Strapdown Inertial Navigation System Research Articles

An Autocollimator Axial Measurement Method Based on the Strapdown Inertial Navigation System.

Autocollimators are widely used optical axis-measuring tools, but their measurement errors increase significantly when measuring under non-leveled conditions and they have a limited measurement range due to the limitations of the measurement principle. To realize axis measurement under non-leveled conditions, this paper proposes an autocollimator axis measurement method based on the strapdown inertial navigation system (SINS). First, the measurement model of the system was established. This model applies the SINS to measure the change in attitude of the autocollimator. The autocollimator was then applied to measure the angular relationship between the measured axis and its own axis, based on which the angular relationship of the axis was measured via computation through signal processing and data fusion in a multi-sensor system. After analyzing the measurement errors of the system model, the Monte Carlo method was applied to carry out a simulation analysis. This showed that the majority of the measurement errors were within ±0.002° and the overall measurement accuracy was within ±0.006°. Tests using equipment with the same parameters as those used in the simulation analysis showed that the majority of the measurement errors were within ±0.004° and the overall error was within ±0.006°, which is consistent with the simulation results. This analysis proves that this method solves the problem of the autocollimator being unable to measure the axis under non-leveled conditions and meets the needs of axis measurement with the application of autocollimators under a moving base.

Improving the underwater navigation performance of an IMU with acoustic long baseline calibration

Underwater acoustic Long-Baseline System (LBL) is an important technique for submarine positioning and navigation. However, the high cost of the seafloor equipment and complex construction of a seafloor network restrict the distribution of the LBL within a small area, making an underwater vehicle difficult for long-distance and high-precision acoustic-based or inertial-based navigation. We therefore propose an acoustic LBL-based Inertial Measurement Unit (IMU) calibration algorithm. When the underwater vehicle can receive the acoustic signal from a seafloor beacon, the IMU is precisely calibrated to reduce the cumulative error of Strapdown Inertial Navigation System (SINS). In this way, the IMU is expected to maintain a certain degree of accuracy by relying solely on SINS when the vehicle reaches out the range of the LBL network and cannot receive the acoustic signal. We present the acoustic LBL-based IMU online calibration model and analyze the factors that affect the accuracy of IMU calibration. The results fulfill the expectation that the gyroscope bias and accelerometer bias are the main error sources that affect the divergence of SINS position errors, and the track line of the underwater vehicle directly affects the accuracy of the calibration results. In addition, we deduce that an optimal calibration trajectory needs to consider the effects of the three-dimensional observability and position dilution of precision. In the experiment, we compare the effects of seven calibration trajectories: straight and diamond-shaped with and without the change of depth, and three sets of curves with the change of depth: circular, S-shaped, and figure-eight. Among them, we find that the figure-eight is the optimal trajectory for acoustic LBL-based IMU online calibration. We take the maintenance period during which the accumulated SINS Three Dimensional (3D) position errors are below 1 km to evaluate the calibration performance. The filed experimental results show that for the Micro-electromechanical Systems-grade IMU sensor, the maintenance period for the IMU calibrated with the proposed algorithm can be increased by 121% and 38.9% compared to the IMU without calibration and with the laboratory default parameter calibration, indicating the effectiveness of the proposed calibration algorithm.

IMU Auto-Calibration Based on Quaternion Kalman Filter to Identify Movements of Dairy Cows.

This work is focused on developing a self-calibration algorithm for an orientation estimation of cattle movements based on a quaternion Kalman filter. The accelerometer signals in the earth's frame provide more information to confirm that the cow is performing a jump to mount another cow. To obtain the measurements in the earth's frame, we propose a self-calibration method based on a strapdown inertial navigation system (SINS), which does not require intervention by the user once deployed in the field. The self-calibration algorithm uses a quaternion-based Kalman filter to predict the angular orientation with bias correction, and update it based on the measurements of accelerometers and magnetometers. The paper also depicts an alternate update to adjust the inclination using only the accelerometer measurements. We conducted experiments to compare the accuracy of the orientation estimation when the body moves similarly to cow mount movements. The comparison is between the proposed self-calibration algorithm with the IvenSense MPU9250 and Bosch BNO055 and the quaternion attitude estimation provided in the BNO055. The auto-calibrating algorithm presents a mean error of 0.149 rads with a mean consumption of 308.5 mW, and the Bosch algorithm shows an average error of 0.139 rads with a mean consumption of 307.5 mW. When we executed this algorithm in an MPU9250, the average error was 0.077 rads, and the mean consumption was 277.7 mW.

