Strapdown Inertial Navigation System Research Articles

Real-time marine PPP-B2b/SINS integrated navigation based on BDS-3

The BeiDou-3 global navigation satellite system was operated successfully in July 2020. It broadcasts precise point positioning (PPP)-B2b signals and provides real-time PPP services free of charge, which greatly meets the navigation needs of real-time users, especially warship navigation. This paper first introduces the PPP-B2b real-time positioning model, and then expounds the two-velocity measurement algorithm of Doppler and carrier phase time difference. Next, it combs the extended Kalman filter (EKF) and factor graph optimization (FGO) integrated navigation algorithm in detail, and finally comprehensively evaluates the real-time integrated navigation performance of PPP-B2b/strapdown inertial navigation system (SINS) through the measured data at sea. The experimental results show that the real-time dynamic positioning accuracy of PPP-B2b can reach the decimeter level, and the positioning accuracy is not significantly improved when integrated with SINS. Furthermore, dynamic alignment experiments results show after adding time-differenced carrier phase and Doppler velocimetry information, the convergence accuracy of yaw misalignment angle has been greatly improved. The accuracy of the EKF algorithm is 16.7% higher than that of the FGO algorithm after the convergence of the yaw angle error.

Estimation of constant ocean current velocity based on SINS/DVL integrated navigation with an augmented observable quantities filter

Ideally, navigation and positioning information for Autonomous Underwater Vehicles (AUVs) can be provided by a combined navigation system based on a velocity-matching Strap-down Inertial Navigation System (SINS) and Doppler velocity log (DVL). However, the velocity accuracy of DVL is affected by ocean currents when the DVL is operating in water track mode in deep ocean scenarios. The velocity of the currents remains stable over small areas of the ocean within a few hours and can be considered a constant value. Estimation and compensation of the ocean current velocity is a prerequisite for high-precision navigation performance and an important topic for oceanographic research. In this paper, we propose an Augmented Observable Quantities (AOQ)-based filter that constructs a new measurement equation from the difference between the velocities of the previous state and the current state to decouple the ocean current velocity from the velocity error of SINS, and without introducing other sources to provide any information on velocity or position. The simulation and lake test show that the AOQ filter can estimate the ocean current velocity and mitigate its effect on navigation accuracy.

Feedback error-state Kalman filter with time-delay compensation for hydroacoustic-aided inertial navigation of underwater vehicles

This article is intended as a tutorial to assist engineers who want to develop and implement low-cost underwater vehicle inertial navigation systems (INS) aided by time-delayed hydroacoustic position measurements. A discrete-time unit quaternion error-state Kalman filter (ESKF) is used for sensor fusion. The ESKF is implemented as a feedback algorithm with reset functionality. This is motivated by the need for long-endurance autonomous underwater vehicles (AUVs). Proprietary navigation systems do not allow users to add more measurement equations to the code if additional sensors are available. However, the open-source filter architecture presented in the article provides for this. The article also aims to make in-house development of strapdown INS accessible and affordable for vendors of low-cost AUV systems. Finally, a case study of an AUV with a standard sensor suite is included to demonstrate the performance of the ESKF aided by time-delayed position measurements.

Neural network model of errors of an autonomous aircraft strapdown inertial navigation system

Neural network model of errors of an autonomous aircraft strapdown inertial navigation system

A performance-enhanced DVL/SINS integrated navigation system based on data-driven approach

With the aid of Doppler velocity logger (DVL), strapdown inertial navigation systems (SINSs) can provide continuous and accurate navigation parameters for unmanned underwater vehicles (UUVs). However, owing to the complex underwater environment, partial DVL beams may fail to be reflected by the seafloor, resulting in DVL measurement outage. In this study, a novel data-driven approach enhancing DVL/SINS integrated navigation system is proposed to improve the robustness and accuracy of UUV navigation with limited DVL beams. First, to make full use of the available beam, the velocities of DVL beams are used to assist the SINS navigation instead of the 3D velocity of DVL. Subsequently, a virtual beam predictor based on multi-output least-squares support vector regression (MLS-SVR) is built to run in parallel with the DVL/SINS integrated system. Specifically, when the DVL operates normally, all four beams can be applied for integrated navigation and stored as the training dataset. Once partial beams are missing, the available beams and the outputs of SINS and pressure sensors can train the MLS-SVR model along with the corresponding missing beams in the training set. Subsequently, the missing beams can be predicted by the trained model for integrated navigation together with the available beams. UUV sea trials indicate that the proposed system can accurately predict unavailable beams and improve the positioning accuracy of the DVL/SINS integrated navigation system.

All-Parameter System-Level Calibration for SINS/CNS Based on Global Observability Analysis

Before using the strap-down inertial navigation system (SINS)/ celestial navigation system (CNS) integrated navigation system, the calibration of its error parameters is a necessary process to improve the system accuracy. In this paper, an all-parameter system-level calibration method has been proposed, which utilizes Kalman filtering for simultaneously estimating the bias, scale factor, misalignments of inertial measurement unit (IMU), and installation errors of the star sensor. The observation has been constructed using the inertial navigation output information and the starlight vector measured by the star sensor. The observability of the error parameters has been analyzed theoretically, and the optimal excitation conditions for each error parameter are obtained. The effects of the angle between the starlight vector and the optical axis of the star sensor, and the attitude of the IMU, on the estimation accuracy of the installation error of the star sensor are also given. Finally, a 10-order rotation scheme has been designed and all the error parameters can be optimally excited. The simulation and experimental results demonstrate that all the error parameters have better stability and repeatability, when compared with the traditional method, and the initial alignment error of 3.4" is better than 13.1" of the traditional method. Moreover, the installation error of the star sensor can be estimated with a high precision only when the angle between the starlight vector and the optical axis of the star sensor exceeds 1°. It is shown that the proposed method can effectively improve the navigation performance of the SINS/CNS integrated navigation system.

