Alignment Of Strapdown Inertial Navigation System Research Articles

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.

A Vision Aided Initial Alignment Method of Strapdown Inertial Navigation Systems in Polar Regions.

The failure of the traditional initial alignment algorithm for the strapdown inertial navigation system (SINS) in high latitude is a significant challenge due to the rapid convergence of polar longitude. This paper presents a novel vision aided initial alignment method for the SINS of autonomous underwater vehicles (AUV) in polar regions. In this paper, we redesign the initial alignment model by combining inertial navigation mechanization equations in a transverse coordinate system (TCS) and visual measurement information obtained from a camera fixed on the vehicle. The observability of the proposed method is analyzed under different swing models, while the extended Kalman filter is chosen as an information fusion algorithm. Simulation results show that: the proposed method can improve the accuracy of the initial alignment for SINS in polar regions, and the deviation angle has a similar estimation accuracy in the case of uniaxial, biaxial, and triaxial swing modes, which is consistent with the results of the observable analysis.

In-Motion Alignment Method of SINS Based on Improved Kalman Filter under Geographic Latitude Uncertainty

To realize the in-motion alignment of the strapdown inertial navigation system (SINS) under the geographic latitude uncertainty, we propose a latitude estimation and in-motion alignment method based on the integral dynamic window and polynomial fitting (IDW-PF) and improved Kalman filter (IKF). First, the integral dynamic window (IDW) is designed to smooth out the high-frequency line motion interference and accelerometer noise. Second, the specific force integral is performed for a cubic polynomial fitting (PF) with time as an independent variable to further suppress the line motion interference. Simultaneously, the latitude is estimated according to the geometric relationship between the angle of the gravitational acceleration vectors at different moments and the latitude. Finally, the IKF based on the multi-fading factor is designed for the in-motion alignment of SINS. A simulation experiment is conducted to verify the proposed latitude estimation and in-motion alignment method. The results indicate that the latitude can be estimated well by the method based on the IDW-PF; the mean and standard deviation of the estimated latitude can achieve −0.016° and 0.013° within 300 s. The trapezoidal maneuvering path is optimal when IKF is used, the pitch error is 0.0002°, the roll error is 0.0009° and the heading error is −0.0047° after the alignment ends at 900 s.

Quaternion Algorithm for Initial Alignment of Strapdown INS Using the A. N. Tikhonov Regularization Method

For the functioning of algorithms of inertial orientation and navigation of strapdown inertial navigation system (SINS), it is necessary to conduct a mathematical initial alignment of SINS immediately before the operation of these algorithms. An efficient method of initial alignment (not calibration!) of SINS is the method of vector matching. Its essence is to determine the relative orientation of the instrument trihedron Y (related to the unit of SINS sensors) and the reference trihedron X according to the results of measuring the projections of at least two non-collinear vectors of the axes on both trihedrons. We address the estimation of the initial orientation of the object using the method of gyrocompassing, which is a form of vector matching method. This initial alignment method is based upon using the projections of the apparent acceleration vectoraand the absolute angular velocity vectorωof the object in the coordinate systems X and Y. It is assumed that the three single-axis accelerometers and the three gyroscopes (generally speaking, the three absolute angular velocity sensors of any type), which measure the projections of the vectorsaandω, are installed along the axes of the instrument coordinate system Y. If the projections of the same vectors on the axes of the base coordinate system X are known, then it is possible to estimate the mutual orientation of X and Y trihedrons. We are solving the problem of the initial alignment of SINS for the case of a fixed base, when the accelerometers measure the projection gi(i = 1, 2, 3) of the gravity acceleration vectorg, and the gyroscopes measure the projectionsui of the vector u of angular velocity of Earth’s rotation on the body-fixed axes. The projections of the same vectors on the axes of the normal geographic coordinate system X are also estimated using the known formulas. The correlation between the projections of the vectorsuandgin X and Y coordinate system is given by known quaternion relations. In these relations the unknown variable is the orientation quaternion of the object in the X coordinate system. By separating the scalar and vector parts in the equations, we obtain an overdetermined system of linear algebraic equations (SLAE), where the unknown variable is the finite rotation vectorθ, which aligns the X and Y coordinate systems (it is assumed that there is no half-turn of the X coordinate system with respect to the Y coordinate system). Thus, the mathematical formulation of the problem of SINS initial alignment by means of gyrocompassing is to find the unknown vectorθfrom the derived overdetermined SLAE. When finding the vectorθdirectly from the SLAE (algorithm 1) and data containing measurement errors, the components of the vector q are also determined with errors (especially the component of the vectorθ, which is responsible for the courseψof an object). Depending on the pre-defined in the course of numerical experiments values of headingψ, rollϑ, pitchγangles of an object and errors of the input data (measurements of gyroscopes and accelerometers), the errors of estimating the heading angle Δψ of an object may in many cases differ from the errors of estimating the roll Δϑ and pitch Δγ angles by two-three (typically) or more orders. Therefore, in order to smooth out these effects, we have used the A. N. Tikhonov regularization method (algorithm 2), which consists of multiplying the left and right sides of the SLAE by the transposed matrix of coefficients for that SLAE, and adding the system regularization parameter to the elements of the main diagonal of the coefficient matrix for the newly derived SLAE (if necessary, depending on the value of the determinant of this matrix). Analysis of the results of the numerical experiments on the initial alignment shows that the errors of estimating the object’s orientation angles Δψ, Δϑ, Δγ using algorithm 2 are more comparable (more consistent) regarding their order.

