Initial Alignment Of Strapdown Inertial Navigation System Research Articles

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.

A fast alignment of marine strapdown inertial navigation system based on adaptive unscented Kalman Filter

This study has presented an efficient adaptive unscented Kalman filter (AUKF) with the new measurement model for the strapdown inertial navigation system (SINS) to improve the initial alignment under the marine mooring conditions. Conventional methods of the accurate alignment in the ship’s SINS usually fail to succeed within an acceptable period of time due to the components of external perturbations caused by the movement of sea waves and wind waves. To speed up convergence, AUKF takes into account the impact of the dynamic acceleration on the filter and its gain adaptively tuned by considering the dynamic scale sensed by accelerometers. This approach considerably improved the corrections of the current residual error on the SINS and decreased the influence due to the external perturbations caused by the ship’s movement. Initial alignment algorithm based on AUKF is designed for large misalignment angles and verified by experimental data. The experimental test results show that the proposed algorithm enhanced the convergence speed of SINS initial alignment compared with some state-of-the-art existing approaches.

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.

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.

Application of reverse processing in SINS initial alignment and SINS/GPS integrated navigation

PurposeThe study aims to propose reverse processing solution to improve the performance of strapdown inertial navigation system (SINS) initial alignment and SINS-/global positioning system- (GPS) integrated navigation. The proposed scheme can be well applied in the fields of aircraft and aerospace navigation.Design/methodology/approachFor the SINS alignment phase, a fast initial alignment scheme is proposed: the initial value of reverse filter is determined by the final result of forward filter, and then, the reverse filter is carried out using the stored data. Multiple iterations are performed until the accuracy is satisfied. For the SINS-/GPS-integrated phase, a forward–reverse navigation algorithm is proposed: first, the standard forward filter is used, and then, the reverse filter is carried out using the initial value determined by the forward filter, and the final fusion results are achieved by the weighted smoothing of the forward and reverse filtering results.FindingsThe simulation and the actual test results show that in the initial alignment stage, the proposed reverse processing method can obviously shorten the SINS alignment time and improve the alignment accuracy. In the SINS-/GPS-integrated navigation data fusion stage, the proposed forward–reverse data fusion processing can, obviously, improve the performance of the navigation solution.Practical implicationsThe proposed reverse processing technology has an important application in improving the accuracy of navigation and evaluating the performance of real-time navigation. The proposed scheme can be not only used for SINS-/GPS-integrated system but also applied to other integrated systems for general aviation aircraft.Originality/valueCompared with the common forward filtering algorithm, the proposed reverse scheme can not only shorten alignment time and improve alignment accuracy but also improve the performance of the integrated navigation.

The Direct Quaternion Method in Initial Alignment of SINS

In this paper, the initial quasi-quaternion method of strapdown inertial navigation system (SINS) is proposed, in order to solve the singularity problem of the initial alignment algorithm. And mathematical simulations is conducted and analysed Simulation results show that the method is feasible.

A Fast SINS Initial Alignment Method Based on RTS Forward and Backward Resolution

For the strapdown inertial navigation system (SINS), the procedure of initial alignment is a necessity before the navigation can commence. On the quasi-stationary base, the self-alignment can be fulfilled with the high quality inertial sensors, and the fine alignment is usually executed to improve the alignment performance. Generally, fast estimating of heading misalignment is still a challenge due to the existence of gyro errors. An innovative data processing strategy called forward and backward resolution is proposed for INS initial alignment. The Rauch-Tung-Striebel (RTS) smoothing is applied to obtain the smoothed attitude estimates with the filter information provided by the forward data processing. The obtained attitudes are then treated as aiding measurements to implement the forward resolution with the repeated data set, the converged sensor biases are used as constraints, and the iterative processing is conducted to obtain the updated attitudes. Simulation studies have been conducted to validate the proposed algorithm. The results have shown that the alignment accuracy and convergence rate have been improved with the added RTS aided forward and backward resolution; more stable heading estimates can be obtained by calibrating with estimated gyro bias. A real test with a high quality inertial sensor was also carried out to validate the effectiveness of the proposed algorithm.

A fast initial alignment for SINS based on disturbance observer and Kalman filter

Initial alignment for a strap-down inertial navigation system (SINS) plays an important role in the following navigation and positioning operation. Initial alignment incorporates two stages: coarse and fine. This paper mainly investigates fine alignment for SINS under static base. A new fast SINS initial alignment scheme, a disturbance observer-based Kalman filter (DOBKF), is proposed to estimate the misalignment angles. As the name implies, the DOBKF is composed of a Kalman filter and a disturbance observer (DO). The Kalman filter is used to estimate horizontal misalignment angles, and the DO is applied to estimate the azimuth misalignment angle. In addition, when the estimations from the Kalman filter reach a steady state, they will be used as input for designing the DO. Compared with traditional filters, such as a Kalman filter used in initial alignment, the filter proposed by this paper not only greatly hastens the overall initial alignment process, but has comparable accuracy. Comparing simulation results shows that the proposed filter satisfies the requirement of SINS alignment.

Fuzzy adaptive strong tracking scaled unscented Kalman filter for initial alignment of large misalignment angles.

In the initial alignment process of strapdown inertial navigation system (SINS), large misalignment angles always bring nonlinear problem, which can usually be processed using the scaled unscented Kalman filter (SUKF). In this paper, the problem of large misalignment angles in SINS alignment is further investigated, and the strong tracking scaled unscented Kalman filter (STSUKF) is proposed with fixed parameters to improve convergence speed, while these parameters are artificially constructed and uncertain in real application. To further improve the alignment stability and reduce the parameters selection, this paper proposes a fuzzy adaptive strategy combined with STSUKF (FUZZY-STSUKF). As a result, initial alignment scheme of large misalignment angles based on FUZZY-STSUKF is designed and verified by simulations and turntable experiment. The results show that the scheme improves the accuracy and convergence speed of SINS initial alignment compared with those based on SUKF and STSUKF.

Strap-down Inertial Navigation System Initial Alignment Based on Iterative Square-Root Cubature Kalman Filter

This paper presents an improved Cubature Kalman filter (CKF) for strap-down inertial navigation system (SINS) initial alignment. In order to enhance the stability and precision of the filter, Newton iteration algorithm and square-root strategy are blended into CKF. Iterative Square-root Cubature Kalman Filter (ISRCKF)makes full use of latest measurement information and directly employs the square root of covariance matrix for recursive update in the iterative process. ISRCKF can effectively avoid non-positive covariance matrix and improve the estimation accuracy. Simulation results show that ISRCKF performs well for SINS initial alignment with large azimuth misalignment.

Parameter Identification Method for SINS Initial Alignment under Inertial Frame

The performance of a strapdown inertial navigation system (SINS) largely depends on the accuracy and rapidness of the initial alignment. The conventional alignment method with parameter identification has been already applied widely, but it needs to calculate the gyroscope drifts through two-position method; then the time of initial alignment is greatly prolonged. For this issue, a novel self-alignment algorithm by parameter identification method under inertial frame for SINS is proposed in this paper. Firstly, this coarse alignment method using the gravity in the inertial frame as a reference is discussed to overcome the limit of dynamic disturbance on a rocking base and fulfill the requirement for the fine alignment. Secondly, the fine alignment method by parameter identification under inertial frame is formulated. The theoretical analysis results show that the fine alignment model is fully self-aligned with no external reference information and the gyrodrifts can be estimated in real time. The simulation results demonstrate that the proposed method can achieve rapid and highly accurate initial alignment for SINS.

A Self-Alignment Algorithm for SINS Based on Gravitational Apparent Motion and Sensor Data Denoising.

