Inertial Navigation Research Articles

Calibration and Compensation of Gyro Drift Errors Based on External Rotational Angle Comparison in a Rotational Inertial Navigation System

The inertial navigation system (INS) is a robust and reliable navigation strategy to provide position, attitude and velocity information of a carrier with signal acquired from inertial sensors without external assistant. However, the lack of external correction information leads to the accumulation of navigation errors, thereby limiting the reliability and applicable range of INS. In a typical INS, the accuracy and robustness of INS are mainly hindered by sensor’s measuring accuracy, installation misalignments and navigation algorithm effectiveness. To address the limitations of navigation accuracy degradation caused by sensor measurement errors, a calibration and compensation method of the gyro bias was proposed to improve the navigation accuracy. Through analyzing the influence of individual navigation errors, we found that the bias noise of gyroscope is the dominant factor in degrading the navigation accuracy. Aiming to improve the performance of navigation, a rotational modulation method is employed to eliminate the influence of gyro bias drift. Specifically, the rotational modulation could average the gyro bias to zero through the periodic rotational mechanism. Furthermore, the rotational turntable output angle can be used to correct navigation-resolved attitude results, which has a highly precise angle and can be used to calibrate the gyro drift. By compensating for gyro bias in a navigation algorithm, the performance of the navigation results is improved by a matter of one order from 7 km to less than 1 km over a period of 6 h. Several individual navigation experiments were also conducted, and the results prove the effectiveness of our method. The theoretical and experimental results show that the proposed error analysis and the compensation method are feasible and can been applied to the practical navigation system.

A Method for Improving Calibration Accuracy of the Inertial Navigation System Based on Gravity Disturbance Compensation

Abstract Accurate calibration of the inertial navigation system (INS) is essential for enhancing its performance. However, gravity disturbance significantly impacts the calibration accuracy of the INS, directly reducing the navigation performance of the high-precision INS. This paper investigates a method for further improving the calibration accuracy of the INS through compensating gravity disturbance. A full-parameter error model incorporating gravity disturbance for INS is established, the impact of gravity disturbance on INS calibration accuracy is analyzed, and gravity disturbance compensation method is proposed. Finally, the 19-position calibration experiment, the static-based navigation experiment and vehicle experiment are carried out to validate the effectiveness of the proposed method. Experiment results indicate that a 20″ meridian vertical deviation introduces a calibration error of 0.001°/h in the X-axis and Y-axis gyro drift, a 10mGal gravity anomaly results in a 10ppm calibration error in the three-axis accelerometer scale factor, while the impact of the prime vertical deviation on the INS calibration accuracy can be ignored. After compensating gravity disturbance during the INS calibration process, the 60min static navigation accuracy improved from RMS (Root Mean Square) 332.81 m to 272.80 m and the 70min dynamic navigation accuracy improved from RMS 1371.8 m to 1067.2 m.

A Robust Navigation Algorithm without GNSS based on Deep Learning and Variational Bayesian Filter

Abstract Integrated navigation systems, combining Inertial Navigation System (INS) and Global Navigation Satellite System (GNSS), are extensively used in land vehicle navigation. However, they often exhibit poor performance during GNSS outages and lack robustness in challenging urban environments. In order to reduce reliance on GNSS and fully leverage the vehicle dynamics hidden in the data, this study proposes a novel robust navigation algorithm without GNSS, based on deep learning and variational Bayesian methods. Firstly, a cascaded Long Short-Term Memory (LSTM) model with an “attitude-velocity” two-step sequential structure is proposed. By incorporating quaternions, it overcomes the non-differentiable property of attitude caused by its bounded nature, resulting in more accurate attitude predictions. Subsequently, the attitude prediction results are utilized to enhance speed prediction, leading to a significant improvement in accuracy. Building upon the cascaded LSTM model, variational Bayesian filtering is employed to further address the complex time-varying error of its results. Through an adaptive data fusion of LSTM predictions and INS data, the data fluctuations are reduced, and the accuracy is significantly improved. The efficacy of the proposed robust navigation algorithm is validated through multiple vehicle experiments conducted on diverse paths. Experimental results demonstrate that even in scenarios where GNSS fails continuously for fifteen minutes, the proposed algorithm maintains of speed and horizontal attitude errors within 0.6m/s (RMSE) and 0.3° (RMSE) respectively. Consequently, the proposed algorithm has broad application prospects in GNSS-denied environments such as building occlusion, underground parking garages, and indoor positioning. In addition, we also provide attempts to improve the model for situations such as odometer assistance and different motion states.

