High-precision Inertial Navigation System Research Articles

An Improved Inertial Preintegration Model in Factor Graph Optimization for High Accuracy Positioning of Intelligent Vehicles

Accurate and reliable positioning is of great importance for the realization of intelligent vehicles (IV). Factor graph optimization (FGO) has been popularized in the field of robotics for state estimation. As a ubiquitous sensor, the IMU is widely used for vehicular positioning based on the preintegration theory using FGO. However, the existing preintegration model fails to consider the earth's rotation, which challenges the attitude and positioning performance of vehicles equipped with high-precision inertial measurement units (IMU). To fill this gap, an accurate IMU factor that accounts for the earth's rotation rate is designed in this paper. First, an exact preintegration measurement model is derived based on a high-precision inertial navigation system (INS) mechanization. The proposed factor is more accurate and it enables the application of the FGO more suitable for inertial-based integrated navigation with different precision IMUs. In both simulation and field tests, the INS/ Global Navigation Satellite System (GNSS) integration, as a representative of inertial-based integrated navigation, is used to verify the performance of the proposed preintegration factor. The navigation results using our experimental car reveal that the proposed model leads to a more accurate estimation, outperforming the traditional preintegration models, especially in the aspect of attitude estimation.

Gravity disturbance compensation for dual-axis rotary modulation inertial navigation system

Gravity disturbance compensation is an important technique for improving the positioning accuracy of high-precision inertial navigation systems (INS). Aiming at the current problems of the resolution of gravity compensation background field and the robustness of gravity compensation algorithm are insufficient for gravity compensation. In this study, the error and frequency characteristics of INS caused by gravity disturbances are investigated. The gravity disturbance with a spatial resolution of 1’ × 1’ from a high-precision satellite altimetry marine gravity field model is preliminarily introduced into the initial alignment and pure INS calculation to implement the gravity compensation of the dual-axis rotary modulation INS. Detailed calculation results show that the east gravity disturbance affects the north attitude, and the north gravity disturbance affects the east attitude in the initial alignment. In the pure INS calculation, the horizontal gravity disturbance causes a navigation error in the form of Schuler oscillation. The INS navigation error caused by horizontal gravity disturbance is mainly affected by its amplitude; however, the horizontal gravity disturbance accuracy from the satellite altimetry model for INS gravity compensation can be ignored in practice. In addition, for low-speed underwater vehicles, the influence of high-frequency gravity disturbance signals on the INS position shows an increasing trend. Finally, the effectiveness of the gravity compensation achieved by the horizontal gravity disturbance from the satellite altimeter model is confirmed by a dynamic shipborne test. The positioning accuracy of the rotary modulation INS is maximally improved by approximately 17.9% after the horizontal gravity disturbance is compensated simultaneously in the pure INS calculation and the initial alignment.

A structure scheme to reduce the influence of the accelerometer inner lever-arm effect on tri-axis inertial navigation systems

The accelerometer inner lever-arm effect is a significant error source for high-precision inertial navigation systems (INSs) and has a marked influence on the speed accuracy—a critical technical index of high-precision weapon systems. Rotation modulation technology is widely applied to reduce the errors of high-precision INS. However, this method fails to work for the inner lever-arm effect. Furthermore, variations in the rotation angular velocity and acceleration during modulation alter the inner lever-arm effect, further complicating the compensation of errors. System self-calibration is currently the principle method adopted to deal with the inner lever-arm effect, yet calculation errors result in residual estimations at the millimeter-level for the inner lever-arm. Such a residual will cause obvious speed errors for high-precision INS, which typically turns over the inertial measurement unit via the rotation modulation. This consequently makes it difficult to fully meet the requirements of high-precision weapon systems. In the current paper, we propose an accelerometer geometric space scheme based on the calculations and structural characteristics of a tri-axis INS. Through a simple structure arrangement, we demonstrate the complete theoretical elimination of the inner lever-arm effect in the absence of complex calibration and compensation processes. The only residual error of the inner lever-arm in the proposed scheme is the accumulated geometric tolerance with a value less than 0.2 mm. Semi-physical simulation results reveal the ability of our scheme to directly reduce the magnitude of the system speed error from 10−2 to 10−5. Moreover, the speed fluctuation disappears during the modulation rolling process, thus fully meeting the requirements of high-precision weapon systems.

