Strapdown Inertial Navigation System Research Articles

Double‐state chi‐square test based sparse grid quadrature filtering algorithm and its application in integrated navigation

AbstractAiming to reduce the impact that the measurement uncertainty of nonlinear system brings to filtering accuracy, a novel sparse grid quadrature filter (SGQF) algorithm based on the double‐state chi‐square test is proposed. And the strap‐down inertial navigation system (SINS)/global navigation satellite system (GNSS) integrated navigation system is used to verify the algorithm. A discrete‐time system model with uncertain measurement is constructed, then the system state through the SGQF algorithm is estimated. To determine the uncertainty of the measurement, the double‐state chi‐square test is introduced. By comparing the results of the state recursor, the chi‐square test value is obtained and it is used to update the measurement noise. Further, the system state and error covariance are re‐estimated. So far a robust sparse grid filter algorithm with statistical adjustment of the measurement noise is obtained. The proposed algorithm can overcome the influence of error statistical characteristic amplification on system filtering accuracy. Taking the SINS/GNSS integrated navigation system as the application object, off‐line simulation experiments and online flight tests verify the robustness of the proposed algorithm.

Impact of Motion-Dependent Errors on the Accuracy of an Unaided Strapdown Inertial Navigation System

The selection of an appropriate measurement system for an inertial navigation system requires an analysis of the impact of sensor errors on the position and orientation determination accuracy to ensure that the selected solution is cost-effective and complies with the requirements. In the current literature, this problem is solved based on the navigation duration only by considering the time-dependent errors due to sensor bias and random walk parameters or by conducting numerous simulations. In the former case, oversimplifying the analysis will not allow accurate values to be determined, while the latter method does not provide direct insight into the emerging dependencies. In contrast, this article introduces an analytic approach with a detailed model. This article presents general formulas, also written in detail for the measurement system model adopted and various manoeuvres. Although general equations are complicated, the use of piecewise constant motion variables allow us to discern fragments of equations corresponding to individual error sources. The results confirm the effect the carouseling has on the reduction of navigation errors. The general formulas presented extend the potential to analyse the influence of the entire host vehicle motion, while the detailed formulas make dependencies between motion and navigational errors evident.

Research on IMU Calibration Model Based on Polar Decomposition.

As an important deterministic error of the inertial measurement unit (IMU), the installation error has a serious impact on the navigation accuracy of the strapdown inertial navigation system (SINS). The impact becomes more severe in a highly dynamic application environment. This paper proposes a new IMU calibration model based on polar decomposition. Using the new model, the installation error is decomposed into a nonorthogonal error and a misalignment error. The compensation of the IMU calibration model is decomposed into two steps. First, the nonorthogonal error is compensated, and then the misalignment error is compensated. Based on the proposed IMU calibration model, we used a three-axis turntable to calibrate three sets of strapdown inertial navigation systems (SINS). The experimental results show that the misalignment errors are larger than the nonorthogonal errors. Based on the experimental results, this paper proposes a new method to simplify the installation error. This simplified method defines the installation error matrix as an antisymmetric matrix composed of three misalignment errors. The navigation errors caused by the proposed simplified calibration model are compared with the navigation errors caused by the traditional simplified calibration model. The 48-h navigation experiment results show that the proposed simplified calibration model is superior to the traditional simplified calibration model in attitude accuracy, velocity accuracy, and position accuracy.

A Polar Integrated Alignment Assisted by DVL Under Large Azimuth Misalignment

The gravity tends to coincide with the earth’s rotation vector in the polar region, degrading the coarse alignment azimuth of the strapdown inertial navigation system (SINS) to a large misalignment. Under a large azimuth misalignment, the linear error model inevitably renders unacceptable theoretical errors in the integrated alignment. In addition, polar region challenge such sensors as a star sensor of celestial navigation, which fails to provide high-precision attitude reference for integrated alignment. Therefore, in allusion to the misalignment mentioned above based on SINS for the polar region, an integrated alignment algorithm is proposed, assisted by the Doppler Velocity Log (DVL). Notably, the work first investigates the extent to which azimuth accuracy deteriorates in the polar region. On the premise of large azimuth misalignment, the nonlinear error model under the transverse frame is derived from the ellipsoid earth model. Additionally, the state and measurement models are constructed, combined with the velocity of DVL as an observation. An adaptive measurement variance matrix is designed for the unscented Kalman filter (UKF) to estimate the attitude error. Eventually, the semi-physical experiments demonstrate that the proposed algorithm significantly improves the initial alignment accuracy of the polar region.

