Scale Factor Error Research Articles

Evaluating the Impact of Convolutional Neural Network Layer Depth on the Enhancement of Inertial Navigation System Solutions

Secure navigation is pivotal for several applications including autonomous vehicles, robotics, and aviation. The inertial navigation system estimates position, velocity, and attitude through dead reckoning especially when external references like GPS are unavailable. However, the three accelerometers and three gyroscopes that compose the system are exposed to various types of errors including bias errors, scale factor errors, and noise, which can significantly degrade the accuracy of navigation constituting also a key vulnerability of this system. This work aims to adopt a supervised convolutional neural network (ConvNet) to address this vulnerability inherent in inertial navigation systems. In addition to this, this paper evaluates the impact of the ConvNet layer's depth on the accuracy of these corrections. This evaluation aims to determine the optimal layer configuration maximizing the effectiveness of error correction in INS (Inertial Navigation System) leading to precise navigation solutions.

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.

Calibration method of DVL based on position observation information

The accuracy of underwater navigation is significantly impacted by the scale factor error and misalignment angle of the Doppler Velocity Log (DVL). A DVL calibration method based on position observation information is proposed as a solution to the integrated navigation system composed of compass, DVL, ultra-short baseline acoustic positioning system, and depth sensor. A transfer model from DVL error parameters to the positioning error of Dead Reckoning (DR) is established. Based on this model, dual-loop Kalman filter (KF)-based and particle swarm optimization (PSO)-based DVL error parameter estimation algorithms are proposed. Compared with classical methods, the proposed methods achieve high-precision DVL calibration in deep-water environments at a lower cost. Simulation and sea trials show that both proposed algorithms exhibit excellent stability, consistency, and accuracy. After calibration, the positioning errors of DR have decreased from 1.56% to 0.28% and 0.23% of the voyage, respectively.

Partial trajectory method to align and validate successive video cameras for vehicle tracking

This paper develops the partial trajectory method to align the views from successive fixed cameras that are used for video-based vehicle tracking across multiple camera views. The method is envisioned to serve as a validation tool of whatever alignment has already been performed between the cameras to ensure high fidelity with the actual vehicle movements as they cross the boundaries between cameras. The strength of the method is that it operates on the output of vehicle tracking in each camera rather than secondary features visible in the camera view that are unrelated to the traffic dynamics (e.g., fixed fiducial points). Thereby providing a direct feedback path from the tracking to ensure the quality of the alignment in the context of the traffic dynamics. The method uses vehicle trajectories within successive camera views along a freeway to deduce the presence of an overlap or a gap between those cameras and quantify how large the overlap or gap is. The partial trajectory method can also detect scale factor errors between successive cameras. If any error is detected, ideally one would redo the original camera alignment, if that is not possible, one could use the calculations from the algorithm to post hoc address the existing alignment.This research manually re-extracted the individual vehicle trajectories within each of the seven camera views from the NGSIM I-80 dataset. These trajectories are simply an input to the algorithm. The resulting method transcends the dataset and should be applicable to most methods that seek to extract vehicle trajectories across successive cameras. That said, the results reveal fundamental errors in the NGSIM dataset, including unaccounted for overlap at the boundaries between successive cameras, which leads to systematic speed and acceleration errors at the six camera interfaces. This method also found scale factor errors in the original NGSIM homographies. In response to these findings, we identified a new aerial photo of the NGSIM site and generated new homographies. To evaluate the impact of the partial trajectory method on the actual trajectory data, the manually re-extracted data were projected into the new coordinate system and smoothed. The re-extracted data shows much greater fidelity to the actual vehicle motion. The re-extracted data also tracks the vehicles over a 14% longer distance and adds 23% more vehicles compared to the original NGSIM dataset. As of publication, the re-extracted data from this paper will be released to the research community.

