Accuracy Of Inertial Navigation System Research Articles

An Automatic Vehicle Navigation System Based on Filters Integrating Inertial Navigation and Global Positioning Systems

The key technologies for advanced autonomous vehicles include those relating to perception, decision making, and execution. Path-tracking control in autonomous vehicles is heavily dependent on their positioning system. Therefore, the development of low-cost and reliable positioning systems is crucial to improving perception and decision-making technologies for autonomous vehicles. Although the accuracy of the global positioning system (GPS) is extremely high, it is vulnerable to interference. Further, despite the low positioning accuracy of inertial navigation systems (INSs), their robustness is notably high. Therefore, an integrated navigation information method based on the Adaptive Particle Filter and the Iterative Kalman Filter (APF-IKF) was developed in this study. Firstly, an integrated navigation system model was established. Then, the IKF was adopted to estimate the speed, latitude and longitude errors of the INS. Thirdly, the newest estimated error results were introduced into the APF to optimize the distribution function, and the particle quality was improved. In this process, the APF can filter non-Gaussian noise, preliminarily estimate the error, optimize the result with the IKF and correct the output information of the INS with the final estimated error. Finally, by using differential GPS positioning as the benchmark, we built a real-vehicle test platform with a low-cost and low-precision GPS and inertial units and carried out a series of real-vehicle tests. The experimental results show that compared with the traditional KF method, APF-IKF can significantly improve the positioning accuracy and robustness of the system.

A damping method of grid strapdown inertial navigation system for polar region

Abstract The conventional north-pointing inertial navigation system (INS) always points to the geographic north. However, when the system crosses the pole in the polar region, the geographic north quickly changes with 180 degrees, and the rate of change of the geographic north direction will be infinite. Secondly, when the latitude approaches to 90 degrees, which will lead to singularities in math for the angular velocity caused by vehicle motion. With its special definition and mechanization, the grid coordinate system can solve the above problems. Nevertheless, the error analysis of the grid strapdown INS shows that there are Schuler periodic and Foucault periodic oscillations, which badly degrade the accuracy of the strap-down INS. To address the problem, the external horizontal damping technology is adopted in this paper, wherein the external velocity is provided by the Doppler velocity log (DVL). Finally, the feasibility and the effectiveness of the external damping technology were verified by simulation.

Improving Target Geolocation Accuracy with Multi-View Aerial Images in Long-Range Oblique Photography

Target geolocation in long-range oblique photography (LOROP) is a challenging study due to the fact that measurement errors become more evident with increasing shooting distance, significantly affecting the calculation results. This paper introduces a novel high-accuracy target geolocation method based on multi-view observations. Unlike the usual target geolocation methods, which heavily depend on the accuracy of GNSS (Global Navigation Satellite System) and INS (Inertial Navigation System), the proposed method overcomes these limitations and demonstrates an enhanced effectiveness by utilizing multiple aerial images captured at different locations without any additional supplementary information. In order to achieve this goal, camera optimization is performed to minimize the errors measured by GNSS and INS sensors. We first use feature matching between the images to acquire the matched keypoints, which determines the pixel coordinates of the landmarks in different images. A map-building process is then performed to obtain the spatial positions of these landmarks. With the initial guesses of landmarks, bundle adjustment is used to optimize the camera parameters and the spatial positions of the landmarks. After the camera optimization, a geolocation method based on line-of-sight (LOS) is used to calculate the target geolocation based on the optimized camera parameters. The proposed method is validated through simulation and an experiment utilizing unmanned aerial vehicle (UAV) images, demonstrating its efficiency, robustness, and ability to achieve high-accuracy target geolocation.

