Gyro Error Research Articles

Laser gyro signal filtering by combining CEEMDAN and principal component analysis

In order to suppress the random shift error of laser gyro and improve the practical precision of inertial navigation system, an improved gyro filtering method is proposed by combining the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and principal component analysis (PCA). Firstly, the gyro signal is decomposed by CEEMDAN, and the noise energy of each intrinsic mode function (IMF) is estimated according to the distribution model of noise energy. Then, on basis of noise energy, the principal component analysis is used to remove the noise IMF to achieve the final denoising of gyro signal. In the proposed method, CEEMD can improve the mode mixing and denoising effect of gyro signal. Moreover, PCA is used to decompose each IMF. According to the noise energy, the noise of each IMF is removed adaptively to avoid the selection of noise IMF and better retain the useful information of the signal. The proposed method is completely dependent on the characteristics of gyro signal and has good adaptability and strong denoising ability. Furthermore, the filtered effect of different methods is analyzed by overlapping Allan variance. The experimental results show that the proposed method can suppress the gyro random drift more efficiently, and the effect of removing noise is better than EMD threshold method and EMD correlation coefficient method.

Suppression of the G-sensitive drift of laser gyro in dual-axis rotational inertial navigation system

The dual-axis rotational inertial navigation system (INS) with dithered ring laser gyro (DRLG) is widely used in high precision navigation. The major inertial sensor errors such as drift errors of gyro and accelerometer can be averaged out, but the G-sensitive drifts of laser gyro cannot be averaged out by indexing. A 16-position rotational simulation experiment proves the G-sensitive drift will affect the long-term navigation error for the rotational INS quantitatively. The vibration coupling and asymmetric structure of the DRLG are the main errors. A new dithered mechanism and optimized DRLG is designed. The validity and efficiency of the optimized design are conformed by 1 g sinusoidal vibration experiments. An optimized inertial measurement unit (IMU) is formulated and measured experimentally. Laboratory and vehicle experimental results show that the divergence speed of longitude errors can be effectively slowed down in the optimized IMU. In long term independent navigation, the position accuracy of dual-axis rotational INS is improved close to 50%, and the G-sensitive drifts of laser gyro in the optimized IMU are less than 0.000 2 °/h. These results have important theoretical significance and practical value for improving the structural dynamic characteristics of DRLG INS, especially the high-precision inertial system.

Machine Learning Gyro Calibration Method Based on Attitude Estimation

This paper proposes a novel machine learning (ML) gyro calibration method that can achieve higher-accuracy gyro calibration and attitude estimation than the classical extended Kalman filter (EKF) approach when high-accuracy measurements are unavailable. The gyro calibration process is modeled as a time-series problem based on the standard EKF output. Then, a designed ML model is trained by the collected time-series data so that it can conduct gyro calibration by generating an ML correction to the gyro measurement. The proposed ML calibration method does not make assumptions in the form of gyro measurement errors, but directly learns it from data when high-accuracy information is available. Therefore, it is possible to outperform the EKF bias calibration when there is only low-accuracy information. To validate the method, a torque-free CubeSat is simulated using sun sensors and magnetometers to generate higher- and lower-accuracy attitude measurements, respectively. The simulation results show that the ML gyro calibration achieves smaller residual errors compared with the standard EKF. Meanwhile, the EKF attitude estimation accuracy is also improved, as the attitude integration is more accurate using the ML-calibrated gyro measurement. Four ML models based on different principles are examined, including multilayer perceptron, convolutional neural network, recurrent neural network, and Gaussian processes. It is found that, usually, a more sophisticated ML model can capture more gyro error information, but all four models can achieve similar performance with well-tuned parameters.

