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In the full paper, I presume Betelgeuse, Bellatrix, and Rigel were used as the three PLs because the publishers had to get three stars into a small diagram.  Did the author get chance to proof-read their finished product?  The cut is tiny.  The maximum angle between Betelgeuse and Rigel for any state of the sky is only about 20 degrees with Bellatrix somewhere in between.  With perfect altitudes, a fancy maths program might come up with some sort of fix, but the heights measured through a periscopic sextant aren’t going to be anything like perfect.  Without a working diagram of the inside of a current US submarine periscope and the gyro horizon parameters, it’s difficult to say much more. DaveP