SINS attitude algorithm based on moving-window overdetermined polynomial fitting of gyro outputs

The attitude algorithm is the most important part of the whole strapdown inertial navigation (SINS) processing. It calculates the attitude of certain parameterization by integrating the gyro outputs or measurements in a specifically tailored way according to the attitude kinematic differential equation. The measurements or some angular velocity models obtained by fitting these measurements are often assumed free of errors in order to assess the numerical errors only. However, the gyro outputs and hence the models from them are by no means free of measurement errors. It is more often than not that the measurement errors dominate the numerical ones in practice. In this study, with coping with the measurement errors as the focus, we aim to improve the angular velocity model which is used as input in an attitude integration algorithm. This is achieved by exploiting the potential of overdetermined least-squares polynomial fitting. In order to avoid reducing the update rate by incorporating more measurements, the moving window trick is employed to re-use measurements in the previous update interval. The conventional attitude algorithm with second-order approximation in solving the differential equation of the equivalent rotation vector is employed as an example; however, the proposed method can be readily applied to other parameterizations such as direction cosine matrix, quaternion or Rodrigues parameters, and other high order approximations in solving the differential equation widely studied recently.

A general method for rotational averages

The theory of nonlinear spectroscopy on randomly oriented molecules leads to the problem of averaging molecular quantities over random rotation. We solve this problem for arbitrary tensor rank by deriving a closed-form expression for the rotationally invariant tensor of averaged direction cosine products. From it, we obtain some useful new facts about this tensor. Our results serve to speed the inherently lengthy calculations of nonlinear optics.

Immersion and Invariance Adaptive Control for Spacecraft Pose Tracking via Dual Quaternions

This paper addresses the simultaneous attitude and position tracking of a target spacecraft in the presence of general unknown bounded disturbances in the framework of dual quaternions, which provides a concise and integrated description of the coupled rotational and translational motions. By virtue of the newly introduced dual direction cosine matrix, the dimension of the dual quaternion-based relative motion dynamics written in vector/matrix form can be lowered to six. Treating the disturbances as unknown parameters, a modular adaptive pose tracking control scheme composed of two separately designed parts is then derived. One part is the adaptive disturbance estimator designed based on the immersion and invariance theory. Driven by the disturbance estimation errors, it can realize exponential convergence of the estimations and has the nice “parameter lock” property, which can hardly be expected in the conventional certainty equivalent adaptive controllers. The other part is a proportional-derivative-like pose tracking controller where the estimated disturbances are directly used. The closed-loop stability of the relative motion system under different kinds of disturbances is proven by Lyapunov stability analysis. Simulations and comparisons with two previous dual quaternion-based controllers demonstrate the novel features and performance improvements of the proposed control scheme.

Error Analysis of Accelerometer- and Magnetometer-Based Stationary Alignment

This paper revisits the stationary attitude initialization problem, i.e., the stationary alignment, of Attitude and Heading Reference Systems (AHRSs). A detailed and comprehensive error analysis is proposed for four of the most representative accelerometer- and magnetometer-based stationary attitude determination methods, namely, the Three-Axis Attitude Determination (TRIAD), the QUaternion ESTimator (QUEST), the Factored Quaternion Algorithm (FQA), and the Arc-TANgent (ATAN). For the purpose of the error analysis, constant biases in the accelerometer and magnetometer measurements are considered (encompassing, hence, the effect of hard-iron magnetism), in addition to systematic errors in the local gravity and Earth magnetic field models (flux density magnitude, declination angle, and inclination angle). The contributions of this paper are novel closed-form formulae for the residual errors (normality, orthogonality, and alignment errors) developed in the computed Direction Cosine Matrices (DCM). As a consequence, analytical insight is provided into the problem, allowing us to properly compare the performance of the investigated alignment formulations (in terms of ultimate accuracy), as well as to remove some misleading conclusions reported in previous works. The adequacy of the proposed error analysis is validated through simulation and experimental results.

Attitude reconstruction from strap-down rate gyros using power series

This paper introduces a power series based method for attitude reconstruction from triad orthogonal strap-down gyros. The method is implemented and validated using quaternions and direction cosine matrix in single and double precision implementation forms. It is supposed that data from gyros are sampled with high frequency and a fitted polynomial is used for an analytical description of the angular velocity vector. The method is compared with the well-known Taylor series approach, and the stability of the coefficients’ norm in higher-order terms for both methods is analysed. It is shown that the norm of quaternions’ derivatives in the Taylor series is bigger than the equivalent terms coefficients in the power series. In the proposed method, more terms can be used in the power series before the saturation of the coefficients and the error of the proposed method is less than that for other methods. The numerical results show that the application of the proposed method with quaternions performs better than other methods. The method is robust with respect to the noise of the sensors and has a low computational load compared with other methods.

MIDDLE RESOLUTION REMOTE SENSING IMAGE CHANGE DETECTION BASED ON VECTOR ANALYSIS OF MIDLINE CHANGE

The extraction and timely updating of land use /cover information is a key issue in remote sensing change detection. The change vector analysis (CVA) is a better method of change detection. However, the CVA method is the blindness of artificial choice of threshold. Moreover, the direction cosine of CVA cannot represent the unique point in change vector space and it can’t distinguish the change category effectively. In order to avoid this defect, the midline vector is added to CVA method. In this paper, we use the midline change vector analysis (MCVA) method to detect the land use /cover change in multi temporal remote sensing images. We proposed the two-step threshold method to get the optimal threshold and determine the change and the unchanged region of the difference remote sensing image. We chose Hefei city of Anhui Province as the study area, and adopted two Landsat5 TM images in 2000 and 2008 year as experiment data. We use the MCVA and two-step threshold method to achieve remote sensing change detection. In order to compare the detection accuracy between MCVA method and the traditional post classification comparison method, the paper choose the same area (178 pixels × 180 pixels) in the two images to analyse the accuracy, and compare the accuracy of MCVA method with that of the traditional post classification comparison method based on SVM. The experiment results show that the MCVA method has higher overall accuracy, lower allocation disagreement and quantity disagreement. What’s more, the overall accuracy of MCVA method can reach nearly 60%, much higher than the traditional post classification comparison method (less than 40%). And the MCVA method can effectively avoid the problem of change vector direction cosine values are not unique, and the result is much better than the traditional post classification (SVM) comparison method. It indicates that MCVA is a more effective method in land use / cover change detection for middle resolution multispectral images.

Performance Evaluation of Direction Cosine Matrix and Madgwick’s as 3D Orientation Estimation Algorithm for Estimating Ground Contour

Contour interval is elevation difference between two contour lines that are adjacent and parallel. Ground Contour interval is an important information that must be provided in a construction. Ground contour interval estimation problem could be viewed as a 3D trajectory estimation problem. One framework, called dead reckoning, is often used for motion (position and orientation) tracking of a mobile systems over time. Dead reckoning requires a precise 3D orientation estimation algorithm. Two competing algorithms are Direction Cosine Matrix and Madgwick’s. To ensure the 3D trajectory estimation gives an accurate result, these two algorithms must be carefully and thoroughly evaluated. This research is part of a complete research on the development of a ground contour estimation and only focuses on comparison between two 3D orientation estimation algorithm.