Statistical theory of d.f. fixing

The paper deals with the location of an object of u nknown position, on which bearings are taken from two or more stations whose positions are known, and provides solutions to the two problems:- (a) Given a set of bearings, what is the most probable position of the object? (b) How far from the true position is the position indicated by the ¿fix¿ likely to be? Diagrams are given to show the results of applying the theory to typical practical cases. It is shown that, subject to certain qualifications, reliability of a fix does not depend on the size of the particular ¿cocked hat¿ from which it is derived. It is proposed that the reciprocal of the root-mean-square error expected in the position of the fix should be adopted as the conventional standard quantity for measuring the reliability of a fix.