Minimum Curvature:
HawkEye uses the minimum curvature method for surveys. The difference between the curvature-radius and minimum-curvature methods is that the curvature radius uses the inclination change for the course length to calculate displacement in the horizontal plane (TVD is unaffected), whereas the minimum curvature method uses the dog-leg severity (DLS) to calculate displacements in both planes. Minimum curvature is considered to be the most accurate method, but it does not lend itself easily to normal, hand-calculation procedures.
ISCWSA:
The ISCWSA website is home to a number of valuable resources, including the mathematical error models used by HawkEye.
At their website, you can also find a very informative free e-book on wellbore positioning: Link to the ebook.
Additionally, there is an informative video which encapsulates the information from the ebook: Link to the video.