Strapdown Inertial Navigation System Research Articles

Application and Prospect of Strapdown Inertial Navigation System in Coal Mining Equipment.

In recent years, with the rapid construction of a safe, clean, efficient and sustainable modern energy system, the intelligence of coal mining has become the inevitable direction of the development of the coal mining industry. The intelligence of coal mining system and equipment is the core of intelligent mining, and the positioning technology of mining equipment is the key to underground intelligent mining. The strapdown inertial navigation system can make up for the shortcomings of traditional GPS positioning systems and laser positioning because of its strong anti-interference, high precision and real-time monitoring, and ability to carry out real-time dynamic positioning of mining equipment in underground coal mines. This paper briefly introduces the basic principle of the strapdown inertial navigation system, analyzes the application of the existing strapdown inertial navigation system in mining equipment, and lists and analyzes the research status of the improvement strategy of the inertial navigation system, such as zero speed correction and integrated navigation technology. Finally, by analyzing the application and future development trend of inertial navigation systems in mining equipment, this paper provides more data and method support for the positioning of mining equipment in the future.

GNSS-assisted optimal alignment method for low-cost SINS motion of vehicle

Abstract To improve the alignment accuracy and environmental applicability of the micro-electromechanical system (MEMS)-based strapdown inertial navigation system (SINS), this study proposes a global navigation satellite system (GNSS)-assisted multi-vector determination of the attitude optimal indirect coarse alignment. Using the inertial information output from the inertial measurement unit and the velocity information from the GNSS, a simplified velocity observation vector is constructed and the velocity lever arm stemming from the mounting position inconsistencies of the GNSS and SINS is fed back into the velocity of the carrier system. When constructing the observation vectors, the integration interval is shortened by reconstructing the two-vector integration formula for reducing the cumulative error of the inertial device. The attitude matrix problem is defined as the Wahba problem, which is solved using the singular value decomposition method. Based on the relationship between gyro zero bias and misalignment angle, the corresponding state and measurement equations are designed. Furthermore, owing to the measurement noise uncertainty, the adaptive traceless Kalman filtering algorithm is introduced to realize the effective adaptation processing of the measurement noise. More accurate attitude matrix estimates are obtained by continuously correcting the carrier system transformation matrix. The running car experiment results show that the proposed method exhibits higher alignment accuracy and environmental applicability than the current MEMS strapdown inertial navigation coarse alignment method and the traditional optimization-based alignment method.

Study on the Robust Filter Method of SINS/DVL Integrated Navigation Systems in a Complex Underwater Environment

This paper proposes an improved adaptive filtering algorithm based on the Sage–Husa adaptive Kalman filtering algorithm to address the issue of measurement noise characteristics impacting the navigation accuracy in strapdown inertial navigation system (SINS)/Doppler Velocity Log (DVL) integrated navigation systems. Addressing the non-positive definite matrix problem prevalent in traditional adaptive filtering algorithms and aiming to enhance measurement noise estimation accuracy, this method incorporates upper and lower thresholds determined by a discrimination factor. In the presence of abnormal measurement data, these thresholds are utilized to adjust the covariance of the innovation, subsequently re-estimating the system’s measurement noise through a decision factor based on the innovation. Simulation and experiment results demonstrate that the proposed improved adaptive filtering algorithm outperforms the classical Kalman filter (KF) in terms of navigation accuracy and stability. Furthermore, the filtering performance surpasses that of the Sage–Husa algorithm. The simulation results in this paper show that the relative position positioning error of the improved method is reduced by 49.44% compared with the Sage–Husa filtering method.

Autonomous Underwater Vehicle Navigation Enhancement by Optimized Side-Scan Sonar Registration and Improved Post-Processing Model Based on Factor Graph Optimization

Autonomous Underwater Vehicles (AUVs) equipped with Side-Scan Sonar (SSS) play a critical role in seabed mapping, where precise navigation data are essential for mosaicking sonar images to delineate the seafloor’s topography and feature locations. However, the accuracy of AUV navigation, based on Strapdown Inertial Navigation System (SINS)/Doppler Velocity Log (DVL) systems, tends to degrade over long-term mapping, which compromises the quality of sonar image mosaics. This study addresses the challenge by introducing a post-processing navigation method for AUV SSS surveys, utilizing Factor Graph Optimization (FGO). Specifically, the method utilizes an improved Fourier-based image registration algorithm to generate more robust relative position measurements. Then, through the integration of these measurements with data from SINS, DVL, and surface Global Navigation Satellite System (GNSS) within the FGO framework, the approach notably enhances the accuracy of the complete trajectory for AUV missions. Finally, the proposed method has been validated through both the simulation and AUV marine experiments.

Global integrated navigation position correction algorithm and virtual polar region technology based on normal vector

To achieve the inherent uniformity of all-earth navigation for autonomous underwater vehicles (AUV), a global integrated navigation position correction algorithm based on the normal vector (n-vector) is proposed. First, a four-element vector comprising the non-singular n-vector and height represents the carrier’s position in the Earth-centered Earth-fixed (ECEF) frame. The integrated navigation systems are designed with the strapdown inertial navigation system (SINS), Doppler velocity log (DVL), and other equipment. Secondly, the reverse navigation algorithm in the ECEF mechanization is derived, and the results of forward and reverse navigation are fused to correct the AUV’s underwater position. Additionally, a virtual polar region technology based on the ECEF attitude, velocity, and height invariant method (E-AVHIM) is proposed to convert the actual test data obtained at low and middle latitudes into high latitudes for more convincing polar region algorithm verification. Simulations and lake trial demonstrated the excellence and efficiency of the proposed algorithm.

Unstructured environment navigation and trajectory calibration technology based on multi-data fusion

In order to effectively improve the accuracy and efficiency of unstructured environment navigation and trajectory calibration, a multi data fusion based unstructured environment navigation and trajectory calibration method was studied. Described the basic principles of the Strapdown Inertial Navigation System and Doppler Log. After introducing DVL velocity information and relative position information of underwater robots into SINS, the Kalman filter fusion algorithm was used to obtain the system's state equation and measurement equation. The navigation parameter error and device error parameters of the system were selected as the state variables. The difference between SINS output speed and DVL measurement speed, as well as the difference between SINS output position and relative position, are used as the speed and position measurements of the measurement system. Error estimation is obtained through indirect filtering, and the accuracy of navigation and positioning is improved through output correction. The experimental results show that the proposed method has a good calibration effect and can effectively improve the accuracy and efficiency of trajectory calibration in unstructured environments.

Maximum correntropy polynomial chaos Kalman filter for underwater navigation

This paper develops an underwater navigation solution that utilizes a strapdown inertial navigation system (SINS) and fuses a set of auxiliary sensors such as an acoustic positioning system, Doppler velocity log, depth meter, and magnetometer to accurately estimate an underwater vessel's position and orientation. The conventional integrated navigation system assumes Gaussian measurement noise, while in reality, the noises are non-Gaussian, particularly contaminated by heavy-tailed impulsive noises. To address this issue, and to fuse the system model with the acquired sensor measurements efficiently, we develop a square root polynomial chaos Kalman filter based on maximum correntropy criteria. The proposed method uses Hermite polynomial chaos expansion to tackle the nonlinearity, and it has the potential to estimate the states in a more accurate way in presence of a non-Gaussian measurement noise. The filter is initialized using acoustic beaconing to accurately locate the initial position of the vehicle. The computational complexity of the proposed filter is calculated in terms of flops count. The proposed method is compared with the existing maximum correntropy sigma point filters in terms of estimation accuracy and computational complexity. It is found from the simulation results that the proposed method is more accurate compared to the conventional deterministic sample point filters and Huber's M-estimator.

Indoor altitude estimation assisted by inertial compensation and online floor modeling

Abstract Indoor pedestrian altitude information plays a key role in such applications as emergency relief and military reconnaissance. However, height errors of inertial positioning grow without boundary because of the altitude channel divergence of the Strap-down Inertial Navigation System (SINS). This article proposes a new vertical location method based on the foot-mounted Inertial Measurement Unit (IMU) and online floor modeling. First, the number of stairs at each step is calculated after the height of each step is corrected by the error compensation model. Second, the prior height is estimated by utilizing the number of stairs and the stair height. Then, the key point library related to the floor is built online. Finally, the error correction of the vertical displacement is carried out by matching the prior height with the key point library. The gait classification shows that the accuracy based on the error compensation model can reach up to 99%. Moreover, the maximum attitude error is less than 1 m and the accumulated vertical positioning errors are eliminated completely when a pedestrian walks up and down inside a multi-story building, and all these have verified accuracy and robustness of vertical indoor positioning.

A Novel Method for Damping State Switching Based on Machine Learning of a Strapdown Inertial Navigation System

A Novel Method for Damping State Switching Based on Machine Learning of a Strapdown Inertial Navigation System

An Experimental Study of Odometer as a Navigation aid for Land Vehicle Application

Strap-down inertial navigation system (SINS) shall provide position, velocity, and orientation information with reference to a pre-defined reference frame. The SINS shall have excellent accuracy over a short duration and is highly self-contained. However, the errors in navigation solutions build up exponentially with time and make the system output very unstable. In order to mitigate these errors, there is a need for a damping mechanism through external aiding sensors. In this article, one such approach is proposed to improve navigation accuracy for land vehicles in the GNSS (Global Navigation Satellite Systems) denied environment. The design and implementation of an odometer are carried out with the use of inductive proximity sensors and a mounting assembly to attach the odometer to one of the non-steering wheels of a vehicle. The odometer gives the pulse-high and pulse-low output with reference to the rotation of the wheel to which it is attached. Vehicle ground velocity is derived through sensed output pulses processed through quadrature decoder circuitry. Odometer measurements along with non-holonomic constraints (NHC) are used for minimizing velocity and position errors in SINS using an extended Kalman Filter (EKF) technique. Field trials are carried out to validate the proposed scheme of hybrid navigation with odometer design and experimental results are presented with a positioning accuracy of 0.05 % of distance travelled (DT).

Autonomous ground vehicle gravity anomaly measurement and dynamic error compensation

Abstract To address the issue that dynamic gravity anomaly measurement is overly dependent on GNSS and can’t be measured autonomously at this stage, this paper proposes an autonomous ground vehicle dynamic gravity anomaly measurement method based on a strapdown inertial navigation system (SINS), odometer (OD), barometer and platform gravimeter. The SINS/OD /barometer integrated navigation solution delivers high-precision navigation parameters, completes the calculation of correction terms, and performs the autonomous dynamic gravity anomaly measurement combined with the primary measurement results of the platform gravimeter. Numerical calculations provide the requirements for the application of the proposed method, and the cut-off frequency for extracting gravity anomalies is 0.02 Hz, as determined by power spectral density analysis. In order to further improve the measurement accuracy and account for dynamic errors caused by vehicle maneuvering, a long-short-term memory (LSTM) model of recurrent neural network (RNN) is introduced. A series of experiments under multiple circumstances with repeated lines were conducted in Tianjin, China, and the static measurements along the line were taken using CG-5 to provide true values of gravity anomalies. The results demonstrate that the autonomous measurement scheme can achieve accuracy comparable to GNSS-assisted, and that dynamic error compensation algorithm based on LSTM improves the dynamic gravity measurements accuracy significantly without sacrificing the spatial resolution of gravity anomalies.

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.

A Low-Cost Redundant Attitude System for Small Satellites, Based on Strap-Down Inertial Techniques and Gyro Sensors Linear Clustering

The significant technological changes related to the manufacturing of the miniaturized sensors produced a higher impact at the level of the detection units equipping the strap-down inertial navigation systems (INSs). Together with miniaturization, many more advantages are brought by these technologies, related to low costs, low necessary energy, high robustness and high potential for adapting the design solutions. However, reducing the dimensions and weight of the sensors is reflected by a decrease in their performance in terms of sensitivity, noise and the possibility of controlling sensitive elements. On the other hand, there is a permanent increase in the need to have in-space applications of miniaturized systems with a high degree of redundancy and to equip miniaturized satellites, miniaturized space robots or space rovers. The paper proposes a new methodology to increase the quality of the signals received from the miniaturized inertial measurement units (IMUs), but also to increase the degree of redundancy, by using low-cost sensors arranged in redundant linear configurations. The presentation is focused on the development of an attitude system based on strap-down inertial techniques which uses a redundant IMU equipped with three linear clusters of miniaturized gyros. For each of the three clusters, a data fusion mechanism based on the maximal ratio combining method is applied. This fusion mechanism reduces the noise power and bias of the signal delivered to the navigation processor. Shown are the theory, software modeling and experimentation results for the attitude algorithm, for the data fusion method, and for the integrated system.

Enhanced Strapdown Inertial Navigation System (SINS)/LiDAR Tightly Integrated Simultaneous Localization and Mapping (SLAM) for Urban Structural Feature Weaken Occasions in Vehicular Platform

LiDAR-based simultaneous localization and mapping (SLAM) offer robustness against illumination changes, but the inherent sparsity of LiDAR point clouds poses challenges for continuous tracking and navigation, especially in feature-deprived scenarios. This paper proposes a novel LiDAR/SINS tightly integrated SLAM algorithm designed to address the localization challenges in urban environments characterized in sparse structural features. Firstly, the method extracts edge points from the LiDAR point cloud using a traditional segmentation method and clusters them to form distinctive edge lines. Then, a rotation-invariant feature—line distance—is calculated based on the edge line properties that were inspired by the traditional tightly integrated navigation system. This line distance is utilized as the observation in a Kalman filter that is integrated into a tightly coupled LiDAR/SINS system. This system tracks the same edge lines across multiple frames for filtering and correction instead of tracking points or LiDAR odometry results. Meanwhile, for loop closure, the method modifies the common SCANCONTEXT algorithm by designating all bins that do not reach the maximum height as special loop keys, which reduce false matches. Finally, the experimental validation conducted in urban environments with sparse structural features demonstrated a 17% improvement in positioning accuracy when compared to the conventional point-based methods.

Analytical quaternion-based bias estimation algorithm for fast and accurate stationary gyro-compassing

This work introduces a novel approach to Strapdown Inertial Navigation System (SINS) alignment, distinct from recursive methods like Kalman filtering. The proposed methodology expedites bias error calculations by utilizing quaternion-based analytical relationships, which bypasses the slow convergence behavior associated with recursive algorithms, particularly in azimuth angle error estimation. In addition, the proposed approach demonstrates comparable accuracy to traditional fine alignment methods. Simulations and experiments validate that in contrast to the 10-min time requirement of traditional fine alignment methods (for azimuth angle estimation in stationary conditions), the proposed approach achieves the same accuracy within 20 s. However, limitations exist as the algorithm is applicable only in stationary conditions, and necessitating a high-grade IMU capable of measuring the earth’s rotation rate.

The Kinematic Models of the SINS and Its Errors on the SE(3) Group in the Earth-Centered Inertial Coordinate System.

In this paper, the kinematic models of the Strapdown Inertial Navigation System (SINS) and its errors on the SE(3) group in the Earth-Centered Inertial frame (ECI) are established. On the one hand, with the ECI frame being regarded as the reference, based on the joint representation of attitude and velocity on the SE(3) group, the dynamic of the local geographic coordinate system (n-frame) and the body coordinate system (b-frame) evolve on the differentiable manifold, respectively, and the high-order expansion of the Baker-Campbell-Haussdorff equation compensates for the non-commutative motion errors stimulated by strong maneuverability. On the other hand, the kinematics of the left- and right-invariant errors of the n-frame and the b-frame on the SE(3) group are separately derived, where the errors of the b-frame completely depend on inertial sensor errors, while the errors of the n-frame rely on position errors and velocity errors. In this way, the errors brought by the inconsistency of the reference coordinate system are tackled, and a novel attitude error definition is introduced to separate and decouple the factors affecting the dynamic of the n-frame errors and the b-frame errors for better attitude estimation. Through a turntable experiment and a car-mounted field experiment, the effectiveness of the proposed kinematic models in estimating attitude has been verified, with a remarkable improvement in yaw angle accuracy in the case of large initial misalignment angles, and the models developed have better robustness compared to the traditional SE(3) group-based model.

Robust adaptive non‐linear alignment algorithm for SINS/DVL integrated navigation system based on variational Bayesian

AbstractThe problem of dynamic attitude alignment for strapdown inertial navigation system (SINS) and Doppler velocity log (DVL) integrated navigation has become a research hotspot. Underwater complex environment makes DVL output vulnerable to non‐Gaussian noise pollution, which makes it difficult to converge the SINS misalignment angle to within 1° based on analytical coarse alignment. This is to say, the performance of SINS fine alignment via Kalman filter will be degraded because the model of initial alignment exhibits non‐linearity. The inaccurate and/or unknown prior information of measurement noise statistical characteristics will also degrade the filtering performance. To ensure the SINS/DVL alignment accuracy under non‐linear, non‐Gaussian and uncertain conditions, this paper proposed a robust adaptive unscented Kalman filter (UKF) based on Variational Bayesian (VB) method (VBRAUKF). The proposed VBRAUKF improves the adaptability and robustness of UKF from the following two main aspects. Firstly, an adaptive estimation strategy for the measurement noise covariance is designed based on the VB algorithm, which can restrain the effect of inaccurate observation model and improve the adaptive ability of the filtering method. Secondly, an expansion factor is designed based on Mahalanobis distance algorithm, which can restrain the effect of non‐Gaussian noise and improve the robustness of the filtering method. The experimental results for the problem of the SINS/DVL dynamic alignment under mixed Gaussian noise and/or outlier conditions demonstrate the superiority of the proposed VBRAUKF over the traditional ones.

Stable solution to the problem of autonomous navigation of moving objects on analytical trajectory intervals based on the results of inertial measurements

Provision of solution of the problem of autonomous navigation on a long time interval is considered. The main problem when using inertial navigation systems is caused by the accumulation of positioning and angular orientation errors. It is shown that this problem can be solved by combining methods of nonlinear filtering in processing the results of inertial measurements of platform-free inertial navigation systems and methods of reducing the dimensionality of the vector of navigation parameters on trajectory sections described by analytical models. Orthodromic (shortest) and circular intervals, most typical for program trajectories of transport objects – highways, railroads, airlines, etc., are considered as such trajectory sections. For circular intervals, analytical dependencies of the spatial coordinates of strapdown inertial navigation systems were obtained for the first time. These dependencies make it possible to reduce the dimension of the vector of navigation parameters and, as a consequence, to build a model of an autonomous observer of navigation parameters to use equations excluded from the general system of these parameters. It is shown that using stochastic nonlinear filtering methods it is possible to solve the problem of noise-resistant autonomous navigation on trajectory intervals described by analytical models. The proposed approach to solving the problem of autonomous navigation of moving objects makes it possible to significantly reduce computational costs in the practical implementation of algorithms for nonlinear filtering of current navigation parameters in comparison with traditional models of strapdown inertial navigation systems. The effectiveness of the proposed approach is illustrated with a numerical example. The results obtained are useful in developing navigation support for various transport objects moving along program trajectories, for example, aircraft for various purposes, railway, road, river transport, etc.

Performance enhancement of PPP/SINS tightly coupled navigation based on improved robust maximum correntropy kalman filtering

Extended kalman filter (EKF) is widely used to integrated navigation system of global navigation satellite system (GNSS) and strapdown inertial navigation system (SINS). However, non-Gaussian noise and the uncertainty of measurement noise can seriously reduce the performance of EKF, so it is difficult to obtain an optimal GNSS/INS integration solution. At present, non-Gaussian noise processing is still a difficult issue in filter research. In this paper, an adaptive and robust maximum correntropy extended kalman filter (MCEKF) method based on Cauchy kernel function is proposed to solve the above problem. Thanks to the excellent properties of Cauchy kernel function, the proposed method can effectively avoid filter faults and has better stability. However, the performance of MCEKF depends on the select of kernel bandwidth parameter, which is a difficult problem in the engineering application of MCEKF. In this paper, the switching kernel bandwidth algorithm is employed to adaptively estimate the kernel bandwidth parameter to solve the tradeoff between convergence rate and steady-state misalignment in the MCEKF algorithm under constant kernel bandwidth. Finally, the performance of the proposed algorithm is verified by two sets of vehicle-mounted precise point positioning (PPP) and SINS tightly coupled integration experiments in urban environment. The results show that compared with EKF, the proposed method can significantly improve the positioning accuracy, that is, the PPP/SINS positioning accuracy based on GE, GR and GRE system is improved by 25.1 %, 2.5 % and 17.0 % in D196 experiment, and 23.5 %, 16.5 % and 31.8 % in D107 experiment, respectively. The velocity and attitude accuracy of the two methods are similar. The velocity errors of all schemes can reach cm/s level. The roll, pitch and heading errors of navigation-grade inertial sensor are all less than 0.12 degree. The roll and pitch errors of MEMS are less than 1.0 degree, the heading error of the G, GE, GR, and GRE systems are 1.719, 1.464, 1.676, and 1.475 degree, respectively.

An Autocollimator Axial Measurement Method Based on the Strapdown Inertial Navigation System.

Autocollimators are widely used optical axis-measuring tools, but their measurement errors increase significantly when measuring under non-leveled conditions and they have a limited measurement range due to the limitations of the measurement principle. To realize axis measurement under non-leveled conditions, this paper proposes an autocollimator axis measurement method based on the strapdown inertial navigation system (SINS). First, the measurement model of the system was established. This model applies the SINS to measure the change in attitude of the autocollimator. The autocollimator was then applied to measure the angular relationship between the measured axis and its own axis, based on which the angular relationship of the axis was measured via computation through signal processing and data fusion in a multi-sensor system. After analyzing the measurement errors of the system model, the Monte Carlo method was applied to carry out a simulation analysis. This showed that the majority of the measurement errors were within ±0.002° and the overall measurement accuracy was within ±0.006°. Tests using equipment with the same parameters as those used in the simulation analysis showed that the majority of the measurement errors were within ±0.004° and the overall error was within ±0.006°, which is consistent with the simulation results. This analysis proves that this method solves the problem of the autocollimator being unable to measure the axis under non-leveled conditions and meets the needs of axis measurement with the application of autocollimators under a moving base.