Integration of SINS, laser doppler Velocimeter, and monocular visual odometry for autonomous navigation in complex road environments

For the integrated navigation method based on the strapdown inertial navigation system (SINS) and laser doppler velocimeter (LDV), the accuracy of the LDV is easily affected by the complex environment, such as sand and dust on the road, which leads to the degradation of the integrated navigation system’s positioning accuracy. In this paper, we propose an integrated navigation method for land vehicles that uses SINS, LDV, and monocular visual odometry (Mono-VO). We considered the boresight errors, lever-arm residual, and scale factor errors of Mono-VO when establishing an error model for the integrated SINS/LDV/Mono-VO navigation system. The new state vector’s observability is investigated. A Huber-based Kalman filter is also used to fuse these data. Finally, simulations and semi-physical simulations are carried out to validate the effectiveness of the proposed method, which demonstrates that positioning accuracy under complex road conditions is superior to that of the SINS/LDV navigation system.

A multi-axis alternating continuous rotation scheme for tri-axis rotational inertial navigation system (RINS) with fiber optic gyro

Benefiting from the rotational modulation technique and the gimbal structure, rotational inertial navigation system (RINS) can improve navigation accuracy by about one order of magnitude compared with the strap-down inertial navigation system (SINS). By continuously rotating around a fixed axis, the constant and slow variability errors perpendicular to the direction of the rotation axis can be effectively restrained while the errors in the direction of the rotation axis cannot be suppressed. Therefore, a multi-axis rotation scheme needs to be designed. Meantime, the fiber optic gyro (FOG), as a very popular inertial device, is well suited for RINS but has a larger scale factor error and poorer stability than the laser gyro; thus, it is not suitable to flip the inertial measurement unit (IMU) around the horizontal axis too much in the rotation scheme to avoid the rapid accumulation of horizontal misalignment angle. Accordingly, we propose a multi-axis alternating continuous rotation scheme for tri-axis RINS with FOG. During the navigation process, the inner, middle and outer gimbals rotate forward and reverse in sequence. The IMU rotates continuously in the three-axis direction can effectively suppress the effects of constant and slow-varying errors and also avoid the large velocity errors oscillation caused by flipping the IMU. The simulations and navigation tests show that the multi-axis alternating continuous rotation scheme can achieve navigation accuracy comparable to the multi-position rotation scheme and reduce the oscillation of velocity errors, which has important research significance and engineering value for the research of RINS with FOG.

Performance improvement of white-light-driven resonant fiber optic gyroscope using four-frequency sawtooth wave modulation technology

In this study, a novel resonant fiber optic gyroscope (RFOG) that relies on four-frequency sawtooth wave modulation technology is proposed. This innovative approach is utilized to demodulate both the light intensity changes of the optical system and the half-wave voltage drift of the multi-functional integrated optical chip (MIOC). The principle of modulation is expounded, and a simulation model is established to evaluate the performance of the system. We conducted synchronous compensation of the bias drift, which is caused by the light intensity changes, and applied closed-loop control to MIOC modulation frequency-shift voltage, effectively reducing the scale factor error. As a result, the system achieved a bias instability (BI) of 0.0055°/h, with a 500 m-long fiber-optic ring resonator (FRR) of 6 cm diameter, at room temperature. Furthermore, the scale factor error was reduced by more than threefold in the temperature range of −40 °C to 70 °C. These results demonstrate the superior performance of the proposed RFOG and its potential for high-precision navigation and other applications.

Research on the anti-interference ability of optically pumped magnetometer

The anti-interference ability of OPM is systematically demonstrated by theoretical analysis and experimental study in this paper. The results show that the transverse modulation mode of the single-beam OPM has the strongest anti-interference ability compared with the dual-beam OPM’s non-modulation and longitudinal modulation modes. Additionally, the OPM built with a larger linewidth cell has a stronger anti-interference ability than that with a smaller linewidth cell. Moreover, a three-axis magnetic field closed-loop control mode of the single-beam OPM is proposed to further enhance the anti-interference ability. The experimental results prove that the OPM operating at the three-axis magnetic field closed-loop mode can provide real-time feedback on the magnetic field so that the performance of the OPM remains unchanged under biased magnetic fields, and the scale factor error is stable within 0.5%. The enhancement of OPM’s anti-interference ability is significant to improve the MEG source localization accuracy of OPM-MEG systems.