Analysis of Deflection of Vertical Compensation for Inertial Navigation System

With the development of high-precision inertial navigation systems, the deflection of vertical (DOV), gravity disturbance, is still one of the main error sources that restrict navigation accuracy. For the DOV compensation of the Strapdown Inertial Navigation System (SINS) problem, the influences of the calculation degree of the spherical harmonic coefficient and the calculation error of the DOV on the compensation effect were studied. Based on the SINS error model, the error propagation characteristics of the DOV in SINS were analyzed. In addition, the high-precision global gravity field spherical harmonic model EIGEN-6C4 was established and the influence comparative analysis of the calculation degree of the spherical harmonic coefficient on the DOV compensation of SINS in different regions was carried out. Besides, the influence of the calculation error of the DOV on the compensation was emphatically analyzed. Finally, the vehicle experiment verified the feasibility of compensation in SINS based on the gravity field spherical harmonic model. The simulation and experiment results show that it is necessary to consider the influence of the calculation degree and the calculation error of the DOV on the compensation for long-time high-precision SINS with the position accuracy of 0.3 nm/h, while the SINS with general requirements for position accuracy can ignore the impact.

Analysis and on-line compensation of gravity disturbance in a high-precision inertial navigation system

Zero velocity update technology (ZUPT) has frequently been used as a tool to reduce divergence when the inertial navigation system (INS) is working in pure inertial mode. In general, the normal gravity model is adopted to calculate the gravity vector, and the effect of gravity disturbance is neglected. We present a new point of view to explain the influence of gravity disturbance on INS and point out that gravity disturbance is one of the most significant error sources of the high-precision INS. Two real-time gravity disturbance compensation methods are proposed. An about 110-km-long vehicle test has been conducted in mountainous terrain with a drastic change of gravity disturbance. The test results proved the correctness of the new explanation and the feasibility of the two on-line compensation algorithms for land vehicles. With gravity disturbance compensation in conjunction with ZUPTs, the total horizontal error at the end of the test was reduced from 8.93 to 3.75 m, and the elevation error was reduced from 1.63 to 0.80 m.

Analysis of Gravity Disturbance Compensation for Initial Alignment of INS

To address the accuracy requirements of initial alignment of high-precision inertial navigation systems (INSs), gravity disturbance compensation for INSs based on a spherical harmonic model is investigated herein. First, the horizontal component of gravity disturbance at an alignment point is calculated using the high-resolution Earth Gravity Model EIGEN-6C4 and then compensated to the initial alignment. Subsequently, the self-alignment algorithm of solidified coordinate frame is used to derive the misalignment angle equation of gravity disturbance affecting the initial alignment. Meanwhile, the coupling relationship between the measurement error of an inertial unit and the gravity disturbance is simulated and analyzed. Finally, a laser strapdown inertial navigation system experiment is performed. The simulation result shows that the pitch angle, roll angle, and heading angle errors reduced by $27.41^{\prime \prime }$ , $- 0.37^{\prime \prime }$ , and $6.72^{\prime \prime }$ , respectively, after the gravity disturbance compensation. Experiment result shows that the alignment performance after compensation has been improved and the heading angle error is reduced by $6.76^{\prime \prime }$ . The simulations and experiments results validate the theoretical analysis.

An Analysis of the Effect of Gravity Anomaly to Height Estimation in High-Precision INS/GNSS Integrated Navigation Systems

In this paper, we focus on how gravity anomaly affects height estimation in the high-precision inertial navigation system (INS) and global navigation satellite system (GNSS) integration. The theoretical analysis based on INS error propagation equations shows that the height error is related to gravity anomaly directly. In addition, the height-related elements in the Kalman gain matrix can be used as an indicator to evaluate the extent of the effect to height estimation. Different precision grade INSs integrated with GNSS, and GNSS of different positioning accuracy integrated with high-precision INS is simulated to analyze the effect of gravity anomaly. The simulation results show that the effect can be ignored in low-precision INS cases, while is more significant in high-precision cases, which agrees well with the former theoretical analysis. At last, a shipborne test is conducted and the experimental results show that the maximum height error of high-precision INS/GNSS integration can reach to 0.5 m if the gravity anomaly is not compensated, while can fall below than 0.1 m after gravity anomaly compensation or modeling. It shows that the existence of gravity anomaly along the track can degrade the vertical positioning accuracy of high-precision INS/GNSS integration, and should be considered in such cases.

Economical High⁻Low Temperature and Heading Rotation Test Method for the Evaluation and Optimization of the Temperature Control System for High-Precision Platform Inertial Navigation Systems.

