Least Squares Adjustment with a Rank-Deficient Weight Matrix and Its Applicability to Image/Lidar Data Processing

IF 1 4区地球科学 Q4 GEOGRAPHY, PHYSICAL

Photogrammetric Engineering and Remote Sensing Pub Date : 2021-10-01 DOI:10.14358/pers.20-00081r3

Radhika Ravi, A. Habib

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引用次数: 5

Abstract

This article proposes a solution to special least squares adjustment (LSA) models with a rank-deficient weight matrix, which are commonly encountered in geomatics. The two sources of rank deficiency in weight matrices are discussed: naturally occurring due to the inherent characteristics of LSA mathematical models and artificially induced to eliminate nuisance parameters from LSA estimation. The physical interpretation of the sources of rank deficiency is demonstrated using a case study to solve the problem of 3D line fitting, which is often encountered in geomatics but has not been addressed fully to date. Finally, some geomatics-related applications—mobile lidar system calibration, point cloud registration, and single-photo resection—are discussed along with respective experimental results, to emphasize the need to assess LSA models and their weight matrices to draw inferences regarding the effective contribution of observations. The discussion and results demonstrate the vast applications of this research in geomatics as well as other engineering domains.

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缺乏秩权矩阵的最小二乘平差及其在图像/激光雷达数据处理中的适用性

本文提出了一种基于秩缺失权矩阵的特殊最小二乘平差模型的求解方法。讨论了权重矩阵中秩不足的两个来源:由于LSA数学模型的固有特性而自然产生的秩不足，以及人为地消除LSA估计中的干扰参数。通过一个案例研究来解决三维线拟合问题，展示了秩不足来源的物理解释，这是在地理信息学中经常遇到的问题，但迄今为止尚未得到充分解决。最后，讨论了一些与地理信息相关的应用——移动激光雷达系统校准、点云配准和单张照片分割——以及各自的实验结果，以强调评估LSA模型及其权重矩阵的必要性，从而得出有关观测结果有效贡献的推论。讨论和结果表明，该研究在地理信息和其他工程领域的广泛应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Photogrammetric Engineering and Remote Sensing 地学-成像科学与照相技术

CiteScore

1.70

自引率

15.40%

发文量

审稿时长

9 months

期刊介绍： Photogrammetric Engineering & Remote Sensing commonly referred to as PE&RS, is the official journal of imaging and geospatial information science and technology. Included in the journal on a regular basis are highlight articles such as the popular columns “Grids & Datums” and “Mapping Matters” and peer reviewed technical papers. We publish thousands of documents, reports, codes, and informational articles in and about the industries relating to Geospatial Sciences, Remote Sensing, Photogrammetry and other imaging sciences.