Rigorous Computation of Classical Horizontal Geodetic Networks

TL;DR

This paper compares two rigorous mathematical models for processing classical horizontal geodetic networks, highlighting their differences and practical implications in terms of accuracy and simplicity.

Contribution

It introduces a new planar network adjustment model with simple, universal ground-to-grid reductions applicable across map projections.

Findings

Differences between models are minimal and practically negligible.

The new model simplifies computations without sacrificing accuracy.

Differences are due to stochastic model variations, not the core adjustment process.

Abstract

This paper examines mathematical models for processing classical horizontal geodetic (triangulation and trilateration) networks. Two rigorous parametric adjustment models are discussed. The first one is a well-known model of adjustment in the geodetic coordinate system. This model is completely rigorous (functional and stochastic parts) and uses unreduced distance and direction observations. The proposed alternative is a model of planar network adjustment with closed-form reductions of observations directly to the mapping plane. These ground-to-grid reductions are simple and universal, regardless of which map projection is used. Slightly different results of the planar network adjustment are obtained. The differences are attributed to a nonrigorous stochastic model. In theory, the stochastic properties of the reduced observations should also be adapted. However, these differences are very small and can always be neglected in geodetic and surveying practice.