) RTK/INS fusion framework. By leveraging INS data, the system can maintain accurate positioning even when the GNSS data are unreliable, allowing for the detection and exclusion of abnormal GNSS measurements. However, in complex urban areas such as Qazvin City in Iran, the fusion method achieved positioning accuracies of approximately 0.380 m and 0.415 m for the Xiaomi Mi 8 and Samsung Galaxy S21 Ultra smartphones, respectively. The subsequent detailed analysis across different urban streets emphasized the significance of choosing the right positioning method based on the environmental conditions. In most cases, RTK positioning outperformed Single-Point Positioning (SPP), offering decimeter-level precision, while the fusion method bridged the gap between the two, showcasing improved stability accuracy. The comparative performance between the Samsung Galaxy S21 Ultra and Xiaomi Mi 8 revealed minor differences, likely attributed to variations in the hardware design and software algorithms. The fusion method emerged as a valuable alternative when the RTK signals were unavailable or impractical. This demonstrates the potential of integrating RTK and INS measurements for enhanced real-time smartphone positioning, particularly in challenging urban environments.

Wearable Multi-Sensor Positioning Prototype for Rowing Technique Evaluation.

The goal of this study is to determine the feasibility of a wearable multi-sensor positioning prototype to be used as a training tool to evaluate rowing technique and to determine the positioning accuracy using multiple mathematical models and estimation methods. The wearable device consists of an inertial measurement unit (IMU), an ultra-wideband (UWB) transceiver, and a global navigation satellite system (GNSS) receiver. An experiment on a rowing shell was conducted to evaluate the performance of the system on a rower's wrist, against a centimeter-level GNSS reference trajectory. This experiment analyzed the rowing motion in multiple navigation frames and with various positioning methods. The results show that the wearable device prototype is a viable option for rowing technique analysis; the system was able to provide the position, velocity, and attitude of a rower's wrist, with a positioning accuracy ranging between ±0.185 m and ±1.656 m depending on the estimation method.

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.

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.

Freehand 3D Ultrasound Imaging Based on Probe-mounted Vision and IMU System.

OBJECTIVES: Freehand three-dimensional (3D) ultrasound (US) is of great significance for clinical diagnosis and treatment, it is often achieved with the aid of external devices (optical and/or electromagnetic, etc.) that monitor the location and orientation of the US probe. However, this external monitoring is often impacted by imaging environment such as optical occlusions and/or electromagnetic (EM) interference. METHODS: To address the above issues, we integrated a binocular camera and an inertial measurement unit (IMU) on a US probe. Subsequently, we built a tight coupling model utilizing the unscented Kalman algorithm based on Lie groups (UKF-LG), combining vision and inertial information to infer the probe's movement, through which the position and orientation of the US image frame are calculated. Finally, the volume data was reconstructed with the voxel-based hole-filling method. RESULTS: The experiments including calibration experiments, tracking performance evaluation, phantom scans, and real scenarios scans have been conducted. The results show that the proposed system achieved the accumulated frame position error of 3.78 mm and the orientation error of 0.36° and reconstructed 3D US images with high quality in both phantom and real scenarios. CONCLUSIONS: The proposed method has been demonstrated to enhance the robustness and effectiveness of freehand 3D US. Follow-up research will focus on improving the accuracy and stability of multi-sensor fusion to make the system more practical in clinical environments.

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.

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.

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°.

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 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.

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.

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.

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.

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.

Seamless MEMS-INS/Geomagnetic Navigation System Based on Deep-Learning Strong Tracking Square-Root Cubature Kalman Filter.