Attitude Algorithm of Gyroscope-Free Strapdown Inertial Navigation System Using Kalman Filter.

A gyroscope-free strapdown inertial navigation system (GFSINS) solves the carrier attitude through the reasonable spatial combination of accelerometers, with a particular focus on the precision of angular velocity calculation. This paper conducts an analysis of a twelve-accelerometer configuration scheme and proposes an angular velocity fusion algorithm based on the Kalman filter. To address the sign misjudgment issue that may arise when calculating angular velocity using the extraction algorithm, a sliding window correction method is introduced to enhance the accuracy of angular velocity calculation. Additionally, the data from the integral algorithm and the data from the improved extraction algorithm are fused using Kalman filtering to obtain the optimal estimation of angular velocity. Simulation results demonstrate that this algorithm significantly reduces the maximum value and standard deviation of angular velocity error by one order of magnitude compared to existing algorithms. Experimental results indicate that the algorithm's calculated angle exhibits an average difference of less than 0.5° compared to the angle measured by the laser tracker. This level of accuracy meets the requirements for attitude measurement in the laser scanning projection system.

Correcting Measurements of Launch Vehicle’s Angular Motion Parameters of a Strapdown Inertial Navigation System with the Use of a Celestial Navigation System

Correcting Measurements of Launch Vehicle’s Angular Motion Parameters of a Strapdown Inertial Navigation System with the Use of a Celestial Navigation System

Ship SINS/CNS Integrated Navigation Aided by LSTM Attitude Forecast

Under the strong interference of sky background noise, the reliability of celestial navigation system (CNS) measurement will drop sharply, which leads to performance deterioration for ships’ strapdown inertial navigation system (SINS)/CNS integrated navigation. To solve this problem, a long short-term memory (LSTM) model is trained to forecast a ship’s attitude to detect the attitude provided by the CNS, and the LSTM forecasted attitude can also be used as a backup in case of CNS failure. First, the SINS/CNS integrated model is derived based on an attitude solution of the CNS, which provides more favorable feature data for LSTM learning. Then, the key techniques of LSTM modeling such as dataset construction, LSTM coding method, hyperparameter optimization and training strategy are described in detail. Finally, an experiment is conducted to evaluate the actual performance of the investigated methods. The results show that the LSTM model can accurately forecast a ship’s attitude: the horizon reference error is less than 0.5′ and the yaw error is less than 0.6′, which can provide reliable reference attitude for the SINS when the CNS is invalid.

Optimizing AUV Navigation Using Factor Graphs with Side-Scan Sonar Integration

For seabed mapping, the prevalence of autonomous underwater vehicles (AUVs) employing side-scan sonar (SSS) necessitates robust navigation solutions. However, the positioning errors of traditional strapdown inertial navigation system (SINS) and Doppler velocity log (DVL) systems accumulated significantly, further exacerbated by DVL’s susceptibility to failure in complex underwater conditions. This research proposes an integrated navigation approach that utilizes factor graph optimization (FGO) along with an improved pre-integration technique integrating SSS-derived position measurements. Firstly, the reliability of SSS image registration in the presence of strong noise and feature-poor environments is improved by replacing the feature-based methods with a Fourier-based method. Moreover, the high-precision inertial measurement unit (IMU) pre-integration method could correct the heading errors of SINS significantly by considering the Earth’s rotation. Finally, the AUV’s marine experimental results demonstrated that the proposed integration method not only offers improved SSS image registration and corrects initial heading discrepancies but also delivers greater system stability, particularly in instances of DVL data loss.

