Scale Factor Error Research Articles

A Dynamic Gyro Scale Factor Error Calibration Method for RINSs

In the rotational inertial navigation system (RINS), the horizontal gyro drift can be modulated when the IMU rotates around the z axis. At the same time, the scale factor error of the z gyro can be offset by forward and reverse rotation. However, in the forward and backward rotation, the gyro scale factor error will still cause the heading angle output error. Moreover, the change of the scale factor error of the fiber optic gyros(FOG) is sensitive to temperature changes, which makes it difficult to calibrate gyro scale factor error accurately. Therefore, in this paper, a method to calibrate the scale factor errors of two RINSs dynamically is proposed. During the movement of vehicle, the heading angle difference between the RINS1 and RINS2 is calculated real time, the scale factor errors of RINS1 and RINS2 could be estimated at the same time with the least squares filtering algorithm. The simulation experiments show that when RINS1 and RINS2 adopt a reasonable rotation strategy, the gyro scale factor errors were less than 0.5ppm. In the vehicle experiment, the heading angle error caused by the gyro scale factor error is kept below 5”. And the method significantly improves the problem that scale factor error affected by temperature changes during navigation process, and at the same time solves the problem of the calibration coefficient error in the dynamic situation.

Position observation-based calibration method for an LDV/SINS integrated navigation system.

With the advantages of high velocity measurement accuracy and fast dynamic response, the laser Doppler velocimeter (LDV) is expected to replace the odometer to be combined with a strapdown inertial navigation system (SINS) to form a higher precision integrated navigation system. However, LDV scale factor error and misalignment angles between LDV and inertial measurement unit will affect the accuracy of navigation. Considering that not all global navigation satellite system (GNSS) receivers can directly provide velocity information and current mainstream calibration methods are sensitive to the measurement noise and outliers of velocity and position information, a robust calibration method aided by GNSS is proposed in this paper, which is based on position observation. Different from current popular calibration methods, the attitude information of the GNSS/SINS integrated navigation system obtained by an adaptive Kalman filter is used to construct the observation vector together with LDV velocity outputs and GNSS position outputs in this method. The LDV scale factor error and the misalignment angle are determined by the ratio of two observation vector modulus and the Davenport's q-method method, respectively. The accuracy and robustness of the calibration method are verified by one vehicle test with normal GNSS signals and one vehicle test with GNSS signals with outliers. And the horizontal position error of dead reckoning of the calibrated LDV/SINS integrated system are less than 0.0314% and 0.1033% of the mileage, respectively.

GNSS/INS/ODO/wheel angle integrated navigation algorithm for an all-wheel steering robot

To suppress the positioning error of wheeled robots in global navigation satellite system (GNSS) denial environments, kinematic constraints should be fully utilized. However, many wheeled robots have independent steering mechanisms for each wheel to move more flexibly, which do not meet the nonholonomic constraint in the vehicle frame. Hence, the conventional GNSS/inertial navigation system (INS)/ODO (odometer) integrated navigation algorithm (GIOW algorithm) is no longer suitable. We propose a GIOW algorithm to meet the need for all-wheel steering robot positioning. In the proposed algorithm, odometer speed and wheel angle are employed together to construct a kinematic constraint for wheeled robots, which can constrain the rapid drifting error of INS. Moreover, the odometer scale factor and wheel angle error are augmented into the error state of the extended Kalman filter to be estimated and compensated online. Field tests were carried out in an open-sky environment with a wheeled robot, which can run in both corner steering mode and all-wheel steering mode. The experimental results showed that the proposed algorithm can be applied to not only the corner steering motion model but also the all-wheel steering motion model. The accuracy of the proposed algorithm was almost the same as that of the conventional GNSS/INS/ODO algorithm in the corner steering motion model. In the all-wheel steering motion model, the accuracy of the proposed algorithm was maintained.

A comprehensive calibration method for non-orthogonal error and scale factor error of triaxial Helmholtz coil.

