Dual-axis Rotational Inertial Navigation System Research Articles

A novel error modulation rotation scheme for dual-axis rotational inertial navigation system

Abstract Dual-axis rotational inertial navigation system (RINS) can effectively suppress the error accumulation of inertial navigation system, thereby improve the long-term navigation accuracy through rotating inertial measurement unit (IMU) according to corresponding rotation scheme. The navigation accuracy of RINS is predominantly contingent on the IMU rotation scheme. A reasonable rotation scheme can effectively attenuate or even obviate the navigation errors stemming from IMU errors, whereas an ill-considered scheme may lead to swift divergence of navigation errors. In this paper, the principle of IMU errors suppression is meticulously analyzed during rotation. By comprehensively evaluating the impact of individual IMU errors on navigation accuracy alongside their corresponding error modulation characteristics, a novel 32-position rotation scheme is devised. The proposed scheme demonstrates a notable capacity to minimize the adverse effects of IMU errors on navigation accuracy and to enhance error suppression efficacy within a modulation cycle. Meanwhile, the long-endurance navigation accuracy of RINS is substantially enhanced. The efficacy of the 32-position scheme posited herein is empirically substantiated through a 24 h simulation and navigation experiment.

Research on propagation mechanism for gyro installation error of dual-axis rotational inertial navigation system in UAV coordinated U-turn

With the development of rotation modulation, dual-axis rotational inertial navigation systems (RINS) are gradually applied to unmanned aerial vehicles (UAV) to cope with the increasing prominence of GNSS spoofing. The urgent need for autonomous navigation has promoted a popular topic of improving RINS accuracy. However, few have delved into error excitation and propagation from the perspective of carrier maneuvering. Starting from the error phenomena in a UAV flight experiment, this paper studies the error propagation mechanism of gyro installation error in dual-axis RINS under coordinated U-turn. Specifically, the coupling between the control strategies of the dual-axis RINS and the UAV typical maneuvers is revealed. On this basis, the error propagation mechanism for the gyro installation error is derived. Simulations validate the analyzed theory and illustrate the severity of this error source through flight and compensation experiments, where regular identification in highly dynamic applications becomes crucial to improve navigation accuracy.

Anti-disturbance self-alignment method for dual-axis rotational inertial navigation system under marine mooring conditions

Under the marine mooring conditions, the inertial navigation system (INS) is often disturbed by angular and linear motions, and it is difficult to perform self-alignment with high accuracy. To solve this problem, an anti-disturbance self-alignment method for dual-axis rotational INS is proposed. The method transforms the self-alignment problem into an attitude matrix solving problem, so as to deal with the disturbance of angular motion. By analyzing the relationship between the amount of measurement data and the accuracy of self-alignment, the optimal integration time is designed and a partial integral algorithm is proposed. Furthermore, the influence of initial velocity error on self-alignment under linear motion disturbance conditions is analyzed, and an initial velocity compensation method is proposed. Experimental results show that high-accuracy self-alignment can be achieved using the proposed method under the joint disturbance of angular and linear motions.

An Encoder-Based Relative Attitude Observation Method for Self-Calibration in Dual-Axis RINS

This study investigates an encoder-based relative attitude observation method for self-calibration in dual-axis rotational inertial navigation system (RINS). First, the calibration error of the gyroscope parameters caused by the velocity and position observations in systematic calibration is analyzed. Second, a relative attitude observation method utilizing photoelectric encoders for gyroscope parameters estimation is proposed. We apply the proposed method in our designed dual-axis RINS to verify its effectiveness in this work. Experimental results show that the calibration accuracy of the gyroscope can be improved to 0.0005 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^ \circ /h$</tex-math></inline-formula> in bias, and 0.98 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ppm$</tex-math></inline-formula> in scale factor using the proposed method. The proposed self-calibration method can be utilized as a high-accuracy self-calibration method in dual-axis RINS when the vehicle is in static condition.

An Improved Online Fast Self-Calibration Method for Dual-Axis RINS Based on Backtracking Scheme.

In the field of high accuracy dual-axis rotational inertial navigation system (RINS), the calibration accuracy of the gyroscopes and accelerometers is of great importance. Although rotation modulation can suppress the navigation error caused by scale factor error and bias error in a static condition, it cannot suppress the scale factor errors thoroughly during the maneuvering process of the vehicle due to the two degrees of rotation freedom. The self-calibration method has been studied by many researchers. However, traditional calibration methods need several hours to converge, which is unable to meet the demand for quick response to positioning and orientation. To solve the above problems, we do the following work in this study: (1) we propose a 39-dimensional online calibration Kalman filtering (KF) model to estimate all calibration parameters; (2) Error relationship between calibration parameters error and navigation error are derived; (3) A backtracking filtering scheme is proposed to shorten the calibration process. Experimental results indicate that the proposed method can shorten the calibration process and improve the calibration accuracy simultaneously.