Online calibration method for SINS/LDV integrated navigation system based on left group error definition

The integration of strapdown inertial navigation system (SINS) and laser Doppler velocimeter (LDV) is a reliable technology for land vehicle positioning. To ensure the best positioning performance of the SINS/LDV integrated navigation system, it is necessary to calibrate it accurately. However, the accuracy of the error model of the traditional calibration method is seriously affected by the large misalignment angle, which in turn affects the accuracy and consistency of the filtering, and eventually leads to the decline of the calibration accuracy. Therefore, this paper introduces the Lie group theory for the first time into the calibration study of the SINS/LDV integrated navigation system. Based on the error state vector defined by the left group error definition in the Lie group, the three calibration models of the SINS/LDV integrated navigation system are derived in the Earth-centered Earth-fixed frame, using velocity, displacement increment, and dead reckoning (DR) position, which are the three common observation information. The most significant advantage of these calibration models is their ability to handle large initial misalignment angles. The calibration models proposed in this paper are comprehensively evaluated by two long-distance vehicle experiments. The test results show that under normal conditions (no large attitude misalignment angle and all sensors are working properly), the Lie group-based calibration methods have similar performance to the traditional calibration method, but they have significant advantages in the case of large initial attitude deviation. In addition, using displacement increment and DR position as observations improves calibration performance compared to velocity.

A water track laser Doppler velocimeter for use in underwater navigation

Doppler velocity log (DVL) is usually employed to suppress the divergency of the Strapdown Inertial Navigation System (SINS) in underwater navigation, which is not concealable due to high transmittance for acoustic wave in the water. To conduct underwater navigation task with high concealment, a differential laser Doppler velocimeter (LDV) working at water track mode is integrated with SINS in this paper. The developed LDV measures the advance velocity of the underwater carrier with respect to the surrounding water in underwater navigation scenario with advantages of high concealment, high real-time performance, high update rate, light weight, and small dimension. A dynamic river test was conducted to validate the underwater navigation performance of SINS/LDV integrated system. The experimental results show that during the voyage of 4493s and 5271.8 m, the maximum horizontal positioning errors of the proposed SINS/LDV integrated underwater navigation system is 27.8 m and the relative position error is less than 0.6% with respect to total distance. Therefore, the water track LDV is practical to aid SINS in underwater navigation environment.

A robust Kalman filter based on Gaussian-Exponential distribution for SINS/USBL integration navigation system

In order to meet the needs of high-precision navigation for underwater vehicles, a strapdown inertial navigation system (SINS)/ultra-short baseline (USBL) tightly coupled integrated strategy is proposed, which can avoid the errors generated in the calculation of absolute position and improve the positioning accuracy of the integrated navigation system compared with the loosely coupled strategy. In addition, due to the influence of environmental noise in the ocean, the measurement of USBL is accompanied by a large number of outliers, which leads to the decrease of the precision of the integrated navigation system based on traditional Kalman filter. Therefore, a robust filter based on Gaussian-Exponential distribution is presented for the SINS/USBL integrated navigation system in this paper. Finally, the feasibility and the superiority of the proposed algorithm is verified through simulation and field test in the Yangtze River.

Experimental Analysis of Deep-Sea AUV Based on Multi-Sensor Integrated Navigation and Positioning

The operation of underwater vehicles in deep waters is a very challenging task. The use of AUVs (Autonomous Underwater Vehicles) is the preferred option for underwater exploration activities. They can be autonomously navigated and controlled in real time underwater, which is only possible with precise spatio-temporal information. Navigation and positioning systems based on LBL (Long-Baseline) or USBL (Ultra-Short-Baseline) systems have their own characteristics, so the choice of system is based on the specific application scenario. However, comparative experiments on AUV navigation and positioning under both systems are rarely conducted, especially in the deep sea. This study describes navigation and positioning experiments on AUVs in deep-sea scenarios and compares the accuracy of the USBL and LBL/SINS (Strap-Down Inertial Navigation System)/DVL (Doppler Velocity Log) modes. In practice, the accuracy of the USBL positioning mode is higher when the AUV is within a 60° observation range below the ship; when the AUV is far away from the ship, the positioning accuracy decreases with increasing range and observation angle, i.e., the positioning error reaches 80 m at 4000 m depth. The navigational accuracy inside and outside the datum array is high when using the LBL/SINS/DVL mode; if the AUV is far from the datum array when climbing to the surface, the LBL cannot provide accurate position calibration while the DVL fails, resulting in large deviations in the SINS results. In summary, the use of multi-sensor combination navigation schemes is beneficial, and accurate position information acquisition should be based on the demand and cost, while other factors should also be comprehensively considered; this paper proposes the use of the LBL/SINS/DVL system scheme.