In order to calibrate the non-orthogonal error and scale factor error of triaxial Helmholtz coil, a comprehensive error calibration method is proposed in this paper. The comprehensive error model is established first, and then the method to generate a frequency-controllable spatial rotating magnetic field whose magnetic field intensity is constant based on triaxial Helmholtz coil is introduced. Based on the fact that the magnetic field intensity generated by the current through the coil is constant, the objective function is constructed and the error parameters are solved using the least-squares fitting method. Simulation experiments and field tests prove the effectiveness and feasibility of this method. The most obvious finding to emerge from this study is that the proposed method is not only suitable for the electromagnetic shielding room environment but also suitable for the field tests in the presence of a background geomagnetic field far away from urban electricity interference. The root mean square error value is reduced to 0.7 nT from 298.2 nT in the electromagnetic shielding room, and it is reduced to 0.8 nT from 299.0 nT in the wild. Compared to the two-step calibration method, the proposed method reduces the sampling time by controlling the frequency of the rotating magnetic field and reduces the influence of the changes of the background geomagnetic field on the experimental results. This method has better anti-interference ability. Because the modulus of the background geomagnetic field has no effect on this method, it gets rid of the dependence on large current or background geomagnetic field shielding devices. Comparative experiments and repetitive experiments verify the practicability and stability of this method.

A system-level calibration method including temperature-related error coefficients for a strapdown inertial navigation system

The calibration of error coefficients for accelerometers and laser gyros is an effective way to improve the navigation precision of strapdown inertial navigation systems. The calibration parameters often change with temperature. This paper proposes a system-level calibration method including temperature-related error coefficients. The method includes an improved 18-step calibration scheme with temperature being changed by using a thermal chamber. A 42-dimensional Kalman filter is applied to estimate the error parameters including the bias, scale factor errors, installation errors and temperature-related error coefficients of accelerometers. This method has the great advantage of simplifying the calibration procedure and is widely applicable to all temperature-related error coefficients. Compared with the traditional calibration method at different temperature points, the calibration time of the proposed method is shortened by 24 h. The feasibility of this method is verified by simulations and navigation experiments. The results of navigation experiments show that the maximum positioning errors in pure inertial navigation decrease by approximately 30% after temperature compensation.

The calibration method for accelerometers in the redundant MEMS inertial navigation system

Compared with the non-redundant inertial navigation system (INS), the redundant INS (RINS) has more error parameters and the system is more complicated. The calibration methods for non-redundant INS are unable to be adopted by RINS directly. Meanwhile, the inner lever arm effect of accelerometers is more severe in RINS, which is not supposed to be ignored in the error compensation. To solve the problems above, this paper proposes a novel calibration method for accelerometers in RINS. First, the paper analyses and models the bias, scale factor error, installation angle error and lever arm error. Based on the error model, two Kalman filters are designed to estimate the error parameters. The calibration is divided into two steps: the bias, scale factor error and installation angle error are calibrated by the static multi-position experiment first, and then the lever arm error is calibrated by the rotation experiment. Experiments prove that the proposed method can effectively calibrate the deterministic error of the accelerometers, that the estimation errors are controlled at 1 × 10−4 level. Further, the paper studies and optimizes the turntable rotation scheme in the lever arm error calibration experiment, and proposes the design principles for the rotation scheme. Comparing with the casually designed scheme, the optimized procedure can improve the accuracy by almost an order of magnitude as well as the time-consumption being shortened by 40%. The design principles are applicable to the other inertial navigation systems to improve the calibration accuracy and reduces the time cost.

Research on light source average wavelength and crystal oscillator frequency for reducing temperature error of the FOG scale factor

Based on the working principle of the digital closed-loop fiber optic gyroscope (FOG), a model for the influence of crystal oscillator frequency on scale factor (SF) temperature error is theoretically derived. Besides, the correlation between the two main light sources average wavelength and the SF temperature error is discussed. The experimental results show that both the crystal oscillator frequency and the light source average wavelength have a greater impact on the FOG SF temperature error. There is a cubic function relationship between crystal oscillator frequency and temperature, the temperature error of the SF is inversely proportional to the crystal oscillator frequency. Using a higher frequency temperature-compensated crystal oscillator, the frequency stability can be improved by two orders of magnitude, from 67.14 ppm to 0.22 ppm, the SF temperature error is also greatly reduced. The SF error is proportional to the relative change in wavelength, and the change caused by the temperature is of the same order of magnitude. Compared with the super luminescent diode (SLD) light source, the Erbium-doped fiber light source has higher average wavelength stability, the SF error caused by it is also smaller. The error can be reduced by 15 ppm and controlled at about 10 ppm after temperature compensation.

