Abstract: A new analytic method for analyzing the stability of hyperbolic intersecting algorithm is given,which is a base principle of underwater GPS positioning system.The formula to resolve underwater target's coordinates are derived under polar coordinates system.Based on the formula,a set of analytic equations are deduced.Numerical tests show that the method is feasible and effective.The results reveal that there exists distinct area in which the hyperbolic intersection algorithm becomes instable when all buoys distribute on an un-radiate network.Because of weak constrains in depth direction,the accuracy of depth resolution is usually got tremendously bad.