Performance Evaluation of Strapdown Inertial Navigation and Beidou Satellite Navigation System Based on Intelligent Image Processing Technology

Performance Evaluation of Strapdown Inertial Navigation and Beidou Satellite Navigation System Based on Intelligent Image Processing Technology

A Digital Track Map-Assisted SINS/OD Fusion Algorithm for Onboard Train Localization

Accurate and reliable speed and position estimation plays an important role in the safety and efficiency of intelligent railway vehicles. Due to the level required of safety, reliability, and strong norms in the current practical application, intelligent railway vehicle positioning heavily relies on a large number of balises laid on the track and the onboard odometer (OD), while the other position method, GNSS introduction, is relatively slow. This article proposed a digital track map-assisted onboard railway location system using strapdown inertial navigation system (SINS) and OD. The proposed method consists of two steps. First, an SINS- and OD-integrated navigation method based on OD velocity integration is in the inner circle. Then, a map-matching algorithm based on vertical projection and heading weighting was employed, and when the matching outer circle results were obtained, the positions obtained from the matching outer circles were used to replace the positions obtained from SINS/OD for the Kalman filter combination. The performance of our algorithm was verified using field tests, and SINS/OD and SINS/OD/MM comparison data processing results prove that our proposed digital track map-assisted SINS/OD algorithm can effectively suppress the accumulation of train position errors. After nearly 80 km of navigation, the position error is 24 m, and the relative mileage accuracy is less than or equal to 0.03% distance.

CALIBRATION OF THE INERTIAL MEASUREMENT UNIT IN CRITICAL CONDITIONS

Calibration of the inertial measuring unit (IMU) is an independent task and is the most important stage in preparing for operation both platform and strapdown inertial navigation systems (INS). The traditional calibration of IMU, containing at least three gyroscopes and three accelerometers, carried out in specialized testing laboratories, has been studied in sufficient detail. However, the widespread use of IMUs using MEMS sensors with characteristic instability of parameters leads to the need for additional calibration of IMUs IMUediately before INS operation in critical or field conditions. Under such conditions, firstly, there is no testing equipment necessary for the full implementation of traditional calibration, and secondly, the recalibration process itself is limited in time.In the article, studies were carried out on the possibility of using the method of successive rotations for the recalibration of IMU in the field. With this approach, in contrast to the test rotation method, there is no need to rotate the IMU by 180 degrees, but it is enough to rotate the IMU by small angles. Calculation ratios are obtained for determining the scale factors and zero signals of the accelerometer unit for two positions of the IMU. The experiment carried out confirmed the validity of the calculated ratios obtained. In addition, a recalibration method is described, which makes it possible to estimate, in addition to scale factors and zero signals of the accelerometer unit, also the tilt angles of the base on which the IMU is installed. To do this, you must have at least five different IMU positions.In addition, the calibration of the gyroscope unit when tactical and navigational accuracy class gyroscopes are used is considered. For gyroscopes of the tactical accuracy class and which are manufactured using MEMS technology, biases are determined in the critical conditions, which are not stable from start to start. Algorithms for determining biases and scale factors were obtained for the calibration of the gyroscope unit of the navigation accuracy class, for which the same two positions in which the accelerometer unit was calibrated were used. That is, during the calibration of the IMU in critical conditions, it is possible to simultaneously calibrate the gyroscope unit and the accelerometer unit, which saves the overall calibration time.