An Online Gyro Scale Factor Error Calibration Method for Laser RINS

The rotational inertial navigation system (RINS) could greatly improve navigation performance by rotating the inertial measurement unit with gimbals. And the self-calibration of error parameters could be achieved conveniently. Among the rate-biased Ring laser gyro (RLG), the input angular velocity can reach tens of degrees per second. Therefore, the attitude errors caused by scale factor is dozens of times that of the other RINS. In this paper, gyro scale factor errors are calibrated through optimal estimation with attitude errors in dual-axis laser RINS. During the movement of vehicle, the dynamic gyro scale factor errors calibration can be performed online by adding parking points. Moreover, the parking points can be accurately determined by the statistical characteristics of accelerometers and gyros output information, without extern sensors. The experiment results indicate that the calibration repeatability scale factor parameters are less than 1ppm, and the attitude errors cause by the scale factor error is reduce from tens of arc seconds to 10 arc seconds, which verifies the effectiveness and accuracy of the method proposed in this paper. Through the compensation of calibration results, the attitude error of RINS is further improved in both the static and dynamic experiment.

Multi-position iterative recursive calibration algorithm of fiber optic gyroscope

The precision of the strapdown inertial navigation system (SINS) depended on the work precision of the gyroscope. However, many errors affect the precision of SINS even if the gyroscopes have perfect principles and structures. Before the application of the inertial navigation system (INS), the inertial components must be calibrated to ensure the performance of components, detect whether the precision of the inertial component satisfied the system, and compensate for the error of INS. According to the mathematical model of fiber optic gyroscope (FOG), we propose a multi-position iterative recursive calibration algorithm to compensate for the error of scale factor and installation of FOG. To guarantee the accuracy of the SINS, the error mathematical model of the FOG is established and compensated in the system. Finally, the calibration parameters of FOG are calibrated by the multi-position iterative recursive calibration (MPIRC) and the six-position method. The calibration results show that the accuracy of components calibration parameters of the MPIRC and the six-position is similar, but the accuracy of SINS using MPIRC is higher than that using six-position.

A Quasi-Newton Quaternions Calibration Method for DVL Error Aided GNSS

Doppler Velocity Logs (DVL) is an important information source for underwater vehicle navigation because it can provide accurate velocity information. As the main system, SINS/DVL integrated navigation is widely used in the underwater vehicle. However, DVL scale factor error, and misalignment with inertial measurement unit (IMU) are the two sources of integration inaccuracy. A novel calibration method aided GNSS is proposed in this paper, which is designed based on velocity observation and position observation respectively. The proposed method combines the Quasi-Newton method and Quaternions method, and we name it Quasi-Newton Quaternion (QNQ) calibration method. In order to verify the performance of the proposed method, another calibration method based on the Kalman filter is introduced in simulation, vehicle tests, and Sea trial. The test results indicate that the proposed calibration method can perform a good estimation of DVL error.

A new method for estimating the noise scale factor (NSF) and random errors in lidar observations

The noise scale factor (NSF) is useful in calculating the random errors of lidar signals. A new method is proposed for estimating the NSF of lidar systems. Instead of measuring the solar background in the traditional method that demands special experiments or additional devices, the new method utilizes the molecular backscattered signal fragments of routinely observed lidar profiles to extract the light intensities and shot noises. Based on a 355 nm lidar system, experiments with the two methods have been carried out. The NSF calculated with the new method is 0.6473, very close to the value resulted from the traditional method, which is 0.6496. The experiments indicate that the new method is feasible and accurate. An example of calculating the random errors and signal to noise ratios (SNR) of lidar signals by using NSF is presented. Compared with the results calculated from multiple lidar profiles, the method using NSF eliminates the influence of aerosols and clouds.

Design and experimental evaluation of block-pulse functions and Legendre polynomials observer for attitude-heading reference system

The main purpose of this paper is design and implementation of a new linear observer for an attitude and heading reference system (AHRS), which includes three-axis accelerometers, gyroscopes, and magnetometers in the presence of sensors and modeling uncertainties. Since the increase of errors over time is the main difficulty of low-cost micro electro mechanical systems (MEMS) sensors producing instable on–off bias, scale factor (SF), nonlinearity and random walk errors, development of a high-precision observer to improve the accuracy of MEMS-based navigation systems is considered. First, the duality between controller and estimator in a linear system is presented as the base of design method. Next, Legendre polynomials together with block-pulse functions are applied for the solution of a common linear time-varying control problem. Through the duality theory, the obtained control solution results in the block-pulse functions and Legendre polynomials observer (BPLPO). According to product properties of the hybrid functions in addition to the operational matrices of integration, the optimal control problem is simplified to some algebraic equations which particularly fit with low-cost implementations. The improved performance of the MEMS AHRS owing to implementation of BPLPO has been assessed through vehicle field tests in urban area compared with the extended Kalman filter (EKF).