An adaptive Kalman filter loosely coupled indoor fusion positioning system based on inertial navigation system and ultra-wide band

An adaptive Kalman filter loosely coupled indoor fusion positioning system based on inertial navigation system and ultra-wide band

Research on Transfer Alignment Algorithms Based on SE(3) in ECEF Frame

The initial attitude error is challenging to satisfy the requirements of the linear model due to the complex nature of the ocean environment. This presents a challenge in the transfer alignment of the ship. In order to enhance the precision and velocity of ship transfer alignment, as well as to streamline the alignment processes, this paper proposes a transfer alignment methodology based on the Earth-Centered Earth-Fixed (ECEF) frame special Euclidean group (SE(3)) matrix Lie group. After introducing the two navigation states, velocity and attitude, from the ECEF frame into SE(3), the nonlinear inertial navigation system error state model and its corresponding measurement equations are derived based on the mapping relationship between the Lie groups and Lie algebra. The method effectively solves the error problem due to linear approximation in the traditional transfer alignment method, and applies to misalignment angles of arbitrary scale. The simulation results verify the effectiveness and rapidity of the proposed alignment method in the case of arbitrary misalignment angles.

Monolithic, fully-differential triaxial accelerometer with low nonlinearity and cross-axis sensitivity

Abstract This paper presents a triaxial capacitive accelerometer with low nonlinearity and cross-axis sensitivity, fabricated using SOG processing. Three single-axis sensor devices are orthogonally integrated on a single die. The signal detection and feedback mechanisms for the lateral (x/y-axis) and vertical (z-axis) accelerometers are implemented in a fully differential configuration, significantly reducing device nonlinearity and external environmental interference. The dynamic characteristics of the mechanical structure of the triaxial accelerometer are derived from a combination of theoretical analysis, numerical simulation, and experimental testing. The signal control circuit utilizes a fourth-order electromechanical sigma-delta modulation (EM-ΣΔM) circuit to validate the sensing characteristics of the triaxial accelerometer. The results indicate that the sensitivities (nonlinearities) of the x-, y-, and z-axes are 590 mV/g (0.66%), 600 mV/g (0.71%), and 58 mV/g (1.19%), respectively, and the corresponding bias instabilities were measured at 0.33 mg, 0.32 mg, and 1.07 mg, respectively. The cross-axis sensitivity ranged from 0.64% to 2.3%, while the low-frequency noise floor varied between 0.30 mg/√Hz and 0.67 mg/√Hz. In light of these performance characteristics, we hope that this work will find extensive applications in the field of inertial navigation measurements.

IC-GLI: a real-time, INS-centric GNSS-LiDAR-IMU localization system for intelligent vehicles

Abstract The integration of multiple sensors plays a vital role in achieving accurate vehicle positioning. However, light detection and ranging (LIDAR) and global navigation satellite system (GNSS) are susceptible to environmental effects, unlike inertial navigation system (INS), which remains unaffected by external factors. To enhance the precise positioning of intelligent vehicles in diverse environments and maximize the use of inertial measurement unit (IMU) data, this study presents a LIDAR, IMU, and GNSS-based positioning method centered around INS. The proposed method employs an IMU pre-integration model that includes the Earth’s rotation and utilizes a factor graph optimization framework to fuse the measurement data from LIDAR, IMU, and GNSS. By assigning appropriate weights to the residuals and dynamically adjusting the contributions of each sensor based on the prevailing environmental conditions, the optimal localization results are obtained through the solution of the maximum a posteriori estimate and the update of the INS state. Finally, the proposed system’s localization performance is validated using intelligent vehicles in the Robot Operating System framework. The results demonstrate that the system achieves high accuracy and robustness across various environments.

An Improved Unscented Kalman Filter Applied to Positioning and Navigation of Autonomous Underwater Vehicles.