Autonomous method for a strapdown inertial navigation system calibration in operation in operation

Strapdown inertial navigation systems (SINS) are widely used in modern air transport. The service life of such systems is decades. During this time, the characteristics of such systems may deteriorate due to the degradation of inertial sensors - gyroscopes and accelerometers. Under these conditions, in order to maintain the required accuracy of the SINS during the entire period of operation, it is necessary either to periodically carry out routine maintenance with the onboard system, or to continuously adapt the used sensor measurement model in terms of compensating for errors that arise. The second direction, which we will call calibration, has the advantage over the first one that it is carried out automatically by the system itself and does not require any additional equipment or additional maintenance work. The known method of SINS recalibration is based on the integration of information from the SINS and from the receiver of satellite radio navigation signals (SRNS). Such calibration, firstly, significantly depends on the availability and quality of satellite information, and secondly, it is possible only for integrated navigation systems in which the inertial subsystem is supplemented by a SRNS receiver. In contrast to the known method, this article solves the problem of autonomous SINS calibration, which is carried out after each flight. The solution is based on a linearized inertial navigation error model based on the boundary conditions of the state vector (at the beginning and end of the flight). The external information used consists only of the initial values of the coordinates and the current measurements of the baroaltimeter. As a result of the decision at the end of the flight, the errors of gyroscopes and accelerometers are determined, as well as the error in determining the final values of latitude and longitude in the SINS. Sensor errors can be used in subsequent system activations, which improves the accuracy of its operation as a whole. The analysis of the suitability and effectiveness of the developed methodology was carried out on a typical flight simulation program.

Orientation Quaternion Norm Correction in SINS Algorithms: Calculation Normalization Schemes and Their Efficiency

The problem of correcting the norm of the computed orientation quaternion in the algorithms for the operation of strapdown inertial navigation systems is considered. Two existing approaches to the correction process are considered, the first approach is to normalize the rotation quaternion at the computation cycle, the second approach is to normalize the resulting quaternion. 5 well-known calculation schemes for norm correction are given. To simulate the test motion, we used an analytical quaternion kinematic rotation model based on a sequence of three rotations corresponding to the Krylov angles. The case of linear dependence of elementary rotation angles on time is considered. The model provides analytical representation of the projections of the angular velocity vector of the rigid body on the associated axes and the corresponding quasi-coordinates on the calculation cycle. The results of numerical simulation of the reference motion for a given set of frequencies are presented as dependences of the projections of the angular velocity vector of the rigid body on time and the constructed trajectories in the configuration space of the orientation parameters.
 To determine the rotation quaternion on a cycle, the Miller algorithm was used, which makes it possible to obtain an increase in the orientation vector based on ideal information from the angular velocity sensors in the form of quasi-coordinates. The transformation into a rotation quaternion occurs with the help of the corresponding expansions of the trigonometric functions of the true rotation angle (modulus of the orientation vector) in a series.
 Based on a numerical experiment, it is shown that the best result of correcting the norm of the calculated quaternion in the sense of the minimum error of the norm is given by one of the finite normalization schemes, for which there is no division operation and ensures the stability of the norm correction in time. The results of numerical simulation of the model rotational motion of a rigid body and the development of schemes for correcting the norm of the calculated orientation quaternion are presented.
 Keywords: orientation quaternion, Miller's orientation algorithm, SINS, norm error, computational drift, analytical reference model, quasi-coordinates, numerical simulation.

Using Functionally Redundant Inertial Measurement Units to Increase Reliability and Ensure Fault Tolerance

This paper aims to assess the possibility of using functionally redundant inertial units to solve problems of increasing reliability and ensuring the fault tolerance of the various classes and purposes of aircraft navigation systems. We present the results of studying failure detection methods to improve the accuracy and reliability of a strapdown functionally redundant inertial unit. The resulting structural redundancy of the strapdown inertial measurement unit is designed to increase the fault tolerance and accuracy of strapdown inertial navigation systems. The methods for detecting sensor failures in functionally redundant inertial units are based on the use of the equations of functionally redundant inertial unit compliance to nominal requirements for the accuracy of measuring the input action vector. To describe the methods for detecting and eliminating failed sensor and algorithm designs based on them, we gave the mathematical models of the measurement vector of functionally redundant inertial units concerning the measured vector and the error identification condition, including the residual of the matching equations with the size due to the level of redundancy, determining the total number of matching equations. The main criterion for determining a failed sensor is non-compliance with the nominal value of the residual included in a certain number of matching equations of the information received from such meters. The developed algorithms are examined using simulation methods. The study of the selected structure of the functionally redundant inertial units shows that the proposed approaches are efficient. Also, we manage to identify the main characteristics of the algorithms for detecting sensor failures that are structurally a part of the functionally redundant inertial units.

