Algebraic Geodesy and Geoinformatics

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While teaching ‘Introduction to Geodesy I and II’ at Stuttgart University, we identified a significant gap that inspired this book: the necessity of algebra skills, particularly in computer algebra, for various topics in geodesy and geoinformatics. From positioning to transformation issues, a solid understanding of algebra and the use of computer algebra software are essential. This book consolidates fundamental concepts of abstract algebra that are crucial for addressing algebraic problems. It presents and tests algebraic computational algorithms designed to solve nonlinear systems of equations, which are vital for obtaining exact solutions. Although the focus is primarily on geodesy and geoinformatics, the concepts and techniques discussed are relevant to other fields facing algebraic computational challenges. For instance, in engineering, network densification and robotics employ resection and intersection techniques that necessitate algebraic solutions. Solving nonlinear systems is a critical task across various geosciences, including geodesy, geoinformatics, and geophysics, as well as in robotics. Such equations are foundational for operations like ranging, resection, and intersection. Specific examples include the three-dimensional resection problem, which is essential for determining the positions and orientations of sensors such as cameras, theodolites, robots, and scanners.