一种基于四元数的空间后方交会全局收敛算法

结合四元数在摄影测量中的良好应用,提出一种基于四元数的空间后方交会全局收敛算法。该算法利用四元数描述影像姿态,采用绝对定向和正交投影两种变换来代替中心投影的共线条件方程,再利用非线性方程直接迭代的方法进行求解,从而无需进行线性化,最后从理论上对算法的全局收敛性进行了证明。试验结果表明该算法正确可靠,对外方位元素初值没有要求,真正做到无初值依赖空间后方交会,具有很好的稳定性和适应性。     

四元数的核线影像生成方法

针对现有核线影像生成方法计算量大、计算复杂等缺点,该文提出了一种基于四元数的核线影像生成算法,建立了四元数核线影像模型。推导了四元数共面条件方程线性化误差方程式,在此基础上依次利用两个四元数消除基线分量,实现了原始影像到核线影像的坐标变换;相比于传统欧拉角核线排列算法,四元数在实现姿态描述唯一性的同时避免了繁琐的三角函数计算。利用航空影像和无人机影像进行实验,建立的核线影像上下平均视差在0.4个像素以内,核线影像前方交会的平面和高程精度优于1m,结果表明四元数核线影像模型基本上消除了上下视差,能够满足摄影测量立体观测的要求。     

基于单位四元数描述的单像空间后方交会

在3维空间里,四元数可以非常方便地表示空间方位、空间向量间的旋转、平移和缩放等关系。将四元数理论引入到摄影测量领域,用单位四元数对坐标旋转矩阵进行描述,提出了一种采用单位四元数描述航摄像片位置与姿态的单张像片空间后方交会新方法。该方法与传统方法相比,在平差时避免了频繁的三角函数运算,不仅收敛速度快,而且精度高。     

残差绝对值和最小法在单线阵CCD卫星影像后方交会粗差探测中的应用

利用残差绝对值和最小法进行单线阵CCD卫星影像的后方交会,一般来说,不仅可以克服外方位元素之间的强相关性,而且可以有效地剔除粗差.实验证明该方法简便、稳健、有效.     

基于单位四元数描述的单像空间后方交会

在3维空间里,四元数可以非常方便地表示空间方位、空间向量间的旋转、平移和缩放等关系.将四元数理论引入到摄影测量领域,用单位四元数对坐标旋转矩阵进行描述,提出了一种采用单位四元数描述航摄像片位置与姿态的单张像片空间后方交会新方法.该方法与传统方法相比,在平差时避免了频繁的三角函数运算,不仅收敛速度快,而且精度高.     

残差绝对值和最小法在单线阵CCD卫星影像后方交会粗差探测中的应用

利用残差绝对值和最小法进行单线阵CCD卫星影像的后方交会，一般来说，不仅可以克服外方位元素之间的强相关性，而且可以有效地剔除粗差。实验证明该方法简便、稳健、有效。     

航空线阵摆扫式相机严格成像模型的构建与验证

对航空线阵摆扫式相机严格成像模型进行了深入研究。在分析航空线阵摆扫式相机的结构及成像几何的基础上,建立了合理的坐标系统用于描述相机物像相对运动的光线旋转关系,构建了线阵摆扫式相机的严格成像模型;利用蒙特卡洛法对严格成像模型的各个误差进行仿真,分析了其对几何定位精度的影响;通过模拟影像数据空间后方交会试验,验证了严格成像模型的正确性。     

资源三号测绘卫星传感器校正产品几何模型

资源三号测绘卫星为了获取较大的幅宽和较高的空间分辨率,其三线阵相机和多光谱相机采用了多片CCD拼接成像的方式获取地面影像。如直接提供分片的CCD影像产品,用户难以使用。传感器校正产品解决了CCD影像拼接的问题,拼接后的影像不仅视觉无缝,同时几何无缝。该产品同时解决了多光谱波段间配准的问题,且生产过程中引入的投影差误差和交会误差可以忽略不计。该产品消除了大部分畸变,故拥有极高的RFM替代严密成像几何模型精度。本文利用安平和登封地区的三线阵数据进行验证,试验区三线阵传感器校正产品RFM替代精度优于1%像元,无地面控制点立体定位精度优于15 m,带控制点平面误差在3 m以内,高程误差在2 m之内,且三线阵平差平面定位精度要优于两线阵。     