To suppress inertial navigation system drift and improve the seamless navigation capability of microelectromechanical system-inertial navigation systems/geomagnetic navigation systems (MEMS-INS/MNS) in geomagnetically unlocked environments, this paper proposes a hybrid seamless MEMS-INS/MNS strategy combining a strongly tracked square-root cubature Kalman filter with deep self-learning (DSL-STSRCKF). The proposed DSL-STSRCKF method consists of two innovative steps: (i) The relationship between the deep Kalman filter gain and the optimal estimation is established. In this paper, combining the two auxiliary methods of strong tracking filtering and square-root filtering based on singular value decomposition, the heading accuracy error of ST-SRCKF can reach 1.29°, which improves the heading accuracy by 90.10% and 9.20% compared to the traditional single INS and the traditional integrated navigation algorithm and greatly improves the robustness and computational efficiency. (ii) Providing deep self-learning capability for the ST-SRCKF by introducing a nonlinear autoregressive neural network (NARX) with exogenous inputs, which means that the heading accuracy can still reach 1.33° even during the MNS lockout period, and the heading accuracy can be improved by 89.80% compared with the single INS, realizing the continuous high-precision navigation estimation.

Application of Adaptive Robust Kalman Filter Base on MCC for SINS/GPS Integrated Navigation.

In this paper, an adaptive and robust Kalman filter algorithm based on the maximum correntropy criterion (MCC) is proposed to solve the problem of integrated navigation accuracy reduction, which is caused by the non-Gaussian noise and time-varying noise of GPS measurement in complex environment. Firstly, the Grubbs criterion was used to remove outliers, which are contained in the GPS measurement. Then, a fixed-length sliding window was used to estimate the decay factor adaptively. Based on the fixed-length sliding window method, the time-varying noises, which are considered in integrated navigation system, are addressed. Moreover, a MCC method is used to suppress the non-Gaussian noises, which are generated with external corruption. Finally, the method, which is proposed in this paper, is verified by the designed simulation and field tests. The results show that the influence of the non-Gaussian noise and time-varying noise of the GPS measurement is detected and isolated by the proposed algorithm, effectively. The navigation accuracy and stability are improved.

Fault-Tolerant SINS/Doppler Radar/Odometer Integrated Navigation Method Based on Two-Stage Fault Detection Structure.

To improve the reliability of strapdown inertial navigation system (SINS)/Doppler radar/odometer integrated navigation system, the federated Kalman filter with two-stage fault detection structure is designed, and a fault-tolerant SINS/Doppler radar/odometer integrated navigation method is proposed. Firstly, the pre-fault detection module sets before the local filter, and the residual chi-square test in the carrier coordinate system is selected to detect the abrupt faults of Doppler radar and odometer. Then, the secondary-fault detection module emplaces between the local filter and the main filter, and the sequential probability ratio test (SPRT) is selected to further detect the ramp faults that are difficult to detect by the residual chi-square test. To address the limitation of the SPRT in accurately determining the end time of faults, an improved SPRT is proposed. The improved SPRT reduces the influence of historical fault on the fault statistics by introducing forgetting factors to improve its sensitivity to the fault end. The simulation experiment indicates that the proposed method can quickly detect and isolate abrupt and ramp faults, and promptly restore normal operation of the integrated navigation system after the fault ends, effectively improving the fault tolerance and reliability of the integrated navigation system.

A Cycle Slip Detection and Repair Method Based on Inertial Aiding for BDS Triple-Frequency Signals.

Cycle slip detection and repair is a prerequisite to obtain high-precision positioning based on a carrier phase. Traditional triple-frequency pseudorange and phase combination algorithm are highly sensitive to the pseudorange observation accuracy. To solve the problem, a cycle slip detection and repair algorithm based on inertial aiding for a BeiDou navigation satellite system (BDS) triple-frequency signal is proposed. To enhance the robustness, the INS-aided cycle slip detection model with double-differenced observations is derived. Then, the geometry-free phase combination is united to detect the insensitive cycle slip, and the optimal coefficient combination is selected. Furthermore, the L2-norm minimum principle is used to search and confirm the cycle slip repair value. To correct the INS error accumulated over time, the extended Kalman filter based on the BDS/INS tightly coupled system is established. The vehicular experiment is conducted to evaluate the performance of the proposed algorithm from a few aspects. The results indicate that the proposed algorithm can reliably detect and repair all cycle slips that occur in one cycle, including the small and insensitive cycle slips as well as the intensive and continuous cycle slips. Additionally, in signal-challenged environments, the cycle slips occurring 14 s after a satellite signal outage can be correctly detected and repaired.

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.

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.