Inertial navigation systems (INSs) use the temperature control system to ensure the stability of the temperature of the inertial sensors for improving the navigation accuracy of the INSs. That is, the temperature control accuracy affects the performance of the INSs. Thus, the performance of temperature control systems must be evaluated before their application. However, nearly all high-precision INSs are large and heavy and require long-term testing under many different experimental conditions. As a result, conducting an outdoor navigation experiment, which involves high–low temperature and heading rotation tests, is time consuming, laborious, and costly for researchers. To address this issue, an economical high–low temperature and heading rotation test method for high-precision platform INSs is proposed, and an evaluation system based on this method is developed to evaluate the performance of the temperature control systems for high-precision platform INSs indoors. The evaluation system uses an acrylic chamber, exhaust fans, temperature sensors, and an air conditioner to simulate the environment temperature change. The outer gimbals of the platform INSs are utilized to simulate the heading rotation. The temperature control system of a high-precision platform INS is evaluated using the proposed evaluation method. The temperature difference of the gyros is obtained in the high–low temperature test, and the temperature fluctuation of the temperature control system is observed in the rotation test. These tests verify the effectiveness of the proposed evaluation method. Then, the corresponding optimization method for the temperature control system of this high-precision platform INS is put forward on the basis of the test results of the evaluation system. Experimental results show that the maximum temperature differences of the two gyros between high- and low-temperature tests are decreased from 1.51 °C to 0.50 °C, and the maximum temperature fluctuation value of the temperature control system is decreased from 0.81 °C to 0.27 °C after the proposed evaluation and optimization processes. Therefore, the proposed methods are cost effective and useful for evaluating and optimization of the temperature control system for INSs.

Raw Data-Based Motion Compensation for High-Resolution Sliding Spotlight Synthetic Aperture Radar.

For accurate motion compensation (MOCO) in airborne synthetic aperture radar (SAR) imaging, a high-precision inertial navigation system (INS) is required. However, an INS is not always precise enough or is sometimes not even included in airborne SAR systems. In this paper, a new, raw, data-based range-invariant motion compensation approach, which can effectively extract the displacements in the line-of-sight (LOS) direction, is proposed for high-resolution sliding spotlight SAR mode. In this approach, the sub-aperture radial accelerations of the airborne platform are estimated via a well-developed weighted total least square (WTLS) method considering the time-varying beam direction. The effectiveness of the proposed approach is validated by two airborne sliding spotlight C band SAR raw datasets containing different types of terrain, with a high spatial resolution of about 0.15 m in azimuth.

Robust finite time second-order sliding mode stabilization control for floated inertial platform

High precision inertial navigation system is one of the main ways to improve the accuracy of the satellite orbit and to prolong life. In order to solve the suspension stabilization problem of the floated inertial navigation platform (or the floated platform), a robust finite time second-order sliding mode control scheme is proposed. This control method can guarantee the stability and rapidity of the system under the complex disturbances. Then, focusing on the design problem of the observer, the nonlinear extended state observer is designed to enhance the adaptability for random uncertainty and to improve the robust performance and the stabilization accuracy of the controller. Finally, the stability and convergence of the control system are proven by the homogeneous theory. The simulation results demonstrate that the proposed method can eliminate the input chattering of the sliding mode control efficiently and the high precision inertial stabilization of the floated inertial platform is realized with the accuracy higher than [Formula: see text].

Application of the spherical harmonic gravity model in high precision inertial navigation systems

The spherical harmonic gravity model (SHM) may, in general, be considered as a suitable alternative to the normal gravity model (NGM), because it represents the Earth’s gravitational field more accurately. However, the high-resolution SHM has never been used in current inertial navigation systems (INSs) due to its extremely complex expression. In this paper, the feasibility and accuracy of a truncated SHM are discussed for application in a real-time free-INS with a precision demand better than 0.8 nm h−1. In particular, the time and space complexity are analyzed mathematically to verify the feasibility of the SHM. Also, a test on a typical navigation computer shows a storable range of cut-off degrees. To further evaluate the appropriate degree and accuracy of the truncated SHM, analyses of covariance and truncation error are proposed. Finally, a SHM of degree 12 is demonstrated to be the appropriate model for routine INSs in the precision range of 0.4–0.75 nm h−1. Flight simulations and road tests show its outstanding performance over the traditional NGM.