A Newton iterative optimization combined with window loop calculation algorithm for estimating accelerometer bias based on gravitational apparent motion with excitation of swinging motion.

The initial alignment method, including the identification of inertial device error parameters, has always been a key issue in an inertial navigation system (INS). This study focuses on the error caused by the random noise of inertial devices that can be compensated by the reconstruction of gravitational apparent motion in an inertial frame under the condition of swinging motion. Attitude angles and accelerometer bias can also be estimated. However, the analysis and simulation results indicate that the existing methods cannot estimate the gyroscope bias. The accelerometer and the gyroscope bias will change over a long time, which will lead to long-term parameter identification accuracy decline or even failure. In this paper, a parameter identification algorithm based on Newton iterative optimization combined with a window loop calculation is designed to solve these problems. Simulation and turntable tests indicate that the proposed new algorithm can fulfill the initial alignment of strapdown INS under the swinging condition and estimate accelerometer bias effectively. Moreover, the new algorithm improves data utilization, which also has better time sensitivity, and the calculated alignment errors can nearly approach zero.

MASGQF with application to SINS alignment

To effectively improve the computation efficiency in the strapdown inertial navigation system (SINS) alignment process, the authors propose a marginalised adaptive sparse-grid quadrature filter (MASGQF). The filtering method combines the virtues of marginalisation technique and accuracy level switching structure to decrease the computational burden and improve the filtering precision simultaneously. With the adaptation criterion and the predefined tolerance value, different integration rules corresponding to the different accuracy levels nested in the proposed filtering method can be adjusted autonomously. It is proved that the MASGQF is exponentially bounded by theoretical analysis. The performance comparison of different filtering methods is demonstrated by the numerical results of the simulation and offline experiment. On the basis of the data performance of the online test, the validity of the proposed MASGQF is verified in the SINS alignment application.

In-Motion Alignment for a Velocity-Aided SINS With Latitude Uncertainty

For situations where accurate attitude information is needed while the position is not readily available or not necessarily required, such as the attitude heading reference system, this article proposes a velocity-aided in-motion alignment scheme for a strapdown inertial navigation system (SINS) during geographic latitude uncertainty. In the coarse alignment stage, a gravitational apparent motion rebuilding method based on the integral velocity smoothing is designed to roughly determine the attitude and latitude information. Then, the SINS/velocity-integrated navigation method uses the recorded data to complete the fine alignment. Due to the adoption of a well-designed backtracking navigation strategy, the storage space and computation load are reduced to the degree that an ordinary navigation computer can work with. Nine ship tests were carried out and the results show that the proposed method can align the azimuth with an accuracy of 0.04° in a moving environment, which is the same as that of normal in-motion alignment with a known position.

Robust cubature Kalman filter method for the nonlinear alignment of SINS

Nonlinear initial alignment is a significant research topic for strapdown inertial navigation system (SINS). Cubature Kalman filter (CKF) is a popular tool for nonlinear initial alignment. Standard CKF assumes that the statics of the observation noise are pre-given before the filtering process. Therefore, any unpredicted outliers in observation noise will decrease the stability of the filter. In view of this problem, improved CKF method with robustness is proposed. Multiple fading factors are introduced to rescale the observation noise covariance. Then the update stage of the filter can be autonomously tuned, and if there are outliers exist in the observations, the update should be less weighted. Under the Gaussian assumption of KF, the Mahalanobis distance of the innovation vector is supposed to be Chi-square distributed. Therefore a judging index based on Chi-square test is designed to detect the noise outliers, determining whether the fading tune are required. The proposed method is applied in the nonlinear alignment of SINS, and vehicle experiment proves the effective of the proposed method.