Permutation fuzzy entropy based ICEEMDAN de-noising for inertial sensors

As one of the critical factors affecting the accuracy of inertial navigation system (INS) positioning, random noise will lead to the accumulation of INS positioning errors, even the failure of the system. Previous studies mainly focus on achieving noise reduction by adopting either the wavelet decomposition method or some relevant methods of the empirical mode decomposition (EMD). However, the former is limited by Heisenberg’s uncertainty principle when processing non-stationary signals, and the latter exhibits numerous mode-mixing phenomena during the decomposition process. In this paper, a permutation fuzzy entropy (PFE) based improved complete ensemble EMD with adaptive noise (ICEEMDAN) de-noising method is proposed to utilize the ICEEMDAN method for signal decomposition, and the PFE as an index to distinguish the effective intrinsic mode functions (IMFs) and the noisy IMFs during the decomposition process. In addition, simulated signals with different noise levels and field data with different durations are utilized to design a group of experiments to test the de-noising performance of the PFE-based ICEEMDAN de-noising method. The experimental results demonstrate that the advantages of our proposed method consists of three main parts: (1) The ICEEMDAN method more effectively alleviates the mode-mixing problem compared to the complete ensemble EMD with adaptive noise (CEEMDAN), thereby enhancing the accuracy of inertial measurement unit (IMU) signal reconstruction; (2) the PFE is more preferable than the permutation entropy for classify IMFs decomposed by the ICEEMDAN method; (3) our proposed method can effectively reduce IMU signal noise and improve the positioning accuracy of inertial sensor.

Strapdown Inertial Navigation System Accuracy Improvement Methods Based on Inertial Measuring Unit Rotation: Analytical Review

Strapdown Inertial Navigation System Accuracy Improvement Methods Based on Inertial Measuring Unit Rotation: Analytical Review

A land vehicle’s INS/GNSS integrated navigation system using left invariant extended kalman filter

Land vehicles need high-precision navigational systems in which multi-sensor integration may be provided. Moreover, land vehicles regularly use Global Navigation Satellite Systems (GNSS) to estimate their position. Unfortunately, several locations, such as tunnels and inside parking garages, where GNSS signals cannot be detected. Several types of research have been conducted to improve positioning information using multi-sensor integration. Then, the vehicle needs another system for finding its location in GNSS-denied conditions, such as Inertial Navigation System (INS). Despite the accuracy of INS in short-time period use, inertial navigation systems (INS) are liable to drifts of their positioning solution due to the inertial sensor errors that are inherent to them; therefore, this problem leads to errors accumulation over time then integration techniques are used to eliminate the resulting errors. Moreover, many filters are used in the process of integration, such as the Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), Particular Filter (PF) and Invariant Extended Kalman Filter (IEKF). Moreover, this work introduces the left-invariant extended Kalman filter (LIEKF) as a navigation filter for a loosely coupled integration to eliminate positioning errors. Furthermore, the LIEKF is based on the symmetry-preserving observer theory, which claims that the estimation error depends on the theory of a Lie group matrix, and the proposed system INS/GPS-based LIEKF converges to constant values, unlike the traditional INS/GPS. Moreover, the proposed system INS/GPS-based LIEKF depends on State-estimate-independent Jacobians, and the LIEKF is more efficient and has better performance due to results such as the 2D position RMS error due to the INS/GPS-based EKF is 19.43m. However, the 2D position RMS error due to the INS/GPS-based LIEKF is 3.32m with 83% improvement. Moreover, the 2D position errors were enhanced using the INS/GPS-based LIEKF system compared to the INS/GPS-based EKF system.

GNSS denied navigation system for the manoeuvring flying objects

PurposeBefore designing a navigation system, it is necessary to analyse possible approaches in terms of expected accuracy, existing limitations and economic justification to select the most advantageous solution. This paper aims to collect possible navigation methods that can provide correction for inertial navigation and to evaluate their suitability for use on a manoeuvring tactical missile.Design/methodology/approachThe review of existing munitions was based on data collected from the literature and online databases. The data collected included dimensions, performance, applied navigation and guidance methods and their achievable accuracy. The requirements and limitations identified were confronted with the range of sensor parameters available on the market. Based on recent literature, navigation methods were reviewed and evaluated for applicability to inertial navigation system (INS) correction in global navigation satellite system-denied space.FindingsThe performance analysis of existing munition shows that small and relatively inexpensive micro-electro-mechanical system-type inertial sensors are required. A review of the parameters of existing devices of this type has shown that they are subject to measurement errors that do not allow them to achieve the delivery accuracy expected of precision missiles. The most promising navigation correction methods for manoeuvring flying objects have been identified.Originality/valueThe information presented in this paper is the result of the first phase of a project and presents the results of the requirements selection, initial sizing and preliminary design of the navigation system. This paper combines a review of the current state of the art in missile systems and an analysis of INS accuracy including the selection of sensor parameters.

