Techniques for providing an improved position estimate for a device in instances of relatively large dilution of precision. In a method, position estimates for a number of transmitters (e.g., GPS satellites and/or base stations) and a set of initial measurements (e.g., pseudo-ranges) are initially received. An Update Vector for a current device position estimate is computed. Non-convergence of the current device position estimate toward a target position estimate is detected and, if true, the Update Vector is adjusted (e.g., reduced in magnitude by a scaling factor) to increase the likelihood of convergence to the target position estimate. The current device position estimate is then updated based on the (possibly adjusted) Update Vector. Non-convergence may be detec ted based on the number of iterations performed without reaching the target position estimate and/or phase reversal in two consecutive Update Vectors. The scaling factor may be increased with each detected event indicative of non-convergence.