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Message:

> Hello everyone,
> 
> first of all, apologies about this long post.
> 
> I'm working on an application that inserts a gyrotheodolite-derived azimuth (final result including its combined standard uncertainty u_Az) as an additional direction observation into an existing JAG3D project (observation group type "Direction", with the orientation unknown disabled so that the value acts as an absolute azimuth). The goal is to simulate how much a network (or a tunnel traverse chain) is tensioned or relaxed by this single additional observation.
> 
> What I'm not sure about is how JAG3D should, internally, most sensibly handle the two limiting cases:
> 
> 1) σ of the gyro direction observation → 0 (essentially a "hard constraint"):
> - Does this effectively only fix the azimuth relationship between the start and end point, while both points otherwise remain free (translation, connection to the rest of the network)? Or is there, in practice/in the source code, a different treatment (e.g. one of the two points effectively behaving like a datum point)?
> - Is there a known numerical lower bound for σ below which the normal equation system becomes unstable/singular? I'm currently only guarding this with a small floor (e.g. 1e-12), but I'm not sure if that matches the approach you'd recommend.
> 
> 2) σ as a real, finite value (derived from an uncertainty budget combining several components):
> - During the adjustment, how is the "tension" from this one direction observation distributed across the other observations connected to the start/end points? Does it depend purely on the weight/redundancy of the overall configuration, or is there any preferential treatment of the start point vs. the end point?
> 
> 3) For the specific use case (gyro azimuth lines along a tunnel drive, some with and some without a forced connection to known points): from your perspective, what would be the methodically cleanest way to introduce such an observation – a highly weighted pseudo-observation with a very small σ, a real observation with a realistic σ, or rather a true constraint equation/datum point construction instead of a weighted observation?
> 
> Thank you very much in advance for your input!
> 
> Best regards

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