For the purpose of source localization, we have proposed a constrained weighted least squares (CWLS) source localization method in our companion paper, which uses static sensors by accounting for random uncertainties in sensor positions. This paper is devoted to developing two recursive algorithms to deal with the source localization problem by using time difference of arrival (TDOA) measurements received by mobile sensors. More specifically, the first one uses the current TDOA measurements to estimate the unknown source position and then treats the estimate as a measurement to update the source localization. For the second approach, we estimate an auxiliary variable with the current TDOA measurements and then rearrange the nonlinear TDOA equations into a set of linear measurement equations to update the source localization. