Analysing Willerding’s formula for solving the planar three point resection problem
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Gerhard Heindl
Abstract
The main mathematical problem in the planar three point resection problem of surveying is to find a necessary and sufficient condition that a point on a plane is uniquely determined if the directions from that point to three given points are known only up to an unknown offset. It will be shown in this paper that such a condition is the applicability of Willerding’s formula for computing the point in question, and that this condition is equivalent to the well-known necessary condition that the four considered points are not located on a circle or a line. Because of this result, the easy evaluation and the short derivation of Willerding’s formula, it can be expected, that this formula will be widely used in surveying, and also for autonomous robot localization.
References
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© 2019 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Research Articles
- Enhancing the predictability of least-squares collocation through the integration with least-squares-support vector machine
- Meridian convergence: An alternate methodology
- Analysing Willerding’s formula for solving the planar three point resection problem
- Contribution of satellite altimetry in modelling Moho density contrast in oceanic areas
- Estimations of GNSS receiver internal delay using precise point positioning algorithm
- Trilateration approaches for seamless out-/indoor GNSS and Wi-Fi smartphone positioning
- Accounting for the differential inter-system bias (DISB) of code observation in GPS+BDS positioning
Artikel in diesem Heft
- Frontmatter
- Research Articles
- Enhancing the predictability of least-squares collocation through the integration with least-squares-support vector machine
- Meridian convergence: An alternate methodology
- Analysing Willerding’s formula for solving the planar three point resection problem
- Contribution of satellite altimetry in modelling Moho density contrast in oceanic areas
- Estimations of GNSS receiver internal delay using precise point positioning algorithm
- Trilateration approaches for seamless out-/indoor GNSS and Wi-Fi smartphone positioning
- Accounting for the differential inter-system bias (DISB) of code observation in GPS+BDS positioning
