In the field application of WiFi external radiation source radar, the location of the indoor radiation source needs to be acquired in real-time. Through detailed analysis of the reflection mode and characteristics of the signal in the indoor environment, the first reflected signal is adopted to establish the Time Difference Of Arrival(TDOA) model of the WiFi radiation source measurement, and the equation is solved by deriving the coordinates of the radiation source. For this nonlinear equation, Taylor expansion is first employed to linearize it at the initial value; and then Gauss-Newton iteration method is adopted to estimate the radiation source coordinates, which has a faster convergence rate. Simulation analysis shows that the proposed algorithm can realize positioning of indoor radiation source, and the accuracy loss caused by the linearization of the equation can be quickly compensated by iteration.