A Combination Scheme of Pure Strapdown and Dual-Axis Rotation Inertial Navigation Systems

Compared with the strapdown inertial navigation system (SINS), the rotation strapdown inertial navigation system (RSINS) can effectively improve the accuracy of navigation information, but rotational modulation also leads to an increase in the oscillation frequency of attitude errors. In this paper, a dual-inertial navigation scheme that combines the strapdown inertial navigation system and the dual-axis rotation inertial navigation system is proposed, which can effectively improve the attitude error accuracy in the horizontal direction by using the high-position information of the rotation inertial navigation system and the stability characteristics of the attitude error of the strapdown inertial navigation system. Firstly, the error characteristics of the strapdown inertial navigation system and the rotation strapdown inertial navigation system are analyzed, and then the combination scheme and Kalman filter are designed according to the error characteristics, and finally, the simulation experiment shows that the pitch angle error of the dual inertial navigation system is reduced by more than 35% and the roll angle error is reduced by more than 45% compared with the rotation strapdown inertial navigation system. Therefore, the combination scheme of double inertial navigation proposed in this paper can further reduce the attitude error of the rotation strapdown inertial navigation system, and at the same time, the two sets of inertial navigation systems can also enhance the reliability of ship navigation.

Error-free strapdown inertial navigation system numerical updating algorithm in the launch-centered Earth-fixed frame for hypersonic vehicles

The two-sample numerical updating algorithm of strapdown inertial navigation systems (SINS) for hypersonic vehicles has a relatively large navigation error. To solve this problem, this paper proposes an error-free SINS numerical updating algorithm in the launch-centered Earth-fixed (LCEF) frame. First, the gyroscopes and accelerometers in SINS output angular increment and velocity increment respectively, while the proposed algorithm takes angular velocity and specific force as input, so the methods of angular increment fitting angular velocity and velocity increment fitting specific force are proposed. Then, according to the SINS differential equation in the LCEF frame, the error-free SINS numerical updating algorithm in the LCEF frame is designed by adopting the Taylor series expansion method. The derivation process of the algorithm shows that the proposed algorithm can achieve precise compensation for the non-exchangeable errors of attitude, velocity, and position, and selecting the LCEF frame as the navigation frame has greater advantages than the local-level frame. Finally, two-sample and error-free numerical updating algorithms are simulated and compared by taking the hypersonic boost-gliding vehicle as the object. Under the influence of a pure SINS algorithm, the velocity error of the two-sample algorithm with a simulation duration of 1100 s is in the order of 10−2 m/s, and the position error is in the order of 10 m. In contrast, the velocity error of the proposed algorithm is in the order of 10−7 m/s, and its position error is in the order of 10−4 m.

The accuracy of determining the coordinates of an unmanned aerial vehicle with a navigation complex integrating an electro-optical positioning system

The article proposes the approaches to updating a strapdown inertial navigation system (SINS) based on data of the airborne electro-optical system (EOS) of an unmanned aerial vehicle (UAV). It is specified that the EOS is presented as a navigation data sensor. The rationale for the feasibility of such an approach is formed, especially in the terms of signal lack or suppression of satellite radio-navigation systems. It is proposed to ensure the accuracy of self-contained navigation by assigning an UAV route, including waypoints with terrestrial references (TRs). Notably, TR-associated image information is preliminarily downloaded into the flight management computer (FMC). The automated TR identification system with denoted coordinates at next waypoints, using airborne data, in fact, allows for alternative global positioning. The reliable operation of such an integrated navigation system over sufficiently extended legs of flight path, first, depends on the accuracy of its constituent elements. Taking into consideration the fact that conventional sensors of navigation information, such as a SINS and an altimeter, are quite well studied in numerous contributions. The article focuses on the UAV airborne electro-optical system and, specifically, on its application features as a navigation sensor. The factors influencing the accuracy of the UAV positioning data determination at waypoints according to the data of the airborne EOS are considered. The developed mathematical model of errors for the UAV inertial optical navigation complex (IONC) is presented. The analysis of the impact of airborne altimeter inaccuracies, earth’s surface features and the shift of the onboard digital camera optical axis, caused by random evolutions of the carrier body in turbulent atmosphere on the positioning accuracy, was conducted. The results of calculating lapses in determining the UAV positioning data, equipped with IONC, are given.

A Coarse Alignment Method Based on Vector Observation and Truncated Vectorized $\boldsymbol{\kappa}$-Matrix for Underwater Vehicle

This paper focuses on the coarse alignment problem for the strapdown inertial navigation system (SINS) applied to the underwater vehicle. The coarse alignment is one of the crucial technologies of underwater navigation and determines whether SINS can work normally. However, the traditional coarse alignment methods suffer from the complicated noises hidden in the inertial sensors’ outputs. To solve this problem, a new coarse alignment algorithm based on vector observation and truncated vectorized <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{\kappa}$</tex-math></inline-formula> -matrix is proposed in this paper. Different from previous methods based on the optimal quaternion, the proposed algorithm makes the matrix state-space formulae of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{\kappa}$</tex-math></inline-formula> -matrix vectorized, and truncates the resulting state vectors by implementing the linear dependence within the components of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{\kappa}$</tex-math></inline-formula> -matrix. On one hand, based on the vectorized and truncated <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{\kappa}$</tex-math></inline-formula> -matrix, a linear reduced model of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{\kappa}$</tex-math></inline-formula> -matrix can be applied to the estimation process, and the measurement errors of inertial sensors can be easily restrained using the estimation algorithm. On the other hand, the proposed approach makes up for the drawbacks of the Optimal-REQUEST algorithm which has a conservative covariance matrix and scalar gain. The simulation test and practical experiment demonstrate that the proposed approach can reduce random noise effectively. Therefore, the performance of coarse alignment algorithm can be improved more enormously than the traditional algorithms.

State transformation extended Kalman filter–based tightly coupled strapdown inertial navigation system/global navigation satellite system/laser Doppler velocimeter integration for seamless navigation of unmanned ground vehicle in urban areas

With the rapid development of unmanned ground vehicle industry, how to achieve continuous, reliable, and high-accuracy navigation becomes very important. At present, the integrated navigation with global navigation satellite system and strapdown inertial navigation system is the most mature and effective navigation technology for unmanned ground vehicle. However, this technique depends on the signal accuracy of global navigation satellite system. When the receiver cannot capture four or more satellite signals for a long time or the satellite completely invalid, it cannot provide accurate navigation and positioning information for the unmanned ground vehicle. Therefore, this article combine the observation information of strapdown inertial navigation system, global navigation satellite system, and laser Doppler velocimeter to propose a high-precision seamless navigation technique of unmanned ground vehicle based on state transformation extended Kalman filter. Under different land vehicle driving environments and global navigation satellite system signal quality conditions, the seamless navigation technique is evaluated through global navigation satellite system interruption simulation and land vehicle experiments. The experimental results show that the strapdown inertial navigation system/global navigation satellite system/laser Doppler velocimeter tightly coupled integration seamless navigation has good environmental adaptability and reliability and can maintain high navigation accuracy under high frequency global navigation satellite system–signal blockage conditions in urban areas.

Methodology of Airborne Gravimetry Surveying and Strapdown Gravimeter Data Processing

The paper presents a methodology of preparing and conducting airborne gravimetry survey using an inertial measuring unit (IMU) or strapdown inertial navigation system as airborne gravimeter. We also discuss the key aspects of developing appropriate postprocessing algorithms and software and their application to gravimeter raw data processing. Solving the strapdown inertial airborne gravimetry problem, we use readings of the IMU sensors (accelerometers and gyroscopes) as primary information. The second equally important source of information is raw (pseudorange, Doppler pseudorange rate, and carrier phase) measurements from the GNSS receivers on board the aircraft and on the ground. The developed methodology, algorithms, and practical recommendations presented in the paper are based on the authors’ long-term experience in airborne gravimetry.

A Fast Intelligent Algorithm-Based Positioning Error Suppression Method for Strap-Down Inertial Navigation System

It is a difficult problem to suppress navigation errors of strap-down inertial navigation system (SINS) when external observation is rejected or discontinuous. With the help of intelligent algorithms, the device errors of SINS can be searched and compensated when the vehicle has no significant linear motion, so as to limit the positioning error of inertial navigation system (INS) to a certain extent in the case of external observation rejection. However, the INS contains long period error terms. In order to suppress the navigation errors, long time data need to be observed and then trained by intelligent algorithms, which limits the usability of the correlation error suppression algorithms in practice. In view of this problem, this article proposes a fast intelligent algorithm (FIA)-based positioning error suppression method for INSs. By virtually extending the inertial navigation update interval, the divergence law of the longitude error could be changed. On this basis, a fast training algorithm based on particle swarm optimization (PSO) is designed. The contributions of the work presented here are twofold. First, the mathematical relationship between the positioning error and the device error of SINS with virtually extended update interval is analyzed. Second, compared with the traditional methods, the amount of data required for training is greatly reduced. Therefore, the device errors of INS could be searched and compensated with short-term observation data. Then, the long-term positioning accuracy of INS can be improved efficiently. Field tests are performed, which validate the efficacy of the proposed method.

A time asynchronous parameters calibration method of high-precision FOG-IMU based on a single-axis continuous rotation scheme

There is a time asynchronous problem with the output signals between each inertial sensor in an actual high-precision fiber optic gyro inertial measurement unit (FOG-IMU), which reduces the velocity update accuracy of the strap-down inertial navigation system in the actual applications. Firstly, the velocity error formulas are derived in the coordinate navigation system considering three time asynchronous errors between the three-axis accelerometers and gyros. Then an error-state Kalman filter is designed with respect to the time asynchronous parameters measurement model in angular dynamic environments. Afterward, a single-axis continuous rotation scheme is developed to calibrate the time asynchronous parameters. In particular, a simple observability analysis model is proposed to verify the rationality of the calibration scheme. Furthermore, the time asynchronous parameters are calculated effectively based on the proposed indirect calibration scheme. Finally, the proposed method is verified effectively through simulations and turntable experiments, which can significantly reduce the measurement errors of high-precision FOG-IMU. As a result, compared with the traditional three-parameter direct calibration method, the eastward and northward velocity errors are reduced by 7.01% and 2.48%, respectively.

Performance Evaluation of Stereo Vision Aided Loosely Coupled GNSS/SINS Integration for Land Vehicle Navigation in Different Urban Environments

In urban environments, the positioning performance of global navigation satellite system (GNSS) degrades severely due to the harsh environment, which will be improved after fused with a strap-down inertial navigation system (SINS). However, due to the error accumulation, the positioning ability of GNSS/SINS integration will also decrease significantly during frequent GNSS outages. To improve the positioning accuracy, we use stereo vision to enhance the performance of GNSS/SINS integration, where GNSS and stereo vision are loosely coupled and tightly coupled with SINS under the Earth-centered Earth-fixed (ECEF) frame, respectively. To evaluate the positioning performance of the multisensor fusion system, two in-field experiments were conducted to assess the contribution of stereo vision. The results show that with the support of stereo vision and SINS, GNSS accuracy can be considerably improved by 60%–80% in complex environments, which also outperforms the GNSS/SINS integration. Besides, detailed analyses in various urban environments further demonstrate that stereo vision can significantly improve the performance of GNSS/SINS integration when a long-term GNSS anomaly occurs, but it shows no improvement for a short-term GNSS anomaly.

МЕТОДОЛОГИЧЕСКИЕ ОСНОВЫ И ПРАКТИЧЕСКИЕ АСПЕКТЫ РЕШЕНИЯ ЗАДАЧ ОПТИМИЗАЦИИ НЕСУЩИХ СИСТЕМ БЕСПЛАТФОРМЕННЫХ ИНЕРЦИАЛЬНЫХ НАВИГАЦИОННЫХ СИСТЕМ

This article describes approaches to solving problems of optimization of bearing structureof strapdown inertial navigation systems (SINS). A typical optimization problem in this case ismultiobjective parametric optimization of the bearing structure of the SINS accelerometer triad inorder to minimize the mass of the bearing structure and minimize deviation angles of the accelerometeraxes under the action of external loads. The ANSYS Mechanical and ANSYSDesignXplorer modules are used as a tool for numerical modeling and optimization, respectively.Practical issues related to parameterization of SINS bearing structure 3D-models, calculation ofaccelerometer axes deviation angles, possible variants of numerical experiment plans, estimationof response sensitivity to input parameters, generation and refinement of the response surface, andmultiobjective optimization are considered. For the rational parametrization of geometry, theSINS device assembly was decomposed, as a result of which the parts and structural elements that have the greatest influence on the considered objective functions were identified. To calculate thedeviation angles of the sensitive elements axes, special two-node finite elements and relations forthe Bryant angles were used, which describe the relative position in space of two coordinate systems.When planning a numerical experiment, at the first stage of optimization, a central compositionplan was used, and at subsequent stages, the parameter space was filled using the Latin hypercubemethod with the option of relations between parameters, which made it possible to avoiddegenerate design options. The response surface was built using the genetic aggregation methodand subsequently refined based on a set of optimal solutions. Optimization for conflicting goals ofmass minimization and stiffness maximization was carried out using a multiobjective genetic algorithm.The described set of approaches to solving optimization problems as a result of an exemplaryseries of calculations made it possible to reduce the mass of a serial SINS bearing structurepart by 23% with fixed stiffness.

Correction of a Strapdown Inertial Navigation System During Descent in the Atmosphere

Correction of a Strapdown Inertial Navigation System During Descent in the Atmosphere

An In-Flight Alignment Method for Global Positioning System-Assisted Low Cost Strapdown Inertial Navigation System in Flight Body with Short-Endurance and High-Speed Rotation

Alignment technology plays an important role in navigation, and is used extensively throughout military and civilian applications. However, the existing in-flight alignment methods cannot be applied to the low-cost based strap-down inertial navigation system/global positioning system integrated navigation system, used in short-endurance and high-speed rotation flight bodies, since they cannot quickly obtain alignment results to meet the accuracy requirements of a flight body with special movement characteristics of short-endurance and high-speed rotation. In this paper, in order to solve this challenging problem of alignment for flight body with short-endurance and high-speed rotation, a fast in-flight alignment method based on the Lie group is proposed. First, an in-flight alignment model based on vector observations was established by using the Lie group. Second, addressing the problem that the alignment accuracy is greatly affected by the low-cost inertial sensor bias, an improved unscented Kalman filter was constructed in the Lie group on the basis of fully considering the characteristics of the system equations to estimate and feedback the correlated errors. Finally, a trajectory simulation of high-speed flight body and field semi-physical test was carried out to evaluate the proposed method. Evaluation of the system performance in comparison with existing state-of-the-art methods indicated that the proposed in-flight alignment method has better alignment accuracy and faster alignment velocity for a low-cost strap-down inertial navigation system/global positioning system integrated navigation system.

