Comments on `Existence and uniqueness of GPS solutions' by J.S.Abel and J.W. Chaffee

The commenter points out that a direct Global Positioning System (GPS) algorithm together with discussions on the existence and uniqueness of the solution appeared in his paper (J. Guidance, Control, and Dynamics, vol.9, p.715-17, Nov./Dec. 1986). Since the GPS solution is reduced to solving a quadratic equation, the existence and uniqueness can be easily tested. J.S. Abel and J.W. Chaffee, in the above-titled paper (ibid., vol.26, no.6, p.748-53, Sept. 1990), show that the GPS solution problem is similar to the hyperbolic-fix problem. The commenter notes that it can be inferred from his later work (ibid., vol.26. no.5, p.748-53, Sept. 1990) that the two solutions exist if and only if the four GPS satellites are coplanar, in which case the two solutions are mirror-symmetric with respect to the GPS plane