机载数字传感器几何标定的模型与算法研究
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摘要
航空数字相机与GNSS/IMU系统结合形成的集成遥感系统,具有数字成像、定位、姿态数据同步获取的能力,解决了全数字化航测成图的首要问题,正逐渐成为航空摄影的主流设备。对成像参数、GNSS/IMU测量及安置误差等进行全面、系统的几何标定,是保证成图精度的关键步骤。
本文将数字航测相机的几何检校作为主要研究对象,解决其中的IMU偏心角、相机参数检校和数字相机自检校等多个关键算法,探索机载数字传感几何检校的技术方法,通过试验验证得出了一些有益的结论。论文完成的主要工作和创新点有:
①详细分析与总结了面阵和多线阵CCD数字相机的各类光学畸变及其表达式,建立了相应的附加参数模型,为数字航测相机的自检校平差提供了理论支持。
②利用GNSS/IMU导航解到外方位元素的转换公式,建立了严格的IMU偏心角模型。采用欧拉角模型、四元数模型和反对称矩阵简化模型进行了IMU偏心角的两步法检校,结果表明本文提出的欧拉角严格模型具有较高的精度。
③采用GNSS/IMU辅助的单片空间后方交会和光束法平差方法,对面阵CCD相机进行了内方位元素的标定,结果均表明GNSS/IMU数据的引入可得到理想而稳定的检校结果。如果GNSS/IMU数据具有较高的精度,利用GNSS/IMU辅助光束法平差方法进行相机内方位元素的检定可不需要地面控制点。
④研究了面阵CCD影像的自检校光束法平差技术,建立了GNSS/IMU辅助光束法自检校平差模型。针对DMC影像通过引入附加参数取得了平面1.0个像元、高程0.4个像元的定位精度,与常规平差方法相比提高幅度分别达到近40%和80%。
⑤基于低阶多项式和定向片内插两种轨道模型,以及ETH和Brown两种附加参数模型建立了机载三线阵影像的自检校光束法平差系统。多架次、多种航线和控制点配置的多组ADS40数据的对比试验表明,自检校平差在三个坐标方向对定位精度的改善分别可达40%、60%和70%以上,并得出了定向片内插是三线阵影像平差的优选模型、ETH和Brown都能有效实现三线阵相机检校的结论。
⑥将四元数引入到三线阵影像的定向片法平差,针对定向片的特点提出了球面线性插值的简化公式和相应的光束法平差算法。试验表明这种简化方法不仅能达到与欧拉角模型相当的定位精度,且显著提高了构建误差方程的效率,同时避免了欧拉角模型的一些缺陷,是三线阵影像平差的另一种可选技术方法。
The integrated remote sensing system of airborne digital camera and GNSS/IMU unit can acquire digital images, position and attitude data simultaneously, which resolves the primary issue of full digital photogrammetric mapping and becomes the mainstream equipment for airborne photography. A complete and systematic geometric calibration for its imaging parameters and GNSS/IMU mounting parameters is the key procedure to ensure final mapping accuracy.
This thesis makes a comprehensive study on the geometric calibration of airborne digital camera. Its aim is to resolve the key algorithms of IMU misalignment angles, camera imaging parameters calibration and digital camera self-calibration, explore the technical methods for airborne digital sensor geometric calibration and draw a few useful conclusions from experimental tests. The main work and innovation of this paper is as follows:
1. Different kinds of optical distortions of frame and multi-line array CCD camera are analyzed and summarized in detail, and corresponding additional parameters is set up, which provides theoretical support for the self-calibration adjustment of airborne digital camera.
2. According to the equations which transform the GNSS/IMU navigation result to photogrammetric exterior orientation elements the rigorous mathematical model of IMU misalignment angles is derived. The Euler angles, unit quaternion and antisymmetric matrix three approaches have been introduced for two-step IMU misalignment calibration, experimental results show that the rigorous IMU misalignment mathematical model described by Euler angles proposed in this paper has better precision.
3. GNSS/IMU supported single image resection and bundle adjustment two methods have been used for the interior orientation parameters calibration of frame CCD camera. Tests show that ideal and stable calibration results can be obtained with the introduction of GNSS/IMU data. If the exterior orientation parameters are measured by GNSS/IMU with high precision, interior orientation calibration with GNSS/IMU may not require ground control points.
4. The self-calibration bundle adjustment of frame CCD images is investigated and GNSSS/IMU supported self-calibration bundle adjustment is set up. With the introduction of addition parameters the accuracy of 1 pixel on plane and 0.4 pixels on height can be obtained using DMC images, and corresponding precision promotion is reach to near 40% and 80% respectively.
5. Based on low-order polynomial and orientation image interpolation two trajectory models and ETH and Brown these two kinds of additional parameters, the self-calibration bundle adjustment system of airborne three-line array images is established. Comparative tests have proved using multiple groups of ADS40 with different flights, different strips and different ground control point configurations that the precision promotion with self-calibration reaches to over 40%, 60% and 70% in three coordinate components. The conclusion that orientation image is the preferable adjustment model for three-line array images and both ETH and Brown are effective additional parameter models for the geometric calibration of three-line camera is drawn.
6. The quaterion is introduced into the bundle adjustment with orientation image method. According to the characteristics of orientation images the simplified Spherical linear interpolation (Slerp) formulas are derived and corresponding bundle adjustment algorithm is proposed. Experimental results prove that this simplified approach can not only obtain equivalent position accuracy compared to traditional Euler angles but also improve the efficiency of error equations construction remarkably, at the same time the defects of Euler angles are avoided, so provides an alternative method for the adjustment of three-line images.