An Improved Rotational Modulation Scheme for Tri-Axis Rotational Inertial Navigation System (RINS) with Fiber Optic Gyro (FOG)

An optimized scheme can improve the navigation accuracy of RINS without changing the inertial devices. In the multi-position stop scheme, the IMU remains stationary for most of the time, which makes motor control easier. However, the installation errors and the scale factor errors of FOG can cause platform misalignment after a certain angle of rotation around the horizontal axis, resulting in a velocity error. Continuous rotation can suppress time-varying errors better, which is of particular importance for FOG, but it can also increase the sawtooth error of the navigation output, and the error in the direction of rotation cannot be offset. To integrate the advantages of both rotation schemes, we propose an improved rotational modulation scheme for tri-axis RINS. In this scheme, the inner gimbal rotates in a two-position and four-order manner, while the middle and outer gimbals rotate continuously in the order of forward-reverse-reverse-forward. Simulation and navigation test results demonstrate that this improved rotational modulation scheme can effectively improve navigation accuracy by 50% and 25% compared with continuous rotation around the azimuth axis and a 16-position scheme with the same inertial devices, which is of great importance for RINS with FOG.

Online Calibration of RIMU Based on Multistage EKF

Redundant inertial measurement units (RIMUs) are more reliable than normal IMUs, but they are suffering from the calibration of non-orthogonal gyroscopes and accelerometers. In this paper, aiming at the problem of relying on the orthogonal axis IMU information and error term coupling in the online calibration of RIMUs, a method based on the multi-stage EKF algorism is proposed. In this method, the calibration model of the inertial system is established, which does not depend on the orthogonality with the inclined axis inertial system, meanwhile, the attitude, velocity, and position information is taken as the measurement, and a filtering model is established based on the EKF method. Based on this model, the observability of the calibration method is proved, and the window and threshold for secondary filtering are set to reduce the coupling effect of scale factor error and installation error. The digital simulation indicates that the proposed method can provide high-precision online calibration results for the inclined axis scale factor error and installation error of RIMUs, and the calibration error is below 10%.

Systematic Measurement of Temperature Errors of Positive and Negative FOG Scale Factors Using a Low-Precision Turntable

Measurement of temperature errors of fiber optic gyro (FOG) scale factor is important in FOG technology. In traditional methods, the measurement errors of FOG scale factors are greatly affected by the turntable’s orientation control errors. This article proposes a systematic method to measure the positive and negative FOG scale factor errors using a low-precision turntable. The relationship between the inertial navigation errors and the complete inertial measurement unit errors is revealed. A simplified tracking algorithm is devised to obtain the change rates of the velocity errors with lower computation. A measurement procedure is designed, with three groups of π and -π rotations around the east axis of the turntable at each temperature. Observation equations are derived to estimate the positive and negative FOG scale factor errors. Simulation and experimental results show that a low-precision turntable can accurately measure the FOG scale factor errors at each temperature. Furthermore, temperature errors of accelerometer biases, scale factors, and nonlinear scale factors can also be measured at the same time using the rotation sequences and formulas in this article without additional rotations.