Global Navigation Satellite System Spoofing Detection in Inertial Satellite Navigation Systems

The susceptibility of global navigation satellite systems (GNSSs) to interference significantly limits the possibility of their use. From the standpoint of possible consequences, the most dangerous interference is the so-called spoofing. Simultaneously, in most cases of GNSS use, an inertial navigation system (INS) or an attitude and heading reference system (AHRS) is also present on the board of mobile objects. In this regard, the research goal is to assess the possibility of detecting GNSS spoofing in inertial satellite navigation systems. This paper examines the method for detecting GNSS spoofing by combining a pair of commercially available GNSS receivers and antennas with an INS or AHRS. The method is based on a comparison of the double differences of GNSS carrier phase measurements performed by receivers under conditions of resolved integer ambiguity and the values of the range double differences predicted using an INS. GNSS carrier phase integer ambiguity can be resolved using a strapdown inertial navigation system (SINS) or AHRS data. The mathematical model of GNSS phase difference measurements and the SINS-predicted satellite range differences model are given. The proposed algorithm calculates the moving average of the residuals between the SINS-predicted satellite range double differences and the measured GNSS carrier phase double differences. The primary criterion for spoofing detection is the specified threshold excess of the moving average of the double difference residuals. Experimental studies are performed using simulation and hardware-in-the-loop simulation. The experimental results allow us to evaluate the efficiency of the proposed approach and estimate the potential characteristics of the spoofing detection algorithm based on it.

An invariant error-based SINS/DVL/USBL tightly coupled integrated navigation algorithm and its robust state estimator

The existing strapdown inertial navigation system (SINS)/Doppler velocity log (DVL)/ultra-short baseline system (USBL) integrated navigation error models directly apply algebraic differences to define the vector error, which is not strictly accurate. Considering that the invariant error definitions derived from Lie group theory have been used in the navigation field to obtain more accurate linear error models, in this paper, a new SINS/DVL/USBL integrated navigation system is investigated based on the invariant error definition and tightly coupled structure. In order to suppress the effect of measurement outliers on navigation accuracy, a new statistical similarity measure (SSM)-based multiple adaptive outlier-robust state estimator (MAORSE) is proposed. It decomposes the noise covariance matrix into multiple sub-matrices. Through the estimation and adjustment of sub-matrices, the influence of abnormal observations on the filtering results is weakened while realizing the full utilization of normal observation information. The test results demonstrate the effectiveness and superiority of the proposed invariant error-based SINS/DVL/USBL tightly coupled integrated navigation algorithm and SSM-based MAORSE.

Improving Strapdown Inertial Navigation System Performance by Self-Compensation of Inertial Sensor Errors

Abstract Microelectromechanical systems (MEMS)-based strapdown navigation systems offer advantages such as small size, low cost and minimal power consumption. However, MEMS sensors are prone to significant low-frequency noise and poor bias repeatability, which can lead to navigational errors over time. These errors make them unsuitable for autonomous navigation applications, even with frequent recalibration. One way in which to solve this problem is by using the rotation modulation (RM) method. This approach is widely recognised but has only been successful with precise laser and fiber optic gyroscopes equipped with precise rotating platforms. This article focuses on the potential of adapting the RM method for the case of inexpensive MEMS sensors that can significantly improve navigation performance, while maintaining the benefits of microelectromechanical technologies. Potential issues of implementation were discussed, and corresponding requirements were formulated. The proposed optimal computation scheme was verified during static tests of the developed inertial measurement unit (IMU). Further steps in studying the adaptation of the RM method for MEMS sensors have also been outlined.