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Is there any case study for this localization algorithm using Nelder-Mead method to refer so that it can be implemented in some real-life scenarios? Can you please share any case study papers based on this or any other similar things with you?

In the computed value returned by eps_tdoa3d (in rust), as all the intermediate elements are summed squared, shouldn't the square root be returned?

Can you please update your code with including the solution for solving TDOA in 3D?

In the vincenty inverse function (I've only checked the rust code), when cos_sq_alpha is not different from 0.0 then cos_sq_alpha is set to 0.0, it should be cos_2_sigma_m which is set to 0.0 according to http://www.movable-type.co.uk/scripts/latlong-vincenty.html

It would also be better to compare cos_sq_alpha to be less than an epsilon value than equality to 0.0

The termination condition is

is_finished = (it_cnt < max_iterations) && (tmp1.sqrt() <= precision_threshold);

shouldn't it be ?

is_finished = (it_cnt > max_iterations) || (tmp1.sqrt() <= precision_threshold);

Fixed in this PR where project files has been upgraded to the SDK format and the library is multi targeting net451, net48 and net5.0

I have a doubt regarding the value of the precision threshold for the termination of the iteration. Why did you choose '1E-8' as the precision threshold value? Can I change it into my own value? In what perspective, you choose that value.

In rust (not checked other) code, the build_base_lines iterate over: 0 .. (base_points.len() - 1) and (i+1) .. base_points.len()
shouldn't it be: 0 .. (base_points.len() - 1) and (i+1) .. base_points.len() - 1 ?

I want to know in what perspective, you have chosen 600 as the value for maximum iteration limit. Can I change it to my own?

Eccentricity is computed as (a*a - b*b) / a*a whereas wikipedia is giving sqrt(1 - (b*b)/(a*a)) for definition.
Did you forget the sqrt in your code ?