基于LM方法的大姿态角影像空间后方交会

针对低空遥感影像存在大姿态角度的特点,提出采用Levenberg-Marquardt(LM)方法实现影像空间后方交会模型的收敛解算。基于仿真数据对该方法进行了验证,并与基于单位四元数的无初值依赖算法比较。结果表明,LM方法具有与单位四元数法相当的可靠性;通过选择合适的阻尼因子,LM法迭代效率更高。     

基于模拟数据的航天线阵CCD传感器定标研究

线阵CCD传感器在航天摄影测量中已获得了广泛的应用,但卫星发射上天后由于多种因素,CCD、镜头的各项参数均发生了变化,原来实验室里标定的值将不再适用.此时卫星遥感影像目标定位必须顾及像点的实际偏差,否则将对定位精度产生很大的影响.本文构建了带有内方位参数的严密成像模型.并通过模拟试验证明了单像空间后方交会和自检校区域网...     

基于单位四元数的无初值依赖空间后方交会

为解决基于欧拉角的传统空间后方交会算法对初值强烈依赖的问题,提出一种利用四元数描述姿态的解算方法。本算法采用单位四元数描述旋转矩阵,然后对严格的共线条件方程进行线性化,并按照带有约束条件的间接平差进行迭代解算。试验表明本算法的可靠性和稳定性不依赖于像片位置和姿态的初值,并具有迭代次数少和解算时间短等优点。     

基于Pope-Hinsken算法的空间后方交会

分析了Pope-Hinsken(P-H)算法的基本原理,将其应用于大角度影像的空间后方交会,给出了误差方程和计算方案,并通过对比实验加以验证。结果表明:1)在空间后方交会中采用单位四元数构造旋转矩阵可显著降低算法的初值敏感性;2)与同类方案相比,该方案具有误差方程更简洁、收敛性更强的特点;3)该方案的解算精度与现有方案一致,稳定可靠。     

A global quality measurement of pan-sharpened multispectral imagery

This letter focuses on quality assessment of fusion of multispectral (MS) images with high-resolution panchromatic (Pan) observations. A new quality index suitable for MS imagery having four spectral bands is defined from the theory of hypercomplex numbers, or quaternions. Both spectral and radiometric distortion measurements are encapsulated in a unique measurement, simultaneously accounting for local mean bias, changes in contrast, and loss of correlation of individual bands, together with spectral distortion. Results are presented and discussed on very high-resolution QuickBird data, through comparisons between state-of-the-art and advanced MS+Pan merge algorithms.     

A Quaternion-based Geodetic Datum Transformation Algorithm

This paper briefly introduces quaternions to represent rotation parameters and then derives the formulae to compute quaternion, translation and scale parameters in the Bursa–Wolf geodetic datum transformation model from two sets of co-located 3D coordinates. The main advantage of this representation is that linearization and iteration are not needed for the computation of the datum transformation parameters. We further extend the formulae to compute quaternion-based datum transformation parameters under constraints such as the distance between two fixed stations, and develop the corresponding iteration algorithm. Finally, two numerical case studies are presented to demonstrate the applications of the derived formulae.     

基于欧氏距离测度的激光点云配准

针对激光扫描测量系统得到的多视角点云数据,提出用离散对应特征和迭代最近点(ICP)算法相结合的方法,对点云模型多视配准技术进行了研究。首先给出单位四元数和旋转矩阵的关系以及线性最小二乘法原理;然后利用基于离散对应特征的方法求出刚体变换的一个初值,并用迭代最近点(ICP)算法精确估计刚体变换参数;最后用工件36副真实点云模型的配准结果证明此方法的有效性。     

A dual quaternion-based,closed-form pairwise registration algorithm for point clouds

The representation of similarity transformation in three-dimensional (3D) space, especially of orientation, is a crucial issue in navigation, geodesy, photogrammetry, robot arm manipulation, etc. Considering the large amount of computer resources required by iterative algorithms designed for spatial similarity transformation, the high dependence on initial values of unknown parameters, and the instability of solving transformation parameters for large-angle registration, a closed-form solution for pairwise light detection and ranging (LiDAR) point cloud registration is proposed. In this solution, dual-number quaternions are used to represent the 3D rotation. The relationship between the rotation matrix-based representation of similarity transformation and the dual quaternion-based representation is described first. Considering that the same features from two neighboring stations coincide after pairwise registration, a dual quaternion-based error norm, which is associated with the sum of the position errors, is constructed. Based on theory of least squares and by extreme value analysis of the error norm, detailed derivations of the model and the main formulas are obtained. Once the similarities between the same features from the two neighboring LiDAR stations are constructed, the rotation matrix, the scale parameter, and the translation vector are simultaneously derived. Two experiments are conducted to verify the feasibility and effectiveness of the proposed algorithm. The proposed algorithm has the advantages of simplicity and ease of implementation, making it better than the traditional methods that use matrices to describe spatial rotation. Moreover, it solves the transformation parameters without the initial estimates of unknown parameters, making it better than iterative algorithms. Most importantly, in contrast to unit quaternion-based algorithms, the proposed algorithm solves seven unknown parameters simultaneously. Therefore, it effectively avoids the accumulation of introduced error in calculation and the negative impact from the inappropriate choice of initial values.     

