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.

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.

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.

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.

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°.

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.

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.

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.

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.

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.

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.

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.

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.

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 New Self-Calibration and Compensation Method for Installation Errors of Uniaxial Rotation Module Inertial Navigation System.

Calibration and compensation techniques are essential to improve the accuracy of the strap-down inertial navigation system. Especially for the new uniaxial rotation module inertial navigation system (URMINS), replacing faulty uniaxial rotation modules introduces installation errors between modules and reduces navigation accuracy. Therefore, it is necessary to calibrate these systems effectively and compensate for the installation error between modules. This paper proposes a new self-calibration and compensation method for installation errors without additional information and equipment. Using the attitude, velocity, and position differences between the two sets of navigation information output from URMINS as measurements, a Kalman filter is constructed and the installation error is estimated. After URMINS is compensated for the installation error, the average of the demodulated redundant information is taken to calculate the carrier's navigation information. The simulation results show that the proposed method can effectively assess the installation error between modules with an estimation accuracy better than 5". Experimental results for static navigation show that the accuracy of heading angle and positioning can be improved by 73.12% and 81.19% after the URMINS has compensated for the estimated installation errors. Simulation and experimental results further validate the effectiveness of the proposed self-calibration and compensation method.

Experimental Results of Attitude Determination Functional Algorithms Implementation in Strapdown Inertial Navigation System.

Strapdown inertial navigation system (SINS) software developers are usually mainly focused on the attitude determination algorithm design and characteristics. Such an algorithm can be based on different mathematical apparatus. An approach to the derivation of attitude determination algorithm equations in strapdown inertial navigation system is proposed. This algorithm is based on direct heading, pitch, and roll calculation. The qualitative differences between the proposed algorithm and the one using a transformation matrix are noted. The main objective of the paper is direct attitude angles calculation algorithm application possibilities analysis in real SINS operating conditions. The analysis is based on a comparison of the proposed algorithm with another frequently used attitude determination algorithm based on the transformation matrix. Attitude determination algorithms performance investigation results based on car and helicopter experimental tests are presented.

Inertial Indoor Pedestrian Navigation Based on Cascade Filtering Integrated INS/Map Information.

Indoor pedestrian positioning has been widely used in many scenarios, such as fire rescue and indoor path planning. Compared with other technologies, inertial measurement unit (IMU)-based indoor positioning requires no additional equipment and has a lower cost. However, IMU-based indoor positioning has the problem of error accumulation, resulting in inaccurate positioning. Therefore, this paper proposes a cascade filtering algorithm to correct the accumulated error using only a small amount of map information. In the lower filter, the zero-velocity correction and the attitude-extended complementary filtering (ECF) algorithm are utilized to initially solve the pedestrian's trajectory. In the upper filter, a particle filter (PF) combined with the map information is adopted to correct the accumulated error of the heading and stride length. In the 2D positioning process, the root mean square error (RMSE) of the proposed algorithm is only 1.35 m. In the altitude correction, this paper proposes a method of clustering floor discrimination to deal with the instability of the barometer resulting from an uneven pressure and temperature. In the final 3D positioning experiment, with a total length of 536.5 m and including the process of going up and down the stairs, the end-point error is only 2.45 m by the proposed algorithm.

Trainable Quaternion Extended Kalman Filter with Multi-Head Attention for Dead Reckoning in Autonomous Ground Vehicles.

Extended Kalman filter (EKF) is one of the most widely used Bayesian estimation methods in the optimal control area. Recent works on mobile robot control and transportation systems have applied various EKF methods, especially for localization. However, it is difficult to obtain adequate and reliable process-noise and measurement-noise models due to the complex and dynamic surrounding environments and sensor uncertainty. Generally, the default noise values of the sensors are provided by the manufacturer, but the values may frequently change depending on the environment. Thus, this paper mainly focuses on designing a highly accurate trainable EKF-based localization framework using inertial measurement units (IMUs) for the autonomous ground vehicle (AGV) with dead reckoning, with the goal of fusing it with a laser imaging, detection, and ranging (LiDAR) sensor-based simultaneous localization and mapping (SLAM) estimation for enhancing the performance. Convolution neural networks (CNNs), backward propagation algorithms, and gradient descent methods are implemented in the system to optimize the parameters in our framework. Furthermore, we develop a unique cost function for training the models to improve EKF accuracy. The proposed work is general and applicable to diverse IMU-aided robot localization models.