Modeling and Compensation of Inertial Sensor Errors in Measurement Systems

In the field of surveying and mapping, inertial sensor deterministic errors are poorly understood, and error calibration and compensation are not carried out. Thus, in this study, the effects of three types of deterministic errors (i.e., bias, scale factor error, and installation error) in a conventional inertial measurement unit (IMU) error model on a navigation system are theoretically deduced and verified by simulation. Subsequently, navigation experiments are carried out to investigate the effects of the three deterministic errors on the navigation system. The experimental results show that the gyro bias has the strongest influence on the navigation and positioning accuracy of the system. Consequently, we designed a two-position continuous calibration scheme to calibrate the IMU. The calibration scheme can simultaneously calibrate the bias error of the gyroscope and the accelerometer. When calibrating the bias error of the 0.005°/h order of magnitude, the maximum relative error is 13.16%, and the rest of the calibration relative errors are less than 10%, which verifies the effectiveness of the calibration path designed in this paper. The system is compensated by using the IMU bias calibration results, and the navigation experiment results show that the position accuracy and heading accuracy are improved by 72.68% and 79.65%, respectively, through the calibration and compensation of IMU bias error. Therefore, the position and heading accuracy of the system will be greatly improved by calibrating and compensating the bias error through the two-position calibration path before the IMU is used.

A GNSS-aided DVL calibration method based on quaternion estimation for underwater vehicles

Doppler velocity logger (DVL) error parameters can significantly influence the navigation accuracy of DVL/strapdown inertial navigation system (SINS) integration for unmanned underwater vehicles (UUV). To improve the navigation accuracy of UUV, this study proposes a two-stage DVL calibration method aided by global navigation satellite system (GNSS) measurements. First, utilizing the velocity of GNSS/SINS integrated navigation, the scale factor error of DVL is calculated by the moduli of velocities in UUV body frame and DVL instrument frame. Then, using the measurements throughout the calibration process, the calibration problem of the installation angle is converted to a nonlinear constraint optimization problem by describing the angle as a unit quaternion. Moreover, an easy-to-implement quaternion estimation algorithm is chosen to solve the problem and obtain the optimal quaternion. Simulation and sea trial indicate that the proposed method can rapidly and accurately estimate the DVL error parameters in different scenarios, and the position accuracy of the DVL/SINS system is improved.

Correction Method of The Cross-type Tensor Based on DA-LM

Magnetic sensor tensor system detection is a weak magnetic target detection. It requires high accuracy for the tensor system. In order to solve the problems of non-orthogonal error, scale factor error, zero error and non-alignment error in tensor system, a tensor error correction method based on DA-LM algorithm is proposed. Using tensor rotation invariance and the principle of scalar correction, a mathematical model including non-orthogonal error, scale factor error, zero error and non-alignment error is established, and the DA-LM algorithm is used to solve the unknown parameters of the equations. This method can not only estimate the parameters accurately. It can also calibrate the observed data to the orthogonal coordinates. The validity of the method is verified by simulation analysis and experiment. The error is reduced from 2500 nT to 0.15 nT in the simulation analysis and from 11000 nT to 200 nT in the experiment, and finally the position error is reduced from 13.15 m to 2.3217 m, which further verifies the validity of the correction algorithm.

Kilometer Sign Positioning-Aided INS/Odometer Integration for Land Vehicle Autonomous Navigation

Land vehicles generally rely on inertial navigation system (INS) and odometer integration system to realize high-precision autonomous navigation in a global navigation satellite system (GNSS)-denied environment. However, the navigation errors of the INS and odometer integration system will still accumulate with time due to the existence of odometer scale factor error and installation deviation angles between the INS and the odometer. To solve the problem, this article proposed an integration method, which utilizes kilometer signs to aid in correcting the navigation errors of the INS/odometer integration system. First, the absolute global positions of the kilometer signs are obtained based on image recognition and data matching. Second, the vehicle visual positioning results are obtained based on monocular camera after compensating lever arm between the kilometer sign and INS. Afterward, the vehicle positions from kilometer sign are fused by a filter to reduce the visual positioning uncertainty of the land vehicle. Finally, two Kalman filters are established to integrate the information from visual positioning, INS, and odometer. Simulation and vehicle experiment results verify the performance of the proposed method, which can improve the autonomous navigation accuracy of the land vehicle.

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.