本文将数字航测相机的几何检校作为主要研究对象,解决其中的IMU偏心角、相机参数检校和数字相机自检校等多个关键算法,探索机载数字传感几何检校的技术方法,通过试验验证得出了一些有益的结论。论文完成的主要工作和创新点有:
①详细分析与总结了面阵和多线阵CCD数字相机的各类光学畸变及其表达式,建立了相应的附加参数模型,为数字航测相机的自检校平差提供了理论支持。
②利用GNSS/IMU导航解到外方位元素的转换公式,建立了严格的IMU偏心角模型。采用欧拉角模型、四元数模型和反对称矩阵简化模型进行了IMU偏心角的两步法检校,结果表明本文提出的欧拉角严格模型具有较高的精度。
③采用GNSS/IMU辅助的单片空间后方交会和光束法平差方法,对面阵CCD相机进行了内方位元素的标定,结果均表明GNSS/IMU数据的引入可得到理想而稳定的检校结果。如果GNSS/IMU数据具有较高的精度,利用GNSS/IMU辅助光束法平差方法进行相机内方位元素的检定可不需要地面控制点。
④研究了面阵CCD影像的自检校光束法平差技术,建立了GNSS/IMU辅助光束法自检校平差模型。针对DMC影像通过引入附加参数取得了平面1.0个像元、高程0.4个像元的定位精度,与常规平差方法相比提高幅度分别达到近40%和80%。
⑤基于低阶多项式和定向片内插两种轨道模型,以及ETH和Brown两种附加参数模型建立了机载三线阵影像的自检校光束法平差系统。多架次、多种航线和控制点配置的多组ADS40数据的对比试验表明,自检校平差在三个坐标方向对定位精度的改善分别可达40%、60%和70%以上,并得出了定向片内插是三线阵影像平差的优选模型、ETH和Brown都能有效实现三线阵相机检校的结论。
⑥将四元数引入到三线阵影像的定向片法平差,针对定向片的特点提出了球面线性插值的简化公式和相应的光束法平差算法。试验表明这种简化方法不仅能达到与欧拉角模型相当的定位精度,且显著提高了构建误差方程的效率,同时避免了欧拉角模型的一些缺陷,是三线阵影像平差的另一种可选技术方法。
The integrated remote sensing system of airborne digital camera and GNSS/IMU unit can acquire digital images, position and attitude data simultaneously, which resolves the primary issue of full digital photogrammetric mapping and becomes the mainstream equipment for airborne photography. A complete and systematic geometric calibration for its imaging parameters and GNSS/IMU mounting parameters is the key procedure to ensure final mapping accuracy.
This thesis makes a comprehensive study on the geometric calibration of airborne digital camera. Its aim is to resolve the key algorithms of IMU misalignment angles, camera imaging parameters calibration and digital camera self-calibration, explore the technical methods for airborne digital sensor geometric calibration and draw a few useful conclusions from experimental tests. The main work and innovation of this paper is as follows:
1. Different kinds of optical distortions of frame and multi-line array CCD camera are analyzed and summarized in detail, and corresponding additional parameters is set up, which provides theoretical support for the self-calibration adjustment of airborne digital camera.
2. According to the equations which transform the GNSS/IMU navigation result to photogrammetric exterior orientation elements the rigorous mathematical model of IMU misalignment angles is derived. The Euler angles, unit quaternion and antisymmetric matrix three approaches have been introduced for two-step IMU misalignment calibration, experimental results show that the rigorous IMU misalignment mathematical model described by Euler angles proposed in this paper has better precision.
3. GNSS/IMU supported single image resection and bundle adjustment two methods have been used for the interior orientation parameters calibration of frame CCD camera. Tests show that ideal and stable calibration results can be obtained with the introduction of GNSS/IMU data. If the exterior orientation parameters are measured by GNSS/IMU with high precision, interior orientation calibration with GNSS/IMU may not require ground control points.
4. The self-calibration bundle adjustment of frame CCD images is investigated and GNSSS/IMU supported self-calibration bundle adjustment is set up. With the introduction of addition parameters the accuracy of 1 pixel on plane and 0.4 pixels on height can be obtained using DMC images, and corresponding precision promotion is reach to near 40% and 80% respectively.
5. Based on low-order polynomial and orientation image interpolation two trajectory models and ETH and Brown these two kinds of additional parameters, the self-calibration bundle adjustment system of airborne three-line array images is established. Comparative tests have proved using multiple groups of ADS40 with different flights, different strips and different ground control point configurations that the precision promotion with self-calibration reaches to over 40%, 60% and 70% in three coordinate components. The conclusion that orientation image is the preferable adjustment model for three-line array images and both ETH and Brown are effective additional parameter models for the geometric calibration of three-line camera is drawn.
6. The quaterion is introduced into the bundle adjustment with orientation image method. According to the characteristics of orientation images the simplified Spherical linear interpolation (Slerp) formulas are derived and corresponding bundle adjustment algorithm is proposed. Experimental results prove that this simplified approach can not only obtain equivalent position accuracy compared to traditional Euler angles but also improve the efficiency of error equations construction remarkably, at the same time the defects of Euler angles are avoided, so provides an alternative method for the adjustment of three-line images.
引文
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