1. A GPS positioning method for estimating a pseudo range from a GPS signal, comprising the steps of: (a) acquiring a signal sample by receiving said GPS signal; (b) acquiring a pseudo range dependent function which is a function of pseudo range in proportion to a marginal posterior probability distribution function of pseudo range from said signal sample on the basis of a condition defined by a predetermined working hypothesis; and (c) determining a value of pseudo range which gives the maximum value of said pseudo range dependent function as an estimated pseudo range wherein said pseudo range dependent function includes a hyperbolic cosine function.