FangSol

Implements Fang's algorithm for computing the position of a vehicle on a plane from its range differences involving three stations

% Bertrand T. Fang: “Simple Solutions for Hyperbolic and Related Position Fixes”;
% IEEE Transactions on Aerospace and Electronic Systems; September 1990, pp 748-753.
%
% INPUTS
% U Distance between Station 1 and Station 2
% Vx Distance between Station 1 and projection of Station 3 onto x-axis
% Vy Distance between Station 1 and projection of Station 3 onto y-axis
% d12 Difference in vehicle's ranges to Station 1 and Station 2 (r1-r2)
% d13 Difference in vehicle's ranges to Station 1 and Station 3 (r1-r3)
%
% OUTPUTS
% xn Vehicle x coordinate for Negative solution
% yn Vehicle y coordinate for Negative solution
% xp Vehicle x coordinate for Positive solution
% yp Vehicle y coordinate for Positive solution
% type -- Two character discription of solution
% First character
% 'S' ==> Special case, d12 = 0
% 'G' ==> General case, d12 <> 0
% Second character
% '-' ==> Negative solution is correct, Positive solution is extraneous
% '+' ==> Positive solution is correct, Negative solution is extraneous
% 'A' ==> Ambiguous case, Either solution might be correct
% '2' ==> Pathological case, Two solutions are identical and correct
% '1' ==> Pathological case, Negative solution is correct,Positive solution is NaN
% 'E' ==> Error, algorithm cannot find a solution