Novel rotation scheme for dual-axis rotational inertial navigation system based on body diagonal rotation of inertial measurement unit

Traditional rotational inertial navigation systems are based on rotation around one or two sensitive axes of inertial sensors. However, as the rotation and sensitive axes of inertial sensors lie along the same direction, it is difficult to modulate the relative error of the inertial sensor in the axial direction. This paper proposes a dual-axis rotation scheme based on the diagonal rotation of the inertial measurement unit (IMU) body. The scheme selects the body diagonal of the three orthogonal inertial sensors of the IMU as the horizontal rotation axis, and sets the vertical rotation axis orthogonal to this axis. As the rotation axis and the inertial sensor are oriented in different directions, at any moment of rotation, the errors of the inertial sensor in the three axial directions can all be modulated, especially the installation error. First, a mathematical model based on the diagonal rotation of the IMU body is established. On this basis, the coordinate transformation relationship and the error equations are derived, and the error propagation characteristics are obtained. Finally, the comprehensive error of the system is tested. Under the same error conditions, the system latitude error is reduced from 0.1089 nautical miles/72 h in the traditional scheme to 0.0368 nautical miles/72 h, and the longitude error is reduced from 0.3587 nautical miles/72 h to 0.1332 nautical miles/72 h. These results verify the effectiveness of the proposed scheme. This method of rotating around the body diagonal of the IMU also exhibits certain advantages when applied to other rotational inertial navigation schemes.

A New Initial Alignment Scheme for Dual-Axis Rotational Inertial Navigation System

A New Initial Alignment Scheme for Dual-Axis Rotational Inertial Navigation System

Research on Innovative Self-Calibration Strategy for Error Parameters of Dual-Axis RINS

The rotational inertial navigation system (RINS) could greatly improve navigation accuracy by rotating the inertial measurement unit with gimbals. But it will also excite and amplify the corresponding error parameters, so it is more necessary to calibrate the typical error parameters accurately. Fortunately, the self-calibration strategy could be achieved conveniently in RINS. In this paper, an innovative self-calibration strategy for error parameters of dual-axis is proposed. The calibration strategy is designed that the inner and outer gimbals rotate at different angular speeds at the same time, and the whole calibration process lasts for 12 min. The relationship between the error parameters to be calibrated and the navigation error is derived, and the principle of error separation is analyzed, which proves the rationality of the strategy. The calibration strategy is verified by simulation and experiment, and the 21 error parameters of the system can be well estimated. The 3h static navigation experiment shows that the position error is less than 0.15nmile/h(CEP) after compensating the error parameters calibrated by the self-calibration strategy, and achieved the expected accuracy of the dual-axis RINS. Finally, it is proved that the calibration strategy has the obvious advantages of short calibration time and simple process, which is of great significance to improve the navigation accuracy of dual-axis RINS.

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.

A High-Accuracy Method for Calibration of Nonorthogonal Angles in Dual-Axis Rotational Inertial Navigation System

The dual-axis rotational inertial navigation system (RINS) can compensate the errors of inertial sensors by rotating the inertial measurement unit (IMU), thereby improving the accuracy of the inertial navigation system. However, in practical applications, nonorthogonal angles exist between the rotating axes, resulting in a decrease in navigation accuracy. In this paper, the error model of dual-axis RINS is established, which includes all nonorthogonal angles. Based on the nonorthogonal angle error model, the transformation matrix between the frames is derived, and the necessity of nonorthogonal angle calibration is discussed. The observability of the system is analyzed, and the degree of observability obtained indicates that the proposed nonorthogonal angles are observable. Then, a new nonorthogonal angle calibration method is proposed, which uses the dual-axis rotation mechanism. The proposed calibration method can calibrate all nonorthogonal angles with high accuracy, and the minimum estimation error is less than 10%. Simulations and experiments prove the effectiveness of the proposed error model and the calibration method, and demonstrate that the navigation accuracy can be significantly improved compared with the previous method.

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.

A rapid and high-accuracy rotation alignment method based on bidirectional process for dual-axis rotational inertial navigation system

For the alignment in rotational inertial navigation system (RINS), which takes velocity errors of the navigation calculation as the filter measurements, the velocity error term caused by the coupling of the accelerometer’s inner lever arms (ILAs) and the gimbals’ angular motion will lead to a decline in the alignment accuracy. In view of that, a simplified model of the ILAs is proposed firstly in combination with the specific dual-axis rotation scheme, and then the ILAs are extended into state variables for filtering estimation, thereby improving the alignment accuracy. On this basis, in order to further improve the alignment rapidity, the bidirectional process-based rotation alignment method for dual-axis RINS is proposed in this paper. The bidirectional process, which combines the backward-forward RINS calculation and the backward-forward Kalman filtering, makes the best use of the stored IMU data repeatedly and is able to quickly obtain the IMU attitude matrix for RINS. The simulations and experiments show that the proposed bidirectional process-based rotation alignment method is able to accomplish the rapid and accurate alignment for the dual-axis RINS.