Initial alignment is always a key topic and difficult to achieve in an inertial navigation system (INS). In this paper a novel self-initial alignment algorithm is proposed using gravitational apparent motion vectors at three different moments and vector-operation. Simulation and analysis showed that this method easily suffers from the random noise contained in accelerometer measurements which are used to construct apparent motion directly. Aiming to resolve this problem, an online sensor data denoising method based on a Kalman filter is proposed and a novel reconstruction method for apparent motion is designed to avoid the collinearity among vectors participating in the alignment solution. Simulation, turntable tests and vehicle tests indicate that the proposed alignment algorithm can fulfill initial alignment of strapdown INS (SINS) under both static and swinging conditions. The accuracy can either reach or approach the theoretical values determined by sensor precision under static or swinging conditions.

A Method for SINS Alignment with Large Initial Misalignment Angles Based on Kalman Filter with Parameters Resetting

In the initial alignment process of strapdown inertial navigation system (SINS), large initial misalignment angles always bring nonlinear problem, which causes alignment failure when the classical linear error model and standard Kalman filter are used. In this paper, the problem of large misalignment angles in SINS initial alignment is investigated, and the key reason for alignment failure is given as the state covariance from Kalman filter cannot represent the true one during the steady filtering process. According to the analysis, an alignment method for SINS based on multiresetting the state covariance matrix of Kalman filter is designed to deal with large initial misalignment angles, in which classical linear error model and standard Kalman filter are used, but the state covariance matrix should be multireset before the steady process until large misalignment angles are decreased to small ones. The performance of the proposed method is evaluated by simulation and car test, and the results indicate that the proposed method can fulfill initial alignment with large misalignment angles effectively and the alignment accuracy of the proposed method is as precise as that of alignment with small misalignment angles.

Moving State Marine SINS Initial Alignment Based on High Degree CKF

A new moving state marine initial alignment method of strap-down inertial navigation system (SINS) is proposed based on high-degree cubature Kalman filter (CKF), which can capture higher order Taylor expansion terms of nonlinear alignment model than the existing third-degree CKF, unscented Kalman filter and central difference Kalman filter, and improve the accuracy of initial alignment under large heading misalignment angle condition. Simulation results show the efficiency and advantage of the proposed initial alignment method as compared with existing initial alignment methods for the moving state SINS initial alignment with large heading misalignment angle.

A Fast SINS Initial Alignment Scheme for Underwater Vehicle Applications

To achieve high Strapdown Inertial Navigation System (SINS) alignment accuracy within a short period of time is still a challenging issue for underwater vehicles. In this paper, a new SINS initial alignment scheme aided by the velocity derived from Doppler Velocity Log (DVL) is proposed to solve this problem. In the stage of the coarse alignment, the velocity of DVL is employed to reduce the impact of the linear motion. With a backtracking framework, the fine alignment runs with the data recorded during the process of the coarse alignment and thus will speed up the overall alignment process. In addition, by using this new scheme, it is equivalent to length the alignment time for both coarse and fine alignments, so the accuracy of the alignments will be improved. In order to reduce the volume of the data that has to be recorded, a new model for SINS fine alignment is derived in the inertial reference frame which makes it feasible for real time applications. The experimental results are presented for both unaided static and in-motion alignment using DVL aiding. It is clearly shown that the proposed method meets the requirement of SINS alignment for underwater vehicles.

Fiber-optic gyros and quartz accelerometers for motion control

In article the opportunity of use strapdown inertial navigation system (SINS) on the base of fiber-optic gyroscopes and quartz accelerometers corrected from star sensors and satellite navigation equipment (SNE) for perspective interplanetary spacecrafts motion control on phases of interplanetary trajectory insertion, trajectory correction, and braking during transition to Mars orbit is investigated. Results of onboard control complex accuracy characteristics estimation are presented at the given dynamic spacecraft scheme which is taking into account the liquid oscillations in tanks and structure elements elasticity. At modelling the errors of measuring devices installation, errors of SINS initial alignment and instrumental errors of SINS sensitive elements, variation of control engines parameters were taken into account. The structure of the developed complex of imitation modelling of interplanetary spacecraft controlled motion is resulted. Estimations of active flight legs realization accuracy were received by a method of statistical modelling of spacecraft controlled motion