Statistical analysis of two 3-D registration and modeling strategies

The paper deals with the registration and modeling of multiple 3-D profile maps acquired from different viewpoints by light striping. We analyze the propagation of measurement and calibration errors to the registration parameters and further to the reconstructed model of the scene consisting of planar patches. The analysis is performed for two strategies. In the first strategy, the maps are registered simultaneously using the Levenberg–Marquardt method to update the registration parameters and the model computed afterwards while in the second one, the maps are registered sequentially against the model reconstructed up till then using the method of unit quaternions to update the registration parameters. Our statistical analysis thus combines the registration and modeling steps, and in registration, we determine the corresponding points either on the parametric domains of the maps or as closest points in 3-D using the information from the parametric domain to restrict the search for the closest points. We also point out the precise estimation of the covariance matrix of the solution given by the Levenberg–Marquardt method. We illustrate the results of our analysis with real data from a scale model of an urban area.     

Calibrating the GOCE accelerations with star sensor data and a global gravity field model

A reliable and accurate gradiometer calibration is essential for the scientific return of the gravity field and steady-state ocean circulation explorer (GOCE) mission. This paper describes a new method for external calibration of the GOCE gradiometer accelerations. A global gravity field model in combination with star sensor quaternions is used to compute reference differential accelerations, which may be used to estimate various combinations of gradiometer scale factors, internal gradiometer misalignments and misalignments between star sensor and gradiometer. In many aspects, the new method is complementary to the GOCE in-flight calibration. In contrast to the in-flight calibration, which requires a satellite-shaking phase, the new method uses data from the nominal measurement phases. The results of a simulation study show that gradiometer scale factors can be estimated on a weekly basis with accuracies better than 2 × 10⁻³ for the ultrasensitive and 10⁻² for the less sensitive axes, which is compatible with the requirements of the gravity gradient error. Based on a 58-day data set, scale factors are found that can reduce the errors of the in-flight-calibrated measurements. The elements of the complete inverse calibration matrix, representing both the internal gradiometer misalignments and scale factors, can be estimated with accuracies in general better than 10⁻³.     

A bundle adjustment approach with inner constraints for the scaled orthographic projection

Bundle adjustment is a method for simultaneously calculating both the interior and exterior orientation parameters of a set of images, and the object-space coordinates of the observed points. In the case of long focal length lenses and narrow field-of-view (FOV) imaging situations, collinearity based (perspective projection) algorithms may result in linear dependencies between parameters that cause solution instability. The use of a scaled orthographic projection model based on linear algebraic formulations was therefore adopted to reduce this risk. Using quaternions, a new mathematical model is derived that includes the partial derivatives as well as the inner constraint equations for a scaled orthographic bundle adjustment. The model was then tested using two image sets of a single, small vessel (about 6 m length) with a cube target of known dimensions at two distinct ranges; perspective solutions were also calculated for comparison. RMS residual errors of 0.74-0.78 pixels associated with the new method compare favorably to a residual error range of 0.59-0.74 pixels using a perspective bundle adjustment of the same target points. Relative precisions (as a ratio of target size) of between 1:1650 and 1:750 have been achieved at ranges of 375 m and 850 m, respectively, given comparisons with the known cube dimensions. A third image dataset consisting of a network of 16 images was solved with a 1:2200 relative precision showing the new method can successfully handle high redundancy. For the experiments that were conducted, the new method was found to produce less precise results than the perspective bundle solution for a FOV of 0.50-0.65° where the object fills 5-8% of the image. However, it was found to match the precision of the perspective model (with an uncalibrated camera) for a FOV of 0.20-0.30° where the object of interest fills only 1-2% of the full image.