Rapid and Accurate INS Transfer Alignment for Air Launched Tactical Missile Using Kalman Filter

An Inertial Navigation System (INS) independently measures the Position, Velocity, and Attitude (PVA) of thevehicle to navigate it towards the target. Since INS is a dead-reckoning system, it requires accurate initialization toprovide the navigation (PVA) solution. In the case of an air-launched tactical missile, the aircraft navigation system(Master INS) information is used to initialize accurately the missile INS (Slave INS). Rapid transfer alignment isneeded in today’s combat operation to converge slave INS initialization in the shortest possible time using aircraftnavigation information. The transfer alignment consists of first initializing the missile INS and establishing anavigation solution (PVA) using the missile IMU rates and accelerations, then a Kalman filter is used to, estimatethe errors between the Slave INS and Master INS. The proposed method’s simulation results show that a tacticalmissile INS can be aligned to an acceptable accuracy in a very short time based on the aircraft’s attitude information and with natural maneuvers experienced during aircraft take-off.

A new method for accurate alignment and calibration of strapdown INS

A new method is proposed for the coarse and fine alignments of the strapdown inertial navigation system (INS) along with the estimation of the INS systematic errors. This is achieved by utilizing an accurate external positioning system such as the global positioning system (GPS) and external gravity disturbances obtained from the Earth gravity models (EGMs) during the INS initialization time. First, a new method for the transformation of the INS acceleration from the sensor frame to the inertial frame using gyro output data is disclosed. Then, using the new method of the transformation, new techniques are developed for the alignment and calibration of the INS using minimizing the variations of the residuals of the gravity disturbances during the back-and-forth rotational motions. The common and conventional initializations cannot be started from any initial orientation, and cannot yield the accurate and actual INS errors. In contrast, under the alignment condition, the accurate and actual estimation of all the INS systematic errors is possible using the developed fine alignment and calibration which can guarantee the accurate autonomous strapdown INS positioning for a long period of time even during high dynamic motions. This is while the estimated error values of the INS by the conventional Kalman filter is unrealistic. In the field of autonomous positioning, a horizontal position with an error less than 200 m and 500 m was achieved during low and high dynamic motions, respectively, after the fine alignment and calibration, for the two hours of the INS positioning for a flight distance about 880 km. The employed INS was a high-performance strapdown INS, the Honeywell LASEREF III.

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.

Algorithms for Complexing an Inertial Navigation System with Angular Acceleration Sensors

In this paper the problem of increasing the accuracy of inertial navigation system of an aircraft in the absence of high-precision additional information sensors, such as GPS, has been studied. It is proposed to install angular acceleration sensors on the gyrostabilized platform of the inertial navigation system. The use of signals from the angular acceleration sensors made it possible to generate correction signals for the inertial navigation system. Correction algorithms have been developed in the structure of the inertial navigation system and in its output signal. The effectiveness of the developed algorithms has been demonstrated using semi-natural simulation with the Ts060K inertial navigation system.

Performance Enhancement of INS and UWB Fusion Positioning Method Based on Two-Level Error Model

In GNSS-denied environments, especially when losing measurement sensor data, inertial navigation system (INS) accuracy is critical to the precise positioning of vehicles, and an accurate INS error compensation model is the most effective way to improve INS accuracy. To this end, a two-level error model is proposed, which comprehensively utilizes the mechanism error model and propagation error model. Based on this model, the INS and ultra-wideband (UWB) fusion positioning method is derived relying on the extended Kalman filter (EKF) method. To further improve accuracy, the data prefiltering algorithm of the wavelet shrinkage method based on Stein's unbiased risk estimate-Shrink (SURE-Shrink) threshold is summarized for raw inertial measurement unit (IMU) data. The experimental results show that by employing the SURE-Shrink wavelet denoising method, positioning accuracy is improved by 76.6%; by applying the two-level error model, the accuracy is further improved by 84.3%. More importantly, at the point when the vehicle motion state changes, adopting the two-level error model can provide higher computational stability and less fluctuation in trajectory curves.

Cold atom inertial sensors for navigation applications

Quantum sensors based on atom interferometers can provide measurements of inertial quantities with unprecedented accuracy and precision. It has been suggested that this sea change in sensing could provide an inertial navigation capability that is comparable with current satellite based navigation systems. However, the accuracy of sensor measurements is not the only factor that limits the accuracy of inertial navigation systems. In this paper, we explore the fundamental limits to inertial navigation, and explain how quantum inertial sensors could be used to alleviate some of the problems encountered in current classical inertial navigation systems, but not to solve the fundamental instability inherent in inertial navigation methods.