A Novel Calibration Method of SINS/DVL Integration Navigation System based on Quaternion

This paper proposes a new quaternion calibration algorithm to calibrate large misalignment angles between Strapdown Inertial Navigation System (SINS) and Doppler Velocity Log (DVL) in SINS/DVL integrated navigation system. A new SINS/DVL/GPS integrated navigation system is derived to complete the SINS alignment and SINS/DVL integrated navigation system calibration. Different from the traditional calibration model, the misalignment angles are described by quaternion, according to the physical properties of misalignment angle and scale factor error, the new measurement equation is derived: zero observation vector is used to estimate the misalignment angles, and velocity error scalar is used to estimate the scale factor error. A switching measurement information Kalman filter is designed to switch between different processes. The performance of the proposed quaternion calibration algorithm is evaluated through simulation comparisons with nonlinear model approaches and experiment. The simulation results demonstrate that the proposed quaternion calibration algorithm has better accuracy and robustness than the nonlinear model approaches. The experiment results show that the proposed quaternion calibration algorithm is effective, the SINS/DVL integrated navigation system positioning error after calibration is less than 1.65% mileage in more than 30km travel.

Consistent ST-EKF for Long Distance Land Vehicle Navigation Based on SINS/OD Integration

This paper presents detailed derivations and further explanations of the state transformation extended Kalman filter (ST-EKF) from the common frame error definition perspective. Both the system error and measurement models of strapdown inertial navigation system (SINS)/Odometer (OD) tightly-coupled navigation are derived based on the ST-EKF. Both theoretical analysis and test results indicate the effectiveness of the proposed velocity error definition on mitigating the covariance-inconsistency problem that is caused by the specific force calculation error in the EKF state transition matrix. The excellent covariance-consistency of the ST-EKF makes it not necessary to remove gyro and accelerometer bias errors from the initial alignment Kalman filter states. This phenomenon can ensure the subsequent integrated navigation performance. Single-position ground SINS alignment experiments by using a navigation grade inertial measurement unit (IMU) showed that the estimated yaw angle from the conventional 15-state EKF slowly diverged over time. Furthermore, this phenomenon became more distinct when the initial yaw angle error was larger. In contrast, the estimated yaw angle from the proposed 15-state ST-EKF was significantly more stable and less degraded by large initial yaw angle errors. Long- distance land-vehicle SINS/OD integrated navigation tests also exhibited the ST-EKF's higher positioning and heading accuracy than the EKF.

Robust fading cubature Kalman filter and its application in initial alignment of SINS

Strapdown inertial navigation system (SINS) is a commonly used autonomous positioning instrument. As an integral calculating system, initial alignment is an essential work of SINS. Cubature Kalman filter (CKF) is a common algorithm for nonlinear initial alignment. Under the condition of inaccurate system model and non-Gaussian observation noise, the filter will appear to unstable or even divergence. In order to solve this problem, an anti-jamming improvement suitable for initial alignment is proposed in this paper. In which the prior covariance matrix and the observation noise covariance matrix are tuned by multiple fading factors. A Chi-square test method is designed to check the filter’s state, determining the introducing method of the fading factors autonomously. Experiment results show that, the proposed algorithm performs better in terms of robustness and adaptability even under the condition of inaccurate model and non-Gaussian observation noise.

GAM-Based Mooring Alignment for SINS Based on An Improved CEEMD Denoising Method.

To solve the self-alignment problem of the Strapdown Inertial Navigation System (SINS), a novel adaptive filter based on Complementary Ensemble Empirical Mode Decomposition (CEEMD) is proposed. The Gravitational Apparent Motion (GAM) is used in the coarse alignment, and the problem of obtaining the attitude matrix between the body frame and the navigation frame is attributed to obtaining the matrix between the initial body frame and the current navigation frame using two gravitational apparent motion vectors at different moments. However, the accuracy and time of this alignment method always suffer from the measurement noise of sensors. Thus, a novel adaptive filter based on CEEMD using an -norm to calculate the similarity measure between the Probability Density Function (PDF) of each Intrinsic Mode Function (IMF) and the original signal is proposed to denoise the measurements of the accelerometer. Furthermore, the advantage of this filter is verified by comparing with other conventional denoising methods, such as PDF-based EMD (EMD-PDF) and the Finite Impulse Response (FIR) digital low-pass filter method. The results of the simulation and experiments indicate that the proposed method performs better than the conventional methods in both alignment time and alignment accuracy.