An improved comprehensive calibration method for ship strapdown inertial navigation system

To restrain the divergence of positioning errors in inertial navigation systems (INSs) and improve long-term navigation and positioning accuracies, comprehensive calibration technology is an important method. This paper improves on the basis of the previous method of determining the misalignment angles and equivalent gyroscope drift by the parameters identification method (PIM), and introduces the normal time-frequency transform (NTFT) method. The main work of this paper are as follows: (1) the relationship between the Schuler period oscillation (SPO) in the INS velocity and the misalignment angles are analyzed, and then the misalignment angles are calculated with the extracted velocity using NTFT; (2) PIM and NTFT are combined for comprehensive calibration, the attitude angles, velocities and latitude are reset, and the longitude is compensated with the equivalent gyroscope drift. Simulation and shipboard dynamic tests show that the NTFT/PIM can effectively restrain the amplitude of SPO error and improve the long-term navigation and positioning accuracies. From the perspective of practical application, the result of this study is a single-point calibration technology that improves the autonomy of the system.

SINS/DVL Linear Initial Alignment based on Lie Group SE3 (3)

This paper investigates the strapdown inertial navigation system (SINS) initial alignment aided by Doppler velocity log (DVL). A linear Kalman filtering method is proposed using the theory of Lie group, which is immune to the initial misalignment. The dead-reckoning position based on the body velocity provided by DVL and attitude provided by SINS is used as measurement. The SINS calculated attitude, velocity, position and DVL dead-reckoning position are formulated together as the elements of Lie group SE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> (3). Since the dead-reckoning position is a type of left-invariant measurement, the corresponding linear error-state model is derived based on the left-invariant group error definition. Although the Lie group state model is not group affine, thesmall attitude error assumption does not introduce accuracy degeneracy in deriving the linear error-state model. This is the core reason why the derived linear error-state model is still applicable for cases with large initial misalignment. Experiments are conducted to verify the feasibility and effectiveness of the proposed methods. The test results show that the proposed method has higher accuracy and faster convergence speed as compared with the existing methods.

Virtual Beam Aided SINS/DVL Tightly Coupled Integration Method With Partial DVL Measurements

Strapdown inertial navigation system (SINS)/ Doppler velocity log (DVL) tightly coupled (TC) fusion is a popular scheme as it offers increased robustness compared to other approaches. In TC, DVL beam velocities are separately integrated with SINS in the navigation filter. To enhance the performance of SINS/DVL TC integration system in situations of partial DVL beam measurements, virtual beam aided solutions are proposed, theoretically derived, and experimentally evaluated. To that end, we analyze the geometrical relation between the DVL beam configuration and a zero velocity vector assumption and derive a zero velocity update (ZUPT) aided virtual beam method to continuously operate the TC fusion. Further, to avoid the precondition limitation of ZUPT method, a least squares support vector machine (LS-SVM) aided virtual beam construction algorithm together with its SINS/DVL TC integration scheme is proposed. Our experiments show the advantages and disadvantages of the ZUPT aided solution under different scenarios, and indicate the effectiveness of the LS-SVM aided virtual beam solution during short partial beam measurement periods.

High‐Precision Positioning Simulation and Experimental Research of Special Operation Vehicles Based on Network RTK

In terms of driverless systems, high‐precision positioning technology is one among the critical aspects of driverless cars to achieve driverlessness. This study analyzed the working principles of GNSS (global navigation satellite system) and SINS (strapdown inertial navigation system) and elaborated the principles of the least square method and LAMBDA algorithm in the integer ambiguity resolution. Based on the network RTK positioning technology and the abovementioned theory, the unmanned automatic work vehicle was used as the research object, and the fusion positioning algorithm of the BDS/GPS system and inertial sensor was used to propose a high‐precision positioning technology for the unmanned automatic work vehicle. The combined navigation system model was studied and constructed. Relevant verification was carried out through simulation and experiment. The results were as follows: the pitch angle error was less than 0.1°, the roll angle error was less than 0.05°, the speed error was less than 0.2 m/s, and the position error was less than 2.1 m. The outcomes indicate that an integrated navigation and positioning algorithm for driverless vehicles can significantly enhance the localisation accuracy and reliability of navigation. The research results are of engineering value and practical application for the development of unmanned automatic special vehicle positioning systems.