What type of coordinate system is this?
The document is about navigation.

By using an online OCR tool (I used this one which is not so good) on page 177 of the document, and then translating from Ukrainian using Google Translate:

  

... I can confirm @Federico 's suggestion: This figure doesn't introduce a new coordinate system, it just tells about rotating a good ol' geographic coordinate system to facilitate navigation / calculation.

A GCS is defined by its equator, rotating it means the equator is not anymore the Earth equator.

Such frame transformation is also used for INS (SINS) to minimize the accumulation of rounding errors. Just changing the frame orientation allows a better use of the same sensors.



This document says, with fig 7.7, that in some cases, depending on the type of mission or route of the aircraft, it is appropriate to rotate the usual GCS (latitude, longitude) to facilitate calculations and increase accuracy of the results. 

An example is, when following a great circle (orthodromy), to align latitude and longitude so that the system equator is parallel to the great circle to follow.

You will easily improve both the OCR rendering and the translation by spending some time on it.



I made this answer a community wiki, so anyone can improve it.