Residual Intensity Modulation Induced Error in Resonator Fiber Optic Gyroscopes With Reciprocal Detection

In the resonator fiber optic gyroscope (RFOG), both the residual intensity modulation (RIM)-induced error and backscattering-induced noise need to be effectively suppressed. When the clockwise and counterclockwise resonance detection adopt the same phase modulation and demodulation scheme, namely reciprocal detection, the reciprocity of the RFOG is improved, and the error induced by the RIM of the phase modulator used for detection (PMD) can be effectively suppressed. However, it is inevitable to add a phase modulator used for frequency shift (PMFS) to suppress the backscattering-induced noise. In this paper, the influence of the RIM of the PMFS on the performance of the RFOG is analyzed, and the model of the RIM-induced error in the RFOG with reciprocal detection is established. The analysis shows that in order to reduce the bias to the level of the shot noise, it is necessary to suppress the error induced by the RIM of the PMFS, and reducing the modulation frequency of the PMFS can effectively suppress the RIM-induced error. When a phase modulator is added to the RFOG with reciprocal detection to further suppress the backscattering-induced noise, the RIM-induced error can still be effectively suppressed by reducing the frequency of the added phase modulation.

Research on temperature error compensation method of vehicle-mounted laser gyro SINS

In order to solve the problem that the measurement accuracy of vehicle-mounted laser gyro strapdown inertial navigation system (SINS) is affected by the temperature change, a temperature error compensation method which can adapt to the full temperature environment is proposed. Based on the phenomenon that the temperature of the inertial sensor is still rising when the temperature of the temperature control box is kept, a continuous temperature change experiment is designed. Then, Pearson correlation analysis of the output of laser gyro and quartz flexible accelerometer with temperature, temperature rate and temperature gradient has been carried out. Based on that, the temperature error models of gyro and accelerometer are constructed, and the temperature compensation method based on polynomial model is proposed. The results show that this method could compensate the temperature error of the laser gyro and the quartz flexible accelerometer effectively, and the zero-bias stability of them are both improved, especially the zero-bias stability of the accelerometer is improved by at least one order of magnitude, the accuracy of inertial measurement in full temperature environment is improved effectively.

A novel MEMS-RIMU self-calibration method based on gravity vector observation

The microelectromechanical system (MEMS) redundant inertial measurement unit (RIMU) is a low-cost navigation system, which can improve reliability effectively. In existing MEMS-RIMU calibration schemes, extra equipment with higher accuracy is required. However, on some occasions, a rotation platform or other reference equipment cannot be provided, and calibration of the MEMS-RIMU is limited. To solve the problem, a novel self-calibration method for the MEMS-RIMU based on gravity vector observation is proposed, which can estimate the bias, scale errors and alignment errors of accelerometers and gyroscopes without extra equipment or rotation platforms. In this paper, a novel calibration model for accelerometers and gyroscopes is built by analyzing the relationship between gravity vector observation and the measurement value of the MEMS-RIMU. There is no attitude information in the calibration model, so the RIMU can be calibrated without attitude references via extra equipment. Then, a derivative unscented Kalman filter is proposed to estimate the bias, scale errors and alignment errors of accelerometers and gyroscopes, which can reduce the computation load. Finally, the simulation and experimental results demonstrate the efficiency and accuracy of the proposed calibration scheme.

A Combined Method for MEMS Gyroscope Error Compensation Using a Long Short-Term Memory Network and Kalman Filter in Random Vibration Environments.

In applications such as carrier attitude control and mobile device navigation, a micro-electro-mechanical-system (MEMS) gyroscope will inevitably be affected by random vibration, which significantly affects the performance of the MEMS gyroscope. In order to solve the degradation of MEMS gyroscope performance in random vibration environments, in this paper, a combined method of a long short-term memory (LSTM) network and Kalman filter (KF) is proposed for error compensation, where Kalman filter parameters are iteratively optimized using the Kalman smoother and expectation-maximization (EM) algorithm. In order to verify the effectiveness of the proposed method, we performed a linear random vibration test to acquire MEMS gyroscope data. Subsequently, an analysis of the effects of input data step size and network topology on gyroscope error compensation performance is presented. Furthermore, the autoregressive moving average-Kalman filter (ARMA-KF) model, which is commonly used in gyroscope error compensation, was also combined with the LSTM network as a comparison method. The results show that, for the x-axis data, the proposed combined method reduces the standard deviation (STD) by 51.58% and 31.92% compared to the bidirectional LSTM (BiLSTM) network, and EM-KF method, respectively. For the z-axis data, the proposed combined method reduces the standard deviation by 29.19% and 12.75% compared to the BiLSTM network and EM-KF method, respectively. Furthermore, for x-axis data and z-axis data, the proposed combined method reduces the standard deviation by 46.54% and 22.30% compared to the BiLSTM-ARMA-KF method, respectively, and the output is smoother, proving the effectiveness of the proposed method.