Research on Error Correction Technology in Underwater SINS/DVL Integrated Positioning and Navigation

Underwater vehicles are key carriers for underwater inspection and operation tasks, and the successful implementation of these tasks depends on the positioning and navigation equipment with corresponding accuracy. In practice, multiple positioning and navigation devices are often combined to integrate the advantages of each equipment. Currently, the most common method for integrated navigation is combination of the Strapdown Inertial Navigation System (SINS) and Doppler Velocity Log (DVL). Various errors will occur when SINS and DVL are combined together, such as installation declination. In addition, DVL itself also has errors in the measurement of speed. These errors will affect the final accuracy of the combined positioning and navigation system. Therefore, error correction technology has great significance for underwater inspection and operation tasks. This paper takes the SINS/DVL integrated positioning and navigation system as the research object and deeply studies the DVL error correction technology in the integrated system.

A new method for accurate alignment and calibration of strapdown INS

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

Simulation Optimization and Application of Shearer Strapdown Inertial Navigation System Modulation Scheme.

The operating attitude of a shearer based on a three-dimensional (3D) space scale is the necessary basic information for realizing intelligent mining. Aiming to address the problem of the insufficient perception accuracy of shearers, in this paper, the rotation model of the actual turning mechanism of the strapdown inertial navigation system (SINS) of shearers is established, and the error propagation characteristics of different single-axis rotation modulation schemes are revealed. Through theory and simulation, the optimal rotation modulation scheme is determined to be the improved four-position turn-stop modulation with a rotation of <360°. The experiment shows that the 24 h positioning error of this scheme is 3.7 nmile, and the heading angle changes by 0.06°, which proves that this scheme can effectively improve the attitude perception accuracy of the inertial navigation system (INS). The field application of the shearer operating attitude perception based on this scheme shows that the positioning error after error compensation is 17% of that before compensation, and the heading angle error is 75% of that before compensation, which verifies that this scheme can significantly improve the accuracy of shearer operating attitude perception in field applications. This scheme can achieve higher precision perception accuracy based on SINS and has broad application prospects in the field of high-precision pose perception of coal mining machines, roadheaders, and other equipment.

In-motion initial alignment method using Cayley–Kalman filter on special orthogonal group

Aiming at the in-motion initial alignment problem of strapdown inertial navigation system (SINS), this paper proposed a precise direct in-motion alignment method based on attitude matrix representation and Cayley–Kalman filter on the special orthogonal group. There are two innovations in this paper. First, as an element of the special orthogonal group [Formula: see text], the error attitude matrix is used to construct an in-motion alignment model, and it is transformed into the vector space to represent the attitude error state. The error matrix was used as a state to decrease the influence of the state-dependent problem. Second, this method uses the Cayley transform to replace the Taylor expansion to derive the update equation, which is a no approximation mapping relation to assure accuracy when deriving the filtering algorithm. Simulation and experimental results demonstrate the proposed alignment method has advantages over the existing methods in alignment accuracy and alignment time and performs well in the in-motion alignment process of SINS.

A novel adaptive nonlinear Kalman filter scheme for DVL-aided SINS alignment in underwater vehicles

The rapid and accurate initial alignment of a strapdown inertial navigation system (SINS) aided by a Doppler velocity logger (DVL) still poses a significant challenge in unmanned underwater vehicle navigation. In this study, a novel adaptive nonlinear filtering alignment scheme is developed for a SINS with a large misalignment angle. In previous studies, the frame-inconsistency problem of the nonlinear SINS error model was neglected. Thus, a modified nonlinear error model of a SINS is derived here rigorously as the process model of the nonlinear Kalman filter. In addition, the noise amplification of applying Sage-Husa adaptive Kalman filter (SHAKF) in alignment is analyzed, and a novel arctangent fading memorial factor is introduced to dynamically adjust the weight of current measurements. Simulations and field experiments indicate that the proposed algorithm is efficient in underwater DVL/SINS in-motion alignment. The alignment accuracy and convergence rate of the modified model are significantly improved compared to those of the traditional model. The arctangent fading memorial SHAKF can reliably estimate the measurement noise and improve the performance of alignment.

An Improved In-Motion Coarse Alignment Method for SINS/GPS Integration with Initial Velocity Error Suppression.

The integrated system with the strapdown inertial navigation system (SINS) and the global positioning system (GPS) is the most popular navigation mode. It has been used in many navigation fields. Before the integrated system works properly, it must determine the initial attitude for SINS. In SINS/GPS-integrated systems, the navigational velocity can be used to carry out the initial alignment when the system is installed in the in-motion vehicle. However, the initial velocity errors are not considered in the current popular in-motion alignment methods for SINS/GPS integration. It is well-known that the initial velocity errors must exist when the initial velocity is obtained from the GPS outputs. In this paper, an improved method was proposed to solve this problem. By analyzing the original observation vectors in the in-motion coarse alignment method, an average operation was used to construct the intermediate vectors, and the new observation vector can be calculated by subtracting the intermediate vector from the original observation vector. Then, the initial velocity errors can be eliminated from the newly constructed observation vector. Thus, the interferences of the initial velocity errors for the initial alignment process can be suppressed. The simulation and field tests are designed to verify the performance of the proposed method. The tests results showed that the proposed method can obtain the higher accurate results than the current methods when the initial velocity is considered. Additionally, the results of the proposed method were similar to the current methods when the initial velocity errors were not considered. This shows that the initial velocity errors were eliminated effectively by the proposed method, and the alignment accuracy were not decreased.

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.