Rapid alignment for SINS based on expansion of observation vectors in polar regions

In polar regions, the rapid convergence of meridians and the small horizontal component of Earth's rotation make traditional North-pointed initial Alignment algorithm (NA) ineffective. While Alignment algorithm based on Pseudo-Earth frame (PA) can solve the problems caused by the rapid convergence of meridians, the observability of Strap-down Inertial Navigation System (SINS) on stationary base is so poor that it takes much time to complete initial alignment. According to this case, in this paper, a novel alignment algorithm based on expansion of observation vectors is proposed to implement rapid initial alignment in polar regions. This paper mainly completes the following works: firstly, a rapid Alignment algorithm based on Expansion of Observation vectors for Pseudo-earth frame (EOPA) is proposed, then the reason for its rapid convergence is explicated by analysis of the error equations; secondly, two observability analysis methods: Singular Value Decomposition (SVD) and the Attitude Dilution Of Precision (ADOP) are adopted to compare the observability of PA with that of EOPA. Finally, semi-physical simulation shows that in polar regions, even in the case of latitude of 89° and initial misalignment angle of 3°, the azimuth misalignment error can be reduced within 0.25° in 40s. It has significant engineering application value.

Rapid Transfer Alignment of SINS with Measurement Packet Dropping based on a Novel Suboptimal Estimator

Transfer alignment (TA) is an important step for strapdown inertial navigation system (SINS) starting from a moving base, which utilises the information proposed from the higher accurate and well performed master inertial navigation system. But the information is often delayed or even lost in real application, which will seriously affect the accuracy of TA. This paper models the stochastic measurement packet dropping as an independent identically distributed (IID) Bernoulli random process, and introduces it into the measurement equation of rapid TA, and the influence of measurement packet dropping is analysed. Then, it presents a suboptimal estimator for the estimation of the misalignment in TA considering the random arrival of the measurement packet. Simulation has been done for the performance comparison about the suboptimal estimator, standard Kalman filter and minimum mean squared estimator. The results show that the suboptimal estimator has better performance, which can achieve the best TA accuracy.

Initial Alignment of SINS Measuring Unit and Estimation of Its Errors Using Satellite Phase Measurements

The paper addresses the problem of initial alignment and periodical estimation of gyro drifts and accelerometer errors in a strapdown inertial navigation system (SINS) on fiber-optic gyros (FOG) of navigation grade onboard a marine vehicle, using satellite phase measurements from multi-antenna equipment. The problem is solved through constructing a tightly-coupled INS/GNSS system which comprises an inertial measuring unit (IMU) of SINS, and a multi-antenna satellite module. The satellite module has two antenna baselines and employs receivers with a common reference oscillator. Based on the SINS data, the ambiguity of phase measurements is excluded, and false measurements are sorted out. The results of joint processing of the bench test data for the navigation grade FOG-based IMU (designed by Concern CSRI Elektropribor, JSC) and a virtual simulated satellite module are presented. The data processing was carried out using the algorithms of integrated system construction in MATLAB (Simulink) package.

A Novel EM Implementation for Initial Alignment of SINS Based on Particle Filter and Particle Swarm Optimization

For nonlinear systems in which the measurement noise parameters vary over time, adaptive nonlinear filters can be applied to precisely estimate the states of systems. The expectation maximization (EM) algorithm, which alternately takes an expectation- (E-) step and a maximization- (M-) step, has been proposed to construct a theoretical framework for the adaptive nonlinear filters. Previous adaptive nonlinear filters based on the EM employ analytical algorithms to develop the two steps, but they cannot achieve high filtering accuracy because the strong nonlinearity of systems may invalidate the Gaussian assumption of the state distribution. In this paper, we propose an EM-based adaptive nonlinear filter APF to solve this problem. In the E-step, an improved particle filter PF_new is proposed based on the Gaussian sum approximation (GSA) and the Monte Carlo Markov chain (MCMC) to achieve the state estimation. In the M-step, the particle swarm optimization (PSO) is applied to estimate the measurement noise parameters. The performances of the proposed algorithm are illustrated in the simulations with Lorenz 63 model and in a semiphysical experiment of the initial alignment of the strapdown inertial navigation system (SINS) in large misalignment angles.