Modelling and dynamic analysis of slippage level for large-scale skid-steered unmanned ground vehicle.

To analyze the turning characteristics of a large-scale skid-steered unmanned ground vehicle (UGV), a mathematical model based on geometric characteristics and kinematics was developed in this work. The turning characteristics, as well as some important geometric and moving features, were seriously considered in the model. A self-designed UGV was employed to conduct targeted experiments. Initial experiment showed that the width of UGV was much larger than that of actual value, because slippage phenomenon made the errors of actual velocity and trajectory length between two sides of the UGV were lower than those obtained from direct wheel velocities measurements and calculations. Further experiments which obtained moving velocity of the UAV by means of a highly accurate Inertial Navigation System (INS) were conducted. Combining this velocity, the slippage levels of the four wheels can be quantitatively measured. In addition, using standard velocities derived from the accurate moving velocity, a true turning radius can be accurately calculated in real time when the slippage characteristics were seriously considered, hence, the mathematical model can be sufficiently validated. The work can realize modelling and dynamic analysis and estimation of the slippage characteristics of this type of UGV.

Temperature compensation for quartz flexible accelerometer based on nonlinear auto-regressive improved model

Temperature variation is an important factor affecting the performance of Quartz flexible accelerometer (QFA). Performance deterioration of QFA degrades the navigation accuracy of inertial navigation system (INS). Normally dramatic change in temperature causes both thermal effect and severe creep effect on the performance of QFA. Previous papers have proved that part of errors caused by thermal effect can be restrained through simple temperature compensation. However, error caused by severe creep effect is seldom considered. In this paper, creep effect and thermal effect in QFA are detailed analyzed, respectively. Furthermore, based on the analysis of thermal effect and creep effect, the novel temperature model based on nonlinear auto-regressive with external input (NARX) improved by wavelet transform (WT) is proposed to address the retardation problem caused by thermal effect. Creep error causing the ruleless deformation of QFA’s structure is separated from overall errors, and only the thermal error whose effect has strong relationship with temperature is compensated by proposed model. Moreover, a 4-point dumpling experiment in temperature control oven is conducted to train and verify the proposed temperature model. The result of the comparative experiments shows that the performance of proposed method is the best among the comparative models. The compensation result based on proposed method improves stability of 1 g output from 776 to 14.6 µg. The proposed temperature compensation method improves the performance of QFA effectively and feasibly, which could be promoted to other applications of INS in temperature changing environment.

An Optimal Indirect In-Motion Coarse Alignment Method for GNSS-Aided SINS

Aiming at the problems of low precision and poor adaptability of traditional in-motion coarse alignment methods for vehicle strapdown inertial navigation system (SINS), an optimal indirect in-motion coarse alignment method aided by global navigation satellite system (GNSS) is proposed. The attitude matrix problem is transformed into Wahba problem to make full use of the observation vectors information. In the process of observation vectors construction, the integral interval of the observation vectors is shortened by the sliding interval method to weaken the accumulation of constant error of inertial devices. The Wahba problem is solved by singular value decomposition (SVD) algorithm. Combined with the output information of GNSS and SINS, the equivalent rotation vector and constant bias of gyroscope are used as state variables to construct the process model and measurement model. The type-2 fuzzy adaptive Kalman filter algorithm is proposed to solve the problem of inaccurate measurement noise in the process of state variables estimation, and the transform matrix of carrier frame is continuously modified to obtain a more accurate attitude conversion matrix. Digital simulation and vehicle experiments show that the proposed algorithm can significantly improve the alignment accuracy of inertial navigation system on moving base.

Study on free oscillations of a micromechanical gyroscope taking into account the nonorthogonality of the torsion axes

