Simultaneous estimation of the range and bearing of near field emitters usually involves a multidimensional search. In this paper we examine an alternative algorithm which involves search in the range direction combined with polynomial rooting, which replaces the search in the azimuth direction. The proposed algorithm requires a smaller amount of computation than algorithms based on two-dimensional search. The performance of the algorithm is evaluated by Monte-Carlo simulation, and is compared to the Cramer Rao bound on the bearing/range estimation errors. Formulas for computing the bound are derived in the Appendix.