Modeling and Calibration of the Gyro– Accelerometer Asynchronous Time in Dual-Axis RINS

Rotational inertial navigation system (RINS) could improve the navigation performance by rotating the IMU around gimbals, and the structure and function of the dual-axis RINS also help realize the process of self-calibration. However, the gyro–accelerometer asynchronous time is not considered in current studies. Coupled into the navigation error, the gyro–accelerometer asynchronous time can lead to velocity accuracy decline during the process of rotation. Therefore, the modeling and calibration of the gyro–accelerometer asynchronous time would enhance the systemic reliability. In this article, in order to solve the abovementioned problem: 1) we model the gyro–accelerometer asynchronous time and perform an error analysis of gyro–accelerometer asynchronous time; 2) we propose a compensation method of the outer lever arm to improve the accuracy of the observed velocity and position; and 3) we derive a continuous linear 40-D RINS error model considering the abovementioned two error parameters compared with the traditional method, the PWCS method, and the SVD method is utilized to provide the observability degrees of the proposed state during the self-calibration process. Experimental results illustrated that the proposed method can improve the accuracy in the long-endurance navigation.

An improved self-calibration method with consideration of inner lever-arm effects for a dual-axis rotational inertial navigation system

In high-precision navigation applications, a well-designed self-calibration method is a convenient approach to ensuring the positioning performance of a rotational inertial navigation system (RINS). Benefiting from the gimbal structure, traditional inertial measurement unit (IMU) sensor errors, including gyro drifts, accelerometer biases, scale factor errors and installation errors, could be estimated through a filter process under a proper rotation scheme. However, when the IMU rotates, inner lever-arm effects may bring additional errors to the observations, which may reduce the self-calibration accuracy. In this paper, an improved self-calibration method that includes consideration of the inner lever-arm effect is proposed for a dual-axis RINS. Based on analysis of the error propagation characteristics, a novel rotation scheme with variable angular rate is designed. By adopting the proposed self-calibration method, traditional IMU sensor errors can achieve much higher accuracy, and the inner lever-arm parameters can also be well calibrated simultaneously. Long-term vehicle navigation indicates that the positioning accuracy was significantly enhanced after the compensation of the calibration results, fully illustrating the effectiveness of the proposed method in ameliorating navigation performance for the dual-axis RINS.

Comprehensive Error Compensation for Dual-Axis Rotational Inertial Navigation System

For rotational inertial navigation system(RINS), the system error can be compensated by rotating the inertial measurement unit (IMU) with one or more axis regularly, and the error compensation effect is determined by the rotation scheme of IMU.A reasonable rotation scheme should remove the system errors caused by inertial sensors errors and meanwhile, should not introduce other additional errors by the rotation. The error compensation demerits of two common rotation schemes are discussed. In these two schemes, the attitude errors caused by installation error are not modulated completely in a whole rotation period, which will cause accumulative velocity errors by integration. The accumulative velocity errors will sequentially increase the amplitude of position oscillation error. Based on the aforementioned analysis, a comprehensive error compensation scheme for dual-axis RINS is proposed. The proposed scheme can not only modulate the constant bias of inertial sensors, but also compensate the scale factor errors and installation errors coupled with IMU rotation. Moreover, the coupling errors are modulated into a zero-mean form with half amplitude of those two traditional schemes. As a result, the system errors of RINS with this rotation scheme can be modulated to a maximum extent. The superiority of the proposed scheme is verified through simulations with 4 different error conditions. Under the same synthesized error condition, the position error of the proposed scheme decreases to 0.37nmile/72hours from 0.98nmile/72hours in the other two schemes.

A self-calibration method for gyro scale factor asymmetry in rotational inertial navigation system

In the rotational inertial navigation system (RINS), the inertial measurement unit (IMU) rotates around the motor shaft, which will stimulate the gyro scale factor asymmetry, so it needs to be effectively calibrated and compensated. In this paper, the influence of gyro scale factor asymmetry on angular velocity error, angle error and velocity error is analysed, and a self-calibration method for it is proposed in the RINS using velocity errors as measurements. A self-calibration rotation strategy is designed for the dual-axis RINS so as to carry out self-calibration for the scale factor asymmetry of x-gyro, y-gyro and z-gyro. The feasibility of this scheme is verified by theoretical analysis and simulation. Experiments are carried out on a set of dual-axis RINS based on fiber optic gyroscope, and the scale factor asymmetry calibration results of three gyros are 2.56 ppm, 10.01 ppm and 0.88 ppm, respectively. In the navigation experiment, the navigation error is improved by 57.45% after compensating the gyro scale factor asymmetry error, which fully illustrates the significance of the proposed self-calibration method in improving the navigation performance of RINS.