Novel Self-Calibration Method for IMU Using Distributed Inertial Sensors

Inertial measurement unit (IMU) calibration is essential to ensure the successful operation of various navigation systems. This article describes a novel method for self-calibration of IMU with distributed sensor architectures. The IMU is composed of modules that are distributed along the measurement axes. Each module is equipped with a single-axis gyroscope and three-axis accelerometer sensors. The modules have also their own signal-conditioning circuits and processors. This enables single-axis calibration of the module with a servo system based on a piezoelectric actuator (PEA). The proposed IMU and calibration method are capable of on-site self-calibration. The calibration is performed with the sinusoidal movements generated by the servo system. Despite the limited displacement of the PEA, high angular velocity and tangential acceleration can be achieved with the servo system. Thus, the gyroscope sensor can be directly calibrated with the angular velocity produced by the servo system. On the other hand, the calibration parameters of the accelerometer are determined by using the tangential and centripetal acceleration produced by the servo system. With the proposed method, the bias, scale factor, and installation errors of accelerometer and gyroscope sensors can be determined. The method has been analyzed by conducting experiments with a prototype IMU. In addition, experiments on 3-DoF turntables have been conducted to confirm the effectiveness of the proposed self-calibration method.

Optimal Path Planning Method for IMU System-Level Calibration Based on Improved Dijkstra’s Algorithm

The calibration path of system-level calibration directly affects the incentive effect of the error term and thus the calibration accuracy. Currently, the planning of system-level calibration paths is predominantly designed based on personal experience, resulting in insufficient incentive for error terms, low calibration accuracy, and long calibration times. Therefore, this study proposes a system-level calibration optimal path planning method based on an improved Dijkstra’s algorithm. First, the system-level calibration optimal path planning problem was modeled as a multi-fork regular root tree model, and the adaptability of Dijkstra’s algorithm was improved. Second, a 30-dimensional Kalman filter model was designed for system-level calibration. Then, simulation experiments were conducted, and the results demonstrated that the calibration accuracy of the error term reached 90% within 330 s. Finally, a Micro-Electro-Mechanical system (MEMS) inertial sensor, model PA-IMU488B, was used for experimental verification, and the results were compared with the discrete calibration results. The results indicate that the bias and scale factor errors of the MEMS inertial sensor reached the target accuracy within 5 min. The optimal path planning method for system-level calibration proposed in this study is not dependent on a high-precision turntable, is applicable to sensors of different accuracies, and decreases calibration time while ensuring calibration accuracy.

Mathematical models of errors of determination of a ground-based SINS orientation angles and latitude of its position

In the paper, a computational algorithm for determination of orientation angles and latitude of position of a strapdown inertial navigation system (SINS) which is mounted on a ground-based transport object is presented. It is assumed that the object is motionless with respect to the Earth’s surface. In the paper, mathematical models of errors of determination of the named angles are also presented. These errors, in their turn, are caused by null shifts and scale factor errors of the SINS sensitive elements – for example, laser gyros and linear accelerometers.

ANALYSIS OF MICRO-ELECTROMECHANICAL INERTIAL MEASUREMENT UNITS FOR UNMANNED AERIAL VEHICLE APPLICATIONS

Typically, an inertial navigation system (INS) is used to determine the position, speed, and orientation of an object moving relative to the earth's surface. The navigation information (position, speed and orientation) of an unmanned aerial vehicle (UAV) is needed to control its flight. Since the resistance of INS to interferences is very high, it is possible to ensure reliable flights in conditions of high-intensity noise. This article explores the principles of constructing inertial measurement units (IMU) that are part of the INS and indicates perspective directions for their development. Micro-electromechanical inertial measurement units were studied in this work, and functional and principal electrical circuits for connecting units of inertial measurements to the microcontroller were developed. The results of practical measurements of units without calibration and after calibration were obtained using the created laboratory device. Based on the obtained results, the necessity of sensor calibration was revealed, and accuracy was improved by performing calibration with the Kalman filter algorithm. The Kalman filter is the heart of the navigation system. In a low-cost system, IMU errors like bias, scale factor error and random walk noise dominate the INS error growth.