Introduction. The paper is devoted to the study on free oscillations of the sensing element of a micromechanical R-Rtype gyroscope of frame construction developed by the Kuznetsov Research Institute of Applied Mechanics, taking into account the nonorthogonality of the torsion axes. The influence of the instrumental manufacturing error on the accuracy of a gyroscope on a movable base in the case of free oscillations is studied. The work objective was to improve the device accuracy through developing a mathematical model of an R-R type micromechanical gyroscope, taking into account the nonorthogonality of the torsion axes, and to study the influence of this error on the device accuracy. The urgency of the problem of increasing the accuracy of micromechanical gyroscopes is associated with improving the accuracy of inertial navigation systems based on micromechanical sensors.Materials and Methods. A new mathematical model that describes the gyroscope dynamics, taking into account the instrumental error of manufacturing the device, and a formula for estimating the error of a gyroscope, are proposed. The dependences of the state variables obtained from the results of modeling and on the basis of the experiment are presented. Methods of theoretical mechanics and asymptotic methods, including the Lagrange formalism and the Krylov-Bogolyubov averaging method, were used in the research.Results. A new mathematical model of the gyroscope dynamics, taking into account the nonorthogonality of the torsion axes, is developed. The solution to the equations of small oscillations of the gyroscope sensing element and the estimate of the precession angle for the case of a movable base are obtained. A comparative analysis of the developed model and the experimental data obtained in the case of free oscillations of the gyroscope sensing element with a fixed base is carried out. The analysis has confirmed the adequacy of the constructed mathematical model. Analytical expressions are formed. They demonstrate the fact that the nonorthogonality of the torsion axes causes a cross-influence of the amplitudes of the primary vibrations on the amplitudes of the secondary vibrations of the sensing element, and the appearance of an additional error in the angular velocity readings when the gyroscope is operating in free mode.Discussion and Conclusions. The results obtained can be used to improve the device accuracy using the algorithm for analytical compensation of the gyroscope error and the method for identifying the mathematical model parameters.

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 Low-Cost MEMS Missile-Borne Compound Rotation Modulation Scheme.

Rotation modulation (RM) has been widely used in navigation systems to significantly improve the navigation accuracy of inertial navigation systems (INSs). However, the traditional single-axis rotation modulation cannot achieve the modulation of all the constant errors in the three directions; thus, it is not suitable for application in highly dynamic environments due to requirements for high precision in missiles. Aiming at the problems of error accumulation and divergence in the direction of rotation axis existing in the traditional single-axis rotation modulation, a novel rotation scheme is proposed. Firstly, the error propagation principle of the new rotation modulation scheme is analyzed. Secondly, the condition of realizing the error modulation with constant error is discussed. Finally, the original rotation modulation navigation algorithm is optimized for the new rotation modulation scheme. The experiment and simulation results show that the new rotation scheme can effectively modulate the error divergence of roll angle and improve the accuracy of roll angle by two orders of magnitude.

Hybrid Deep Recurrent Neural Networks for Noise Reduction of MEMS-IMU with Static and Dynamic Conditions.

Micro-electro-mechanical system inertial measurement unit (MEMS-IMU), a core component in many navigation systems, directly determines the accuracy of inertial navigation system; however, MEMS-IMU system is often affected by various factors such as environmental noise, electronic noise, mechanical noise and manufacturing error. These can seriously affect the application of MEMS-IMU used in different fields. Focus has been on MEMS gyro since it is an essential and, yet, complex sensor in MEMS-IMU which is very sensitive to noises and errors from the random sources. In this study, recurrent neural networks are hybridized in four different ways for noise reduction and accuracy improvement in MEMS gyro. These are two-layer homogenous recurrent networks built on long short term memory (LSTM-LSTM) and gated recurrent unit (GRU-GRU), respectively; and another two-layer but heterogeneous deep networks built on long short term memory-gated recurrent unit (LSTM-GRU) and a gated recurrent unit-long short term memory (GRU-LSTM). Practical implementation with static and dynamic experiments was carried out for a custom MEMS-IMU to validate the proposed networks, and the results show that GRU-LSTM seems to be overfitting large amount data testing for three-dimensional axis gyro in the static test. However, for X-axis and Y-axis gyro, LSTM-GRU had the best noise reduction effect with over 90% improvement in the three axes. For Z-axis gyroscope, LSTM-GRU performed better than LSTM-LSTM and GRU-GRU in quantization noise and angular random walk, while LSTM-LSTM shows better improvement than both GRU-GRU and LSTM-GRU networks in terms of zero bias stability. In the dynamic experiments, the Hilbert spectrum carried out revealed that time-frequency energy of the LSTM-LSTM, GRU-GRU, and GRU-LSTM denoising are higher compared to LSTM-GRU in terms of the whole frequency domain. Similarly, Allan variance analysis also shows that LSTM-GRU has a better denoising effect than the other networks in the dynamic experiments. Overall, the experimental results demonstrate the effectiveness of deep learning algorithms in MEMS gyro noise reduction, among which LSTM-GRU network shows the best noise reduction effect and great potential for application in the MEMS gyroscope area.