Evaluation of errors in parameters determination for the Earth highly anomalous gravity field

Subject of Research. The paper presents research results and the simulation of errors caused by determining the Earth gravity field parameters for regions with high segmentation of gravity field. The Kalman filtering estimation of determining errors is shown. Method. Simulation model for the realization of inertial geodetic method for determining the Earth gravity field parameters is proposed. The model is based on high-precision inertial navigation system (INS) at the free gyro and highaccuracy satellite system. The possibility of finding the conformity between the determined and stochastic approaches in gravity potential modeling is shown with the example of a point-mass model. Main Results. Computer simulation shows that for determining the Earth gravity field parameters gyro error model can be reduced to two significant indexes, one for each gyro. It is also shown that for regions with high segmentation of gravity field point-mass model can be used. This model is a superposition of attractive and repulsive masses the so-called gravitational dipole. Practical Relevance. The reduction of gyro error model can reduce the dimension of the Kalman filter used in the integrated system, which decreases the computation time and increases the visibility of the state vector. Finding the conformity between the determined and stochastic approaches allows the application of determined and statistical terminology. Also it helps to create a simulation model for regions with high segmentation of gravity field.

Вопросы реализации на целочисленной ЦВС (типа «Малахит-3») алгоритма тарировки датчиков БИНС в полете по информации от высокоточной ИНС

The paper is devoted to the formulation of the problem for vector matching for strapdown inertial navigation system (SINS), allows to gauge gyro and accelerometer sensors of SINS, and to the problems of realization an vector matching algorithm on digital computing system (DCS), which operates with a fixed point number, an example of which is the DCS “Malachite-3”. The results of mathematical modeling for gauging 4 gyro sensors of SINS, based on a fiber optic gyroscope, via vector matching with the high-precision inertial navigation system, based on the gyroscopestabilized platform, are presented. The results of algorithm realization for vector matching on DCS “Malachite-3” with 32-bit arithmetic are presented. Also presented the estimated time required for computation of the algorithm.

Three axis electronic flight motion simulator real time control system design and implementation.

A three axis electronic flight motion simulator is reported in this paper including the modelling, the controller design as well as the hardware implementation. This flight motion simulator could be used for inertial navigation test and high precision inertial navigation system with good dynamic and static performances. A real time control system is designed, several control system implementation problems were solved including time unification with parallel port interrupt, high speed finding-zero method of rotary inductosyn, zero-crossing management with continuous rotary, etc. Tests were carried out to show the effectiveness of the proposed real time control system.

An improved motion compensation method for high resolution UAV SAR imaging

The polynomial and sinusoidal motion errors always exist in the unmanned aero vehicle (UAV) SAR due to the small size and low velocity of the platform, causing serious spectrum compressing/stretching and significant spectral replicas of the azimuth signal. The motion errors induce serious blurring of the SAR image and “ghost targets”, and can hardly be precisely estimated by the conventional motion compensation (MOCO) method. In this paper, an improved MOCO method is proposed to estimate and eliminate the motion errors in the high resolution UAV SAR without high precision inertial navigation system (INS) data. The time domain range walk correction (RWC) operation in the coarse phase error estimation process of the proposed MOCO method is the key operation that ensures the estimation accuracy of the whole MOCO method. Finally, the validity of the improved MOCO method is verified by computer simulations and real UAV SAR data processing.

Self-calibration method based on navigation in high-precision inertial navigation system with fiber optic gyro

A rotary inertial navigation system requires higher calibration accuracy of some error parameters owing to rotation. Conventional multiposition and rotation calibration methods are limited, for they do not consider sensors’ actual operating condition. In order to achieve these parameters’ values as closely as possible to their true values in application, their influence on navigation is analyzed, and a relevant new calibration method based on a system’s velocity output during navigation is designed for the vital error parameters, including inertial sensors’ installation errors and the scale factor error of fiber optic gyro. Most importantly, this approach requires no additional devices compared to the conventional method and costs merely several minutes. Experimental results from a real dual-axis rotary fiber optic gyro inertial navigation system demonstrate the practicability and higher precision of the suggested approach.

Alignment Method for FOG Single-Axis Rotation-Modulation SINS

Aircrafts with common attitude maneuverability (e.g. helicopter) are in more and more urgent need of low cost and high precision inertial navigation system (INS). To meet this demand, a scheme of fiber-optic gyroscope (FOG) strapdown inertial navigation system (SINS) with single-axis to and fro rotation-modulation method is adopted. A short-time alignment method bases on open-loop mathematic platform misalignment model is studied. The test results from the actual system show that this method has characteristic of high accuracy and simple, reliable operation. The estimate accuracy of azimuth error and is less than 2’. And the estimate error of north drift achieves 0.001º/h. Simultaneously, the input-axis accelerometer bias and gyroscope drift are estimated exactly.