To enhance the positioning accuracy of autonomous underwater vehicles (AUVs), a new adaptive filtering algorithm (RHAUKF) is proposed. The most widely used filtering algorithm is the traditional Unscented Kalman Filter or the Adaptive Robust UKF (ARUKF). Excessive noise interference may cause a decrease in filtering accuracy and is highly likely to result in divergence by means of the traditional Unscented Kalman Filter, resulting in an increase in uncertainty factors during submersible mission execution. An estimation model for system noise, the adaptive Unscented Kalman Filter (UKF) algorithm was derived in light of the maximum likelihood criterion and optimized by applying the rolling-horizon estimation method, using the Newton-Raphson algorithm for the maximum likelihood estimation of noise statistics, and it was verified by simulation experiments using the Lie group inertial navigation error model. The results indicate that, compared with the UKF algorithm and the ARUKF, the improved algorithm reduces attitude angle errors by 45%, speed errors by 44%, and three-dimensional position errors by 47%. It can better cope with complex underwater environments, effectively address the problems of low filtering accuracy and even divergence, and improve the stability of submersibles.

Chip-scale integrated optical gyroscope based on a multi-mode co-detection technique

Gyroscopes are crucial components of inertial navigation systems, with ongoing development emphasizing miniaturization and enhanced accuracy. The recent advances in chip-scale optical gyroscopes utilizing integrated optics have attracted considerable attention, demonstrating significant advantages in achieving tactical-grade accuracy. In this paper, a new, to our knowledge, integrated optical gyroscope scheme based on the multi-mode co-detection technology is proposed, which takes the high-Q microcavity as its core sensitive element and uses the multi-mode characteristics of the microcavity to achieve the measurement of rotational angular velocity. This detection scheme breaks the tradition of optical gyroscopes based on a single mode within the sensitive ring to detect the angular rotation rate, which not only greatly simplifies the optical and electrical system of the optical gyroscope, but also has a higher detection accuracy. The gyroscope based on this detection scheme has successfully detected the Earth’s rotation on a 9.2 mm diameter microcavity with a bias instability as low as 1 deg/h, which is the best performance among the chip-scale integrated optical gyroscopes known to us. Moreover, its high dynamic range and highly simplified and reciprocal system architecture greatly enhance the feasibility of practical applications. It is anticipated that these developments will have a profound impact on the field of inertial navigation.

Underwater DVL Optimization Network (UDON): A Learning-Based DVL Velocity Optimizing Method for Underwater Navigation

As the exploration of marine resources continues to deepen, the utilization of Autonomous Underwater Vehicles (AUVs) for conducting marine resource surveys and underwater environmental mapping has become a common practice. In order to successfully accomplish exploration missions, AUVs require high-precision underwater navigation information as support. A Strapdown Inertial Navigation System (SINS) can provide AUVs with accurate attitude and heading information, while a Doppler Velocity Log (DVL) is capable of measuring the velocity vector of the AUVs. Therefore, the integrated SINS/DVL navigation system can furnish the necessary navigational information required by an AUV. In response to the issue of DVL being susceptible to external environmental interference, leading to reduced measurement accuracy, this paper proposes an end-to-end deep-learning approach to enhance the accuracy of DVL velocity vector measurements. The utilization of the raw measurement data from an Inertial Measurement Unit (IMU), which includes gyroscopes and accelerometers, to assist the DVL in velocity vector estimation and to refine it towards the Global Positioning System (GPS) velocity vector, compensates for the external environmental interference affecting the DVL, therefore enhancing the navigation accuracy. To evaluate the proposed method, we conducted lake experiments using SINS and DVL equipment, from which the collected data were organized into a dataset for training and assessing the model. The research results show that the DVL vector predicted by our model can achieve a maximum improvement of 69.26% in terms of root mean square error and a maximum improvement of 78.62% in terms of relative trajectory error.

Gravity-aided navigation using Viterbi map matching algorithm

Abstract In Global Navigation Satellite Systems (GNSS)-denied environments, aiding a vehicle's inertial navigation system (INS) is crucial to reducing the accumulated navigation drift caused by sensor errors (e.g. bias and noise). One potential solution is to use measurements of gravity as an aiding source. The measurements are matched to a geo-referenced map of Earth's gravity to estimate the vehicle's position. In this paper, we propose a novel formulation of the map matching problem using a hidden Markov model (HMM). Specifically, we treat the spatial cells of the map as the hidden states of the HMM and present a Viterbi style algorithm to estimate the most likely sequence of states, i.e. most likely sequence of vehicle positions, that results in the sequence of observed gravity measurements. Using a realistic gravity map, we demonstrate the accuracy of our Viterbi map matching algorithm in a navigation scenario and illustrate its robustness compared with existing methods.

Research on Inertial Isolation Rotation Modulation of Dual-Axis Inertial Navigation Based on Multi-Error Coupling Characteristics

Currently, research on the rotational modulation of dual-axis inertial navigation for isolated carrier motion does not provide sufficient solutions for the compensation of the gyroscope scale factor error caused by the Earth’s rotation. Moreover, it is primarily applied to ships with low maneuverability and has not yet been implemented in the field of pure inertial guidance weapons. A dual-axis inertial isolation rotation modulation method is proposed to address this issue, taking into account the application characteristics of long-endurance guided weapons. An analysis of the system error characteristics under the coupling of multiple error sources acting on IMU was conducted, and it was found that the angular velocity of the inertial isolation carrier can significantly reduce the output error of the IMU. A dual-axis inertial isolation shaft system installation error compensation algorithm was designed, and an improvement was made based on the traditional sixteen-sequence rotation scheme to compensate for the projection components of the Earth’s rotation and carrier motion on the inner and outer frame rotation axes, achieving the inertial isolation rotation modulation function of dual-axis inertial navigation. Based on the attitude changes in long-range guided weapons, Monte Carlo simulation verification was conducted, and the results showed that this scheme can improve inertial navigation accuracy by 10% to 20%.

A calibration method for accelerometer combination on centrifuge based on norm-observation method

Abstract To realise the overall calibration of the error model coefficients of accelerometers in an inertial combination and to improve the navigation accuracy of the inertial navigation system, a norm-observation method is applied to the calibration, especially for the quadratic coefficient of the accelerometer. The Taylor formula is used to expand the solution of the acceleration model, and the intermediate variables with error model coefficients are obtained using the least square method. The formulas for calculating the quadratic term coefficient, scale factor and bias of the accelerometer are given. A 20-position method is designed to calibrate the accelerometer combination, the effectiveness of the method is verified by simulation, and the effects of installation misalignment and rod-arm error on calibration accuracy are analysed. The results show that the installation misalignments and rod-arm errors have little influence on the coefficient calibration, less than 10−8, and can be neglected in a practical calibration process.

Research on a Hybrid Correction Method for SINS/DVL Kalman Filter Integrated Navigation Based on Convergence Factor Judgment

Abstract The strapdown inertial navigation system (SINS)/doppler velocity log (DVL) integrated navigation is one of the primary methods for underwater navigation, providing autonomous underwater vehicles with precise information on position, velocity, and attitude. The core idea of the SINS/DVL integrated navigation using the Kalman filter is to establish the state and observation equations to estimate the SINS navigation error using DVL velocity. The optimal state estimation and correction strategies are critical to the accuracy of integrated navigation. To address this, this paper proposes a hybrid correction method for SINS/DVL Kalman filter integrated navigation based on a convergence factor judgment (HCKF-CFJ). First, the convergence factor for the Kalman filter is constructed using the diagonal elements of the estimated error covariance matrix corresponding to the velocity error state. Then, the filter's stability is assessed based on this convergence factor. When stability is confirmed, direct feedback correction is applied to the SINS velocity, and indirect feedback correction is applied to the SINS position. SINS velocity and position undergo feedforward correction if the stability condition is not met. Finally, ship experiments validate the effectiveness of the proposed method.

Robust Onboard Orbit Determination Through Error Kalman Filtering

Accurate and robust on-board orbit determination is essential for enabling autonomous spacecraft operations, particularly in scenarios where ground control is limited or unavailable. This paper presents a novel method for achieving robust on-board orbit determination by integrating a loosely coupled GNSS/INS architecture with an on-board orbit propagator through error Kalman filtering. This method is designed to continuously estimate and propagate a spacecraft’s orbital state, leveraging real-time sensor measurements from a global navigation satellite system (GNSS) receiver and an inertial navigation system (INS). The key advantage of the proposed approach lies in its ability to maintain orbit determination integrity even during GNSS signal outages or sensor failures. During such events, the on-board orbit propagator seamlessly continues to predict the spacecraft’s trajectory using the last known state information and the error estimates from the Kalman filter, which were adapted here to handle synthetic propagated measurements. The effectiveness and robustness of the method are demonstrated through comprehensive simulation studies under various operational scenarios, including simulated GNSS signal interruptions and sensor anomalies.