An improved nonlinear filter based on adaptive fading factor applied in alignment of SINS

This paper investigates the non-linear initial alignment for strapdown inertial navigation system(SINS) with main focus on improving the robustness of alignment filter. Conventional Kalman filter (KF) assumes that the statistic characteristics of the system noise are known in advance and keep unchanged during the filtering process. However, it is difficult to predict the noise characteristics in practice, which may cause the degradation in filter performance. In view of this problem, improved fading unscented Kalman filter (UKF) is proposed. The square of the Mahalanobis distance of the innovation vector, which is found to be chi-square distributed, is used as the judging index. Hypothesis test is performed to test the filter state. If the null hypothesis should be rejected, it means that the abnormal noises exist in the system model, and the fading factors should be introduced to rescale the covariance of the innovation vector. The multiple fading factors are calculated by forcing the estimated value of innovation sequence covariance to be equal to its nominal value. Simulation and experiment results show that, the new alignment algorithm performs better in terms of robustness and convergence in the condition of complex measurement noise.

In-Motion Attitude and Position Alignment for Odometer-Aided SINS Based on Backtracking Scheme

In-motion alignment of navigation-grade strapdown inertial navigation system (SINS) combined with odometer (OD) is one of the challenging issues for the land vehicle navigation, while most current in-motion alignment methods still rely on the measurements of the global positioning system or only aim at improving the attitude alignment, thus neglecting the position alignment. Thus, one of the main obstacles during the in-motion alignment for SINS/OD is to autonomously and simultaneously obtain the high-precision attitude and position within specified time. In this paper, an in-motion alignment scheme based on the backtracking scheme is presented to solve this problem. The proposed method consists of two steps. First, an improved optimization-based coarse alignment (IOBCA) is employed to obtain the attitude and position with reasonable precision, and the gravity deflexion error projection in inertial frame caused by the positioning error is diminished, which contributes to better alignment results for the subsequent process. Second, initialized with the alignment results provided by IOBCA, a backtracking-scheme-based fine alignment combined with the Kalman filter is investigated to make a further improvement in the precision of attitude and position, during which the known initial binding position and zero velocity have been utilized again. The car-mounted field experimental results illustrate that the proposed method can not only autonomously improve the precision of attitude within a short time but also simultaneously achieve the position with high precision.

Application of improved fifth-degree cubature Kalman filter in the nonlinear initial alignment of strapdown inertial navigation system.

This paper addresses the state estimation of the nonlinear initial alignment of the strapdown inertial navigation system (SINS), which mainly focuses on the initial alignment on the swaying base and under the in-motion condition with the measurement uncertainties. In order to achieve a higher alignment precision, stronger numerical stability, and lower computational cost for the initial alignment of SINS on the swaying base, a new discrete large azimuth misalignment error model of SINS is established, and an improved fifth-degree cubature Kalman filter (5th-CKF) algorithm is proposed, which combines the 5th-CKF and a simplified dimensionality reduction filtering algorithm. The 5th-CKF is introduced to solve the nonlinear filtering problem, a simplified dimensionality reduction algorithm is derived to reduce the large calculation values of 5th-CKF. Furthermore, under the Bayesian framework, a novel filtering approach named the fifth-degree variational Bayesian (VB) adaptive cubature Kalman filter is deduced for the in-motion alignment with a large azimuth misalignment angle and unknown and time-varying measurement noise statistics, which combines the iterative VB approach and 5th-CKF. The 5th-CKF is exploited to handle the nonlinear initial alignment model, and the VB approach is utilized to iteratively estimate the sufficient statistics of the measurement noise. Mathematical simulation, turntable, and vehicle experiments are performed to demonstrate the effectiveness and the superiority of the proposed approaches.

On the measurement selection for stationary SINS alignment Kalman filters

This paper presents a comprehensive study aiming at the optimal measurement selection for Kalman filters applied to the stationary fine self-alignment of strapdown inertial navigation systems (SINS). On the basis of the definition of nonholonomic constraints, two very important measurement strategies for alignment purposes are investigated and mathematically derived: the standalone “zero velocity update” (ZVU) strategy, and an augmented measurement strategy, formed from the ZVU constraint in addition to the “constant Earth rate and gravity update” (CERGU) constraint. As main contribution of this paper, we analytically prove, trough the Cholesky factorization of the observability information matrix, that the augmented strategy is able to improve the convergence rate of the stationary fine self-alignment Kalman filter. For complying with the SINS rapidity requirement, the augmented measurement strategy is considered superior to the traditional standalone ZVU strategy. Simulated and experimental results confirm the adequacy of the outlined conclusions.