A computer-implemented method and device for determining a user position, implemented in a user handheld computing device programmed to perform the method. The method includes solving for the position of a user based on ranges, which are computed by estimating power loss between a user and a number of Wi-Fi Access Points. Embodiments of the present invention includes a method that is designed to accommodate the non-linear nature of solving a position solution using power estimates. This method includes solving a two-dimensional solution grid of position residuals, or magnitudes of error between true and computed ranges, using signal strength measurements from multiple Wi-Fi access points in order to determine local minima of the position residuals indicating a user position. Standard approaches in the area such as a Least Squares Solution overly simplify the non-linear components resulting in poor performance.