A full-scale simulator for research of navigation and filtering algorithms of a strapdown inertial navigation system using the Matlab-Simulink environment

Due to the increasing complexity of aircraft navigation equipment and the growing demands placed on them, there is a need to study and improve existing navigation and filtering algorithms by solving problems of developing full-scale research simulators. The article presents the results of work in the field of creating a full-scale simulator for research of navigation and filtering algorithms for a strapdown inertial navigation system (SINS) comprising: primary navigation data sensors made using microelectromechanical system technology (MEMS), servos and a navigation platform with two-degrees-of-freedom in roll and pitch. The article presents the features of the design, hardware and algorithmic implementation of the test rig taking into account the prospects for its development in terms of using the number of degrees of freedom of the platform (pitch, roll and yaw channels). The implemented principle of integrating the Simulink model of the control object is described. The control object consists of a controller based on the Arduino platform, a GPS sensor, a GY-91 sensor with an inertial measurement unit consisting of three orthogonally located: angular velocity meter, accelerometer and the single-channel barometer based on the MP280 MEMS. An algorithm for positional (manual) control of the navigation platform by pitch and roll angles using two servos, through a control stick and a virtual COM port is implemented. A diagram illustrating the logic of interaction of the structural elements of the simulator, a part of the software implementation of the complementary filter used, as well as the function of its calculation and simulation links of the Simulink model are presented. The information exchange between the PC and the Arduino microcontroller is considered. A conclusion was made about the feasibility of creating and using the developed simulator to justify the use of a particular navigation and filtering algorithm for a specific type of aircraft.

NIGWO-iCaps NN: A Method for the Fault Diagnosis of Fiber Optic Gyroscopes Based on Capsule Neural Networks.

When using a fiber optic gyroscope as the core measurement element in an inertial navigation system, its work stability and reliability directly affect the accuracy of the navigation system. The modeling and fault diagnosis of the gyroscope is of great significance in ensuring the high accuracy and long endurance of the inertial system. Traditional diagnostic models often encounter challenges in terms of reliability and accuracy, for example, difficulties in feature extraction, high computational cost, and long training time. To address these challenges, this paper proposes a new fault diagnostic model that performs a fault diagnosis of gyroscopes using the enhanced capsule neural network (iCaps NN) optimized by the improved gray wolf algorithm (NIGWO). The wavelet packet transform (WPT) is used to construct a two-dimensional feature vector matrix, and the deep feature extraction module (DFE) is added to extract deep-level information to maximize the fault features. Then, an improved gray wolf algorithm combined with the adaptive algorithm (Adam) is proposed to determine the optimal values of the model parameters, which improves the optimization performance. The dynamic routing mechanism is utilized to greatly reduce the model training time. In this paper, effectiveness experiments were carried out on the simulation dataset and real dataset, respectively; the diagnostic accuracy of the fault diagnosis method in this paper reached 99.41% on the simulation dataset; the loss value in the real dataset converged to 0.005 with the increase in the number of iterations; and the average diagnostic accuracy converged to 95.42%. The results show that the diagnostic accuracy of the NIGWO-iCaps NN model proposed in this paper is improved by 13.51% compared with the traditional diagnostic methods. It effectively confirms that the method in this paper is capable of efficient and accurate fault diagnosis of FOG and has strong generalization ability.

A vision-inertial interaction-based autonomous UAV positioning algorithm

Abstract In wartime scenarios where global navigation satellite system (GNSS) may be compromised, the cumulative errors associated with inertial navigation systems (INSs) can lead to significant positional deviations during long-distance navigation of drones. To address this issue, this study proposes an innovative vision-inertial interactive autonomous positioning algorithm that integrates visual positioning with inertial measurement unit-based methods, aiming to achieve enhanced system robustness and optimal positioning accuracy. The algorithm first implements an adaptive tile map level selection mechanism based on prior positional information from INS and onboard barometric pressure data, thereby mitigating the impact of inconsistent image scales. Subsequently, the proposed feature point extraction algorithm (Super Point V) effectively filters out invalid and interfering feature points from aerial images and tile maps. Finally, a novel matching mechanism for map expansion based on direction weights is employed to facilitate image matching and positioning, ensuring real-time accuracy and precision. Experimental results across various terrain conditions demonstrate that this approach not only enables accurate real-time computation of latitude and longitude but also effectively corrects the accumulated positioning errors of INS, achieving an average positioning accuracy error of only 4.94 m, comparable to that of conventional civilian GNSS, while maintaining excellent robustness.