Photoelectric pod drift calibration method based on navigation system

The accuracy of stability control is an important indicator of photoelectric pod system. In order to reduce the effect of gyro drift on stability accuracy in stabilized sighting control, the gyro drift needs to be compensated. A method of drift measurement and compensation was introduced for the photoelectric pod based on the navigation system, which was designed to calculate the component of earth rotation in the platform by the position and attitude data of airborne navigation system and pod angle during drift measurement phase of photoelectric pod, so as to obtain a more accurate gyro error. And in the stable phase, the gyro error and earth rotation component were compensated respectively by the navigation system. This method could effectively separate the earth rotation component and gyro error in the gyro drift measurement stage and adjust earth rotation component in the stable stage, so that the stability precision of stabilized sighting system could be improved. The experimental results show that, by comparing the results of 10-minute traditional drift measurement and drift measurement based on the navigation system, the accumulated drift error is stably controlled, the pitch angle is reduced from 1.80° in traditional method to 0.04°, and the heading angle is reduced from 0.77° to 0.04°.

Gradient Descent Optimization-Based SINS Self-Alignment Method and Error Analysis

In this paper, the self-alignment for stationary strapdown inertial navigation system (SINS) is formulated as an optimization problem, and two gradient descent optimization-based SINS self-alignment methods (GD1 and GD2) are proposed. The highlight lies in that two quaternion-based objective functions are firstly formulated to solve the stationary SINS self-alignment problem. Different from conventional initial alignment methods, we firstly construct a quaternion-based objective function for stationary SINS using gravity, Earth rate and local latitude information in GD1, and employs gradient descent method to achieve the minimum of the objective function. Secondly, we further improve the quaternion-based objective function in GD2 by using the measurements from IMU to represent the Earth rate instead of using the local latitude directly. Thus, GD2 method is more competent for SINS self-alignment when the local latitude information is not available. In addition, we also analyze the bias errors of accelerometer and gyroscope and the quaternion normality error for GD1 and GD2 method respectively. Moreover, based on the analysis results, a scale factor is also introduced to reduce the alignment errors of GD1 caused by gyroscope biases. Simulation and static experiment are implemented to test the performances of GD1 and GD2 method, and the results verify the accuracy and speed of the proposed methods.

A new IMU error parameter estimation method for hypersonic vehicle based on hybrid neural network

To realize the effective estimation of the inertial measurement unit (IMU) error parameters of a hypersonic vehicle and satisfy the high-precision navigation requirements, a hybrid neural network (HYNN) method that consists of a quasi-Newton semi-determined weight neural network (QNSWNN) and a semi-determined weight recurrent neural network (SWRNN) is proposed. In contrast to conventional neural networks, the weights of the HYNN model, which are determined by the IMU error parameters, have physical meanings. First, the IMU error model and strap-down inertial navigation system (SINS) navigation model are established. Second, the QNSWNN model is constructed based on the SINS/celestial navigation system (CNS) integrated navigation system information. The quasi-Newton is used to adjust the weights, which include the gyroscope error. The rest weights of QNSWNN are fixed based on a SINS attitude calculation model. The gyroscope error parameters can be estimated during the QNSWNN training process. Lastly, the SWRNN model is constructed based on the SINS/GPS integrated navigation system information. The BP algorithm is used to adjust the weights, which include the accelerometer error. The rest weights of SWRNN are fixed based on the SINS navigation calculation model. The accelerometer error parameters can be estimated during the SWRNN training process. The simulation results show that the IMU error parameter can be effectively estimated by the HYNN, and the relative errors are below 25%. Moreover, when the signal of the auxiliary navigation system is interrupted, the HYNN method still has high prediction accuracy for the SINS navigation parameters.

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.