A self-calibration method of inner lever arms for dual-axis rotation inertial navigation systems

In an inertial navigation system (INS), it is generally assumed that three accelerometers in an inertial measurement unit measure the acceleration input at the same point in space. However, there are error vectors between the respective sensitive point of the three accelerometers and the theoretical measurement point, typically termed as inner lever arms (ILAs). In strapdown INS, the ILAs coupled with the carrier’s angular motion lead to a decline in navigation accuracy, while for dual-axis rotational INS (RINS), the ILAs coupled with the gimbals’ angular motion further introduce new navigation errors. Therefore, the calibration and compensation for the ILAs are important for enhancing the systemic reliability. In this paper, an ILA self-calibration method is proposed by leveraging the rotation gimbals of the RINS. To be able to obtain all the ILA parameters, we establish an error model by considering the ILAs, and design a reasonable rotation scheme to ensure all parameters observable. The simulations and experiments show that the proposed self-calibration method is able to accomplish the rapid and accurate estimation of all the ILAs and the velocity stage and slope errors are greatly corrected after compensation by the calibration results.

A System-Level Self-Calibration Method for Installation Errors in A Dual-Axis Rotational Inertial Navigation System.

In a dual-axis rotational inertial navigation system (RINS), there are two kinds of installation errors, nonorthogonal installation errors of inertial sensors, and installation errors between the inertial measurement unit (IMU) and rotation axes. Traditionally, these two errors are not considered simultaneously. Thus, they are calibrated separately by different estimation algorithms and rotation schemes. In this paper, a system-level self-calibration method for installation errors of a dual-axis RINS is proposed. Based on the Kalman filter, the measurement model is reestablished to ensure that all installation errors can be estimated together. First, the relationship between the initial attitude and subsequent attitude of IMU during rotation is used as a constraint to estimate nonorthogonal installation errors of accelerometers, and installation errors between the IMU and rotation axes. Then, the angular rate of the rotation mechanism is used as a reference to estimate nonorthogonal installation errors of the gyros. The rotation scheme of the IMU is designed to make all installation errors observable, and the observability of the system is analyzed based on the piecewise constant system method. Simulation and laboratory experiment results suggest that installation errors can be effectively estimated by the proposed method, thereby avoiding the complex separating process.

Dynamical analysis and experimental verification of deviation angles caused by rubber dampers deformation in high precision mechanically dithered RLG dual-axis RINS

Abstract Deviation angles between inertial measurement unit (IMU) and turntable in dual-axis rotational inertial navigation system (RINS) degrade the navigation attitude precision seriously. And rubber dampers deformation is an unavoidable and crucial factor in deviation angles when turntable rotates for high precision mechanically dithered ring laser gyroscope (RLG) dual-axis RINS. In this paper, in order to accurately analyze the deviation angles caused by rubber dampers deformation, a novel dynamic analysis and experimental verification method for these deviation angles in dual-axis RINS is proposed. Firstly, a 3-D Voigt model for rubber damper was proposed, and then a 6-DOF dynamic model of mechanically dithered RLG dual-axis RINS was built based on the proposed 3-D Voigt model. Secondly, dynamic equations were derived based on the proposed model for inner gimbal rotation and outer gimbal rotation respectively. Then dynamic equations were solved analytically by decoupling method and the decoupling method was validated by comparing analytic solutions against numerical solutions got by Runge-Kutta method. Afterwards, rotation experiments for turntable were conducted to obtain actual deviation angles caused by rubber dampers deformation. Finally the proposed model and dynamic analysis method were validated by comparing it against the real deviation angles measured by rotation experiments for turntable.

Online Calibration of the Geographic-Frame-Equivalent Gyro Bias in Dual-Axis RINS

Dual-axis rotational inertial navigation system (RINS) has been widely used in long-term marine navigation for recent years. With all constant biases averaged out, those gyro biases related to geomagnetic or gravitational field, which cannot be averaged out, become the main error source. In this paper, the geographic-frame-equivalent (G-F-E) gyro bias is defined by integrating the gyro biases caused by all kinds of external fields. A practicable online calibration method is proposed by deducing the error propagation rules. The calibration equation is established by observing position errors at three points, and the optimal solution of the G-F-E gyro bias is obtained using the least square method. Static and sailing experimental results show that the G-F-E gyro bias can be calibrated during the 6-h initial alignment. The proposed calibration method can further improve the position accuracy of a dual-axis RINS by 30% compared with the previous method when the G-F-E gyro bias changes.