Reducing the Effect of the Accelerometer-Slope Bias Error on the Calibration Error of a High-Precision RLG INS System-Level Fitting Method

In recent years, navigation technology has rapidly developed. System-level calibration technology for inertial navigation system (INS) has been widely used because it does not rely on high-precision equipment. However, INS introduces a bad coupling error in high-precision ring laser gyroscope (RLG) scale-factor error estimation, accompanied by a large accelerometer-slope bias error. To solve this problem, an improved system-level fitting calibration method is proposed, which changes the 90° rotation increment to 450°, while maintaining the original calibration sequence. Compared with the traditional system-level calibration method, the calibration error of the gyroscope scale-factor error is reduced to 0.2 times, under simulation conditions, without affecting the calibration accuracy of the other parameters. The extreme difference of the gyroscope scale-factor calibration error on multiple experiments reduces from 4.75 to 1.40 ppm under experimental-verification conditions. The mean values of the gyroscope scale factor were closer to the real reference values (no more than 2 ppm). The integral calibration results meet the requirements of a high-precision RLG INS. The proposed method maintains the original calibration sequence and exhibits small changes with high practicability. The proposed method is suitable for applications with high requirements for gyroscope scale factor accuracy, such as highly dynamic aircraft.

Об оценивании параметров модели погрешностей вращающегося измерительного модуля на ВОГ бесплатформенной ИНС в условиях объекта

The paper studies the possibility of updating the parameters of error model of a rotating inertial measurement unit (IMU)with fiber-optic gyroscopes (FOG) in a strapdown inertial navigation system (SINS)under operating conditions. The IMU is placed in a two-axis gimbal for modulation rotation.The main focus is made on the estimation of scale factor errors of the FOG and accelerometers, non-orthogonality of their sensitive axes, and relative time delays (group delays) of inertial sensors during the IMU normal rotation according to the navigation solution of the INS in the observation mode of its operation. Also, the paper presents the description and results of estimation of so-called rhumb drifts of the IMU, which may occur due to the perturbingforces associated with the geographical axes or the axes of the system central device body.The research is based on the results of FOG-based INS simulation.

Three-position characterization for the adjustment of MEMS accelerometer scale factor

Up/down static and the six-position least squares calibration methods are commonly used in research conducted on adjustment of the micro-electromechanical systems (MEMS) accelerometer scale factor (or sensitivity). When applying these methods, it is difficult to adjust the accelerometer measuring axis parallel to the gravity direction, causing an error in the accelerometer scale factor. In this paper, a three-position scale factor characterization that does not require corrections of the precise coincident of the measuring axis with the direction of gravity is studied. The method uses the up/down calibration method to obtain the coarse scale factor and bias. The coarse adjustment coefficient is then used to convert the accelerometer output data in the horizontal, up, and down positions into acceleration. The horizontal acceleration is used to estimate the scale factor error. Next, the estimated scale factor error is used to modify the coarse scale factor, producing a more accurate scale factor. The adjustment results from simulation and experiments on triaxial MEMS accelerometers show that the proposed method can effectively correct the scale factor error caused by inability to align the accelerometer measurement axis parallel to the gravity line, with a relative scale factor error of 0.07%, improving the accuracy of the accelerometer scale factor.

In-Run Scale Factor Compensation for MEMS Gyroscope Without Calibration and Fitting

This paper presents an in-run scale factor error compensation for the micro-electro-mechanical system (MEMS) gyroscope without system calibration and data fitting. The causes of three scale factor errors (instability, nonlinearity, and asymmetry) are analyzed. Next, the instability and nonlinearity by open-loop detection (Mode I), and closed-loop detection (Mode II) are discussed according to the specific comb capacitance and the front-end detection circuit. The closed-loop detection transfer function is studied, and a series of equivalent conversions are performed to obtain a method (Mode III) for improving the temperature stability of scale factor. The results of the experiment indicated that the nonlinearity and asymmetry of the Mode II and Mode III are increased by 1.8 times and 3.5 times than that of Mode I. Furthermore, the instability of Mode II and Mode III is reduced by 10 times and 19 times over -20°C to 40°C. Besides, the mode III does not affect the static and dynamic performance of gyroscope according to the test results of bias and bandwidth.

A high-precision and high-order error model for airborne distributed POS transfer alignment

Distributed position and orientation systems (DPOSs) can provide abundant time-spatial information for interferometric synthetic aperture radar (InSAR) in airborne earth observation systems. However, some key error terms have not been taken into consideration in the traditional low-order error model, which suppresses the performance of the slave POS and further cannot meet the compensation precision of InSAR. To improve the compensation precision, a precise high-order error model with 45 dimensions was derived. Not only does it take into account the influence of scale factor errors and installation errors of the gyro and accelerometer, but it also makes use of random constants and a first-order Markov process model to describe the gyro drift and accelerometer bias. In addition, the flexure angle and its angular rate were added to the state variables of the transfer alignment model. Based on the model, a measurement equation for attitude errors that considers flexure was deduced. Then, a transfer alignment model based on the matching algorithm including position-velocity-attitude was designed. Finally, the proposed model was validated by simulated and real tests, and the experimental results show that its performance is obviously better than that of the traditional model.

Reinforcement Metalearning for Interception of Maneuvering Exoatmospheric Targets with Parasitic Attitude Loop

This Paper uses Reinforcement Meta-Learning to optimize an adaptive integrated guidance, navigation, and control system suitable for exoatmospheric interception of a maneuvering target. The system maps observations consisting of strapdown seeker angles and rate gyroscope measurements directly to thruster on/off commands. Using a high fidelity six-degree-of-freedom simulator, this Paper demonstrates that the optimized policy can adapt to parasitic effects including seeker angle measurement lag, thruster control lag, the parasitic attitude loop resulting from scale factor errors and Gaussian noise on angle and rotational velocity measurements, and a time-varying center of mass caused by fuel consumption and slosh. Importantly, the optimized policy gives good performance over a wide range of challenging target maneuvers. Unlike previous work that enhances range observability by inducing line of sight oscillations, this Paper’s system is optimized to use only measurements available from the seeker and rate gyros. Through extensive Monte Carlo simulation of randomized exoatmospheric interception scenarios, this Paper demonstrates that the optimized policy gives performance close to that of augmented proportional navigation with perfect knowledge of the full engagement state. The optimized system is computationally efficient and requires minimal memory and should be compatible with today’s flight processors.

Improving Positioning Accuracy of UWB in Complicated Underground NLOS Scenario Using Calibration, VBUKF, and WCA

Accurate localization of the shearer is key to achieving efficient, automated, unmanned mining. Unfortunately, the existing positioning algorithms usually yields low-precision, insufficient applicability, and unreliable final estimation due to the existence of non-line-of-sight (NLOS) error and also because they ignore the position error of anchor nodes (ANs). To bridge this technology gap, we developed a novel localization strategy by incorporating calibration, variational Bayesian unscented Kalman filter (VBUKF), total least squares (TLS), and water cycle algorithm (WCA) to enhance the location estimation accuracy of ultrawideband (UWB) positioning system in a complicated underground environment. First, calibration was implemented based on the selection of appropriate reference nodes (RNs) in line-of-sight (LOS) scenarios to estimate the scale-factor error, bias, and position errors for each AN; then the VBUKF smoothing with the consideration of time-variant measurement noise was used to reduce the interference of NLOS owing to the difficult separation of bias and NLOS error. Second, the TLS method was implemented to calculate the target node's position based on the smoothed distances and calibrated positions of ANs. Lastly, the WCA embedded scheme was executed to further ameliorate estimation accuracy. The experimental results demonstrated that the proposed TLS-WCA approach, after the implementation of calibration and VBUKF, was best able to improve the localization accuracy remarkably, and outperformed the other compared methods, which can efficiently attain higher estimation accuracy, highlighting the outstanding localization performance.

Optimization on the Precision of the MEMS-Redundant IMU Based on Adhesive Joint Assembly

In order to improve the precision of the spaceborne Inertial Measurement Unit (IMU), this paper proposes an adhesive joint assembly of the MEMS-redundant IMU. That is the application of special redundant installation of multiple MEMS gyroscopes in the IMU, which can improve the reliability of the MEMS-redundant IMU on the basis of reducing the weight of IMU. However, with the change of working environment, the traditional mechanical assembly of MEMS-redundant IMU will produce the large packaging stress and cause the deformation of MEMS gyroscope. This change will lead to changes in installation errors, scale factor errors, and bias errors of the MEMS gyroscope, resulting in a significant reduction in measurement precision of the MEMS-redundant IMU. Therefore, this paper selects the adhesive material that matches the thermal physical parameters of the material with the circuit board by analyzing the requirements of MEMS gyroscope on working environment at first. Then, by optimizing the bonding process, the installation error of each axis of MEMS-redundant IMU under different temperatures is better than the traditional mechanical connection mode. The experiment results of thermal vacuum show that the new assembly method can reduce the influence of temperature on the bias. Compared with the traditional method, the new assembly which is based on adhesive joint assembly can improve the measurement precision of MEMS-redundant IMU by an order of magnitude.