Maximum Mixture Correntropy Criterion-Based Variational Bayesian Adaptive Kalman Filter for INS/UWB/GNSS-RTK Integrated Positioning

The safe operation of unmanned ground vehicles (UGVs) demands fundamental and essential requirements for continuous and reliable positioning performance. Traditional coupled navigation systems, combining the global navigation satellite system (GNSS) with an inertial navigation system (INS), provide continuous, drift-free position estimation. However, challenges like GNSS signal interference and blockage in complex scenarios can significantly degrade system performance. Moreover, ultra-wideband (UWB) technology, known for its high precision, is increasingly used as a complementary system to the GNSS. To tackle these challenges, this paper proposes a novel tightly coupled INS/UWB/GNSS-RTK integrated positioning system framework, leveraging a variational Bayesian adaptive Kalman filter based on the maximum mixture correntropy criterion. This framework is introduced to provide a high-precision and robust navigation solution. By incorporating the maximum mixture correntropy criterion, the system effectively mitigates interference from anomalous measurements. Simultaneously, variational Bayesian estimation is employed to adaptively adjust noise statistical characteristics, thereby enhancing the robustness and accuracy of the integrated system’s state estimation. Furthermore, sensor measurements are tightly integrated with the inertial measurement unit (IMU), facilitating precise positioning even in the presence of interference from multiple signal sources. A series of real-world and simulation experiments were carried out on a UGV to assess the proposed approach’s performance. Experimental results demonstrate that the approach provides superior accuracy and stability in integrated system state estimation, significantly mitigating position drift error caused by uncertainty-induced disturbances. In the presence of non-Gaussian noise disturbances introduced by anomalous measurements, the proposed approach effectively implements error control, demonstrating substantial advantages in positioning accuracy and robustness.

Development Status and Future Prospects of Strapdown Inertial Navigation Technology

Background: Inertial navigation is a comprehensive technology involving precision machinery, computer technology, microelectronics, optics, automatic control, materials, and other disciplines and fields. Strapdown inertial navigation systems have gradually developed into the mainstream and direction of inertial navigation systems because of their small size, low cost, simple structure, and high reliability. The angular rate and acceleration information of the carrier relative to the inertial space are measured by the inertial measurement unit (IMU), and the instantaneous velocity and position information of the carrier are automatically calculated by Newton's law of motion. It has the characteristics of not relying on external information, not radiating energy to the outside world, not being disturbed, and good concealment. Therefore, it is widely used in aerospace, aviation, and navigation, especially in the military field. Objective: This paper describes the development history of the Strapdown Inertia Navigation System summarizes the research status of the Strapdown Inertia Navigation System, and looks forward to its future development direction. Method: The key technologies of strapdown inertial navigation systems are investigated, and the related research on strapdown inertial navigation technology is understood in detail. The hardware composition and related algorithms of the strapdown inertial navigation system are analyzed in detail. Results: Nowadays, strapdown inertial navigation technology is the mainstream of inertial navigation technology. Compared with the gimbaled inertial navigation system technology, the strapdown inertial navigation system has higher precision, smaller volume, and lower cost. At present, the initial alignment technology, error compensation technology, navigation algorithm technology, and inertial device technology of strapdown inertial navigation technology have made full development. Conclusion: With the development of initial alignment technology, error compensation technology, navigation algorithm technology, and inertial device technology, the accuracy, response speed and anti-interference ability of strapdown inertial navigation technology have been significantly improved. The development of strapdown inertial navigation is closely related to the gyroscope technology which belongs to inertial device technology. The strapdown inertial navigation system based on optical gyroscopes such as laser gyroscopes and fibre optic gyroscopes is mature, and the MEMS strapdown inertial navigation system has a wide application prospect compared with the optical gyroscope strapdown inertial navigation system.