This paper describes least squares estimation algorithms used for tracking the physical location of radioactive sources in real time as they are moved around in a facility. We present both recursive and moving horizon nonlinear least squares estimation algorithms that consider both the change in the source location and the deviation between measurements and model predictions. The measurements used to estimate position consist of four count rates reported by four different gamma ray detectors. There is an uncertainty in the source location due to the large variance of the detected count rate, and the uncertainty in the background count rate. This work represents part of a suite of tools which will partially automate security and safety assessments, allow some assessments to be done remotely, and provide additional sensor modalities with which to make assessments. Published by Elsevier Science Ltd.