Research on multi-sensor pedestrian dead reckoning method with UKF algorithm

In order to solve the problem that the positioning error of pedestrian dead reckoning (PDR) with inertial measurement unit will accumulate over time, an indoor pedestrian space estimation method based on multi-sensor fusion is proposed. Based on the low-cost multi-sensor of smart mobile device, the initial alignment based on the unscented Kalman filter (UKF) is designed and four threshold conditions are set for carrying out the step state detection. In the process of walking, aiming at solving the cumulative problem of the step error and the heading angle error, the method of combining zero velocity update (ZUPT), zero angle rate update (ZARU), and magnetometer based on UKF is used to correct the error, where ZUPT corrects the speed error, the combination of ZARU and magnetometer corrects the gyro error and the heading angle error, which effectively reduce the position error and improve the pedestrian positioning accuracy. The experimental results show that the method proposed in this paper can effectively reduce the average position deviation of PDR, and the positioning error is about 1.5% of the total walking distance. Compared with the original PDR system algorithms, the proposed method uses low-cost multi-sensor to obtain better positioning accuracy.

Simulation Platform for SINS/GPS Integrated Navigation System of Hypersonic Vehicles Based on Flight Mechanics.

In this study, a simulation platform for an integrated navigation algorithm for hypersonic vehicles based on flight mechanics is designed. In addition, the generation method of inertial measurement unit data and satellite receiver data is introduced. First, the interface relationship between a high-precision six-degree-of-freedom (6DoF) model and the simulation platform in the launch-centered Earth-fixed frame is introduced. Three-axis theoretical specific force and angular velocity are output by the 6DoF model. Accelerometer and gyroscope error models are added, and integral processing of the specific force and angular velocity is performed to obtain velocity increment of the accelerometer and the angular increment of the gyroscope. These data are quantified to obtain the accelerometer and gyroscope pulses. The satellite’s pseudo-range and pseudo-range rate as well as its position and velocity are obtained from the theoretical position, velocity, the attitude of the hypersonic vehicle’s 6DoF model output, and the global positioning system (GPS) satellite broadcast ephemeris. The simulation data can be used for the verification of the loose and tight coupling integrated navigation algorithms. The simulation test verifies the accuracy of the designed method.

The Stellar-INS Navigation Performance Influence Mechanism of Star Vector Orientation in the Field of View

The star sensor field of view varies from several arc-minutes to 20 degrees, which directly determines the star vector orientation in the field of view (FOV). Although the relationship between star vector orientation in the FOV and attitude accuracy has been revealed, the influence mechanism of star vector orientation on the integrated navigation performance of a stellar inertial navigation system has not been analysed. In order to improve the integrated accuracy, the main errors such as star sensor installation error, gyro error and initial platform angle error should be estimated online. It is significant to study the influence mechanism of star vector orientation on estimation of the above errors. In this paper, the star sensor sensitivity and the geometry factor are defined to feature the difference between the optical axis direction and the non-optical axis direction. The formulised mechanism and quantification results between star vector orientation and integration attitude and error estimation accuracy are clearly given. Simulation and ground testing were conducted and it was found that the larger the star vector orientation along the optical axis, the better the error estimation accuracy. In contrast, the attitude accuracy is weakly sensitive to the orientation of the star vector in conditions of appropriate posture adjustment and star observation scheme. This conclusion can offer universal guidance for the design and evaluation of stellar inertial navigation systems with narrow field of view or large field of view star sensors.

Measuring upper arm elevation using an inertial measurement unit: An exploration of sensor fusion algorithms and gyroscope models

Many sensor fusion algorithms for analyzing human motion information collected with inertial measurement units have been reported in the scientific literature. Selecting which algorithm to use can be a challenge for ergonomists that may be unfamiliar with the strengths and limitations of the various options. In this paper, we describe fundamental differences among several algorithms, including differences in sensor fusion approach (e.g., complementary filter vs. Kalman Filter) and gyroscope error modeling (i.e., inclusion or exclusion of gyroscope bias). We then compare different sensor fusion algorithms considering the fundamentals discussed using laboratory-based measurements of upper arm elevation collected under three motion speeds. Results indicate peak displacement errors of <4.5° with a computationally efficient, non-proprietary complementary filter that did not account for gyroscope bias during each of the one-minute trials. Controlling for gyroscope bias reduced peak displacement errors to <3.0°. The complementary filters were comparable (<1° peak displacement difference) to the more complex Kalman filters.

Data Fusion Method of Measurement Lag Compensation for Multirate MIMU/FOG/GNSS Compound Navigation

In the future, smart intelligent ammunition will be widely applied in the military field. Small volume microelectromechanical system inertial measurement units (MIMUs) have become the mainstream solution for a smart intelligent ammunition navigation system; however, the accuracy of the IMU is the main factor limiting the accuracy of the strikes. To improve the navigation accuracy of the MIMU, various integrated methods have been proposed, for example, the integration of a global navigation satellite system (GNSS) and a magnetometer. In this study, a compound navigation system (CPNS) is designed to improve the navigation accuracy of the MIMU. The CPNS consists of an oblique single-axis fiber optic gyroscope (FOG), a MIMU and a GNSS. The proposed method solves two problems: the calibration of the MEMS gyro and GPS measurement lag. With a FOG as the measurement, MEMS gyro errors are calibrated online by the designed Kalman filter. Thus, the accuracy of the CPNS-IMU can be improved. When GPS measurement lag occurs, the accuracy of the traditional Kalman filter will deteriorate. To reduce the data fusion error of the CPNS under measurement lag, a distributed optimal fusion estimation method is proposed based on the multi-scale theory. The hardware-in-the-loop simulation results demonstrate that the constant bias, scale factor errors, and misalignment errors of the MEMS gyro are effectively suppressed by configuring the FOG to the MIMU. The navigation error of the CPNS-IMU is reduced by more than 50% as compared with the navigation error of the MIMU. In the CPNS with the measurement lag, the fusion error is reduced by approximately 33% in the proposed method as compared with the existing methods.

Analysis of Assembly Error Effect on Stability Accuracy of Unmanned Aerial Vehicle Photoelectric Detection System

A photoelectric detection system is a typical type of device widely used for detecting purposes based on unmanned aerial vehicles (UAV). Stability accuracy is the key performance index. Compared to traditional analysis methods aimed at unpredictable error-causing sources, assembly errors can be easily controlled during the manufacturing processes. In this research, an analysis method of assembly error effect on stability accuracy is proposed. First, by using kinematics analysis of homogeneous coordinate transformation, stability accuracy is comprehensively modeled and simulated. Then, by analyzing the manufacturing process, assembly errors of axis perpendicularities, run-outs and gyroscopes are defined and modeled. By simulating different carrier movements, the effects caused by assembly errors under various environments are studied. Finally, error sensitivity is proposed by using standard deviation analysis. Results show that the most sensitive assembly errors are identified, and ranked in order of sensitivity as follows: x-component of pitch axis perpendicularity, y-component of the azimuth gyroscope assembly, and z-component of the pitch gyroscope assembly. In conclusion, the results can be used as standards of manufacturing process improvements, and the proposed methods can be used to provide valuable references for real application scenarios.

Attitude Calculation Based on Sequential Correction of Gravity Field and Geomagnetic Field

Aiming at the problems of gyroscope error divergence and magnetometer susceptibility to soft magnetic environment in attitude calculation of unmanned system, a method of attitude calculation based on gravity field and geomagnetic field sequential correction is proposed. In this method, gyroscope output is used to construct the state equation of attitude quaternion, and then the quaternion is sequentially corrected twice by using accelerometer and magnetometer data in order to obtain accurate attitude output. The experimental results show that, compared with the three traditional attitude calculation algorithms, this algorithm can effectively suppress the gyroscope drift error and improve the attitude output accuracy under the environment of magnetic interference. The static accuracy of the attitude angle is not greater than that of the dynamic accuracy, which meets the application requirements of the unmanned system.

Analysis of Centroid Variation of Three-floating Gyroscope Based on Error Sensitivity

The surface error of the three-floating gyroscope caused the centroid variation of the three-floating gyroscope, which caused the navigation accuracy to decrease. In this paper, the error sensitivity model of three-floating gyroscope was established by using the geometric error transfer theory, the influence of each surface error to the three-floating gyroscope’s centroid was calculated, and the results were verified using modeling software. Finally, this paper evaluated the assembly capabilities of the assembly surface. This paper has guiding significance for the three-floating gyroscope to reduce production cost under the premise of ensuring navigation accuracy.

基于改进GM(1,1)模型的激光陀螺仪随机误差预测

基于改进GM(1,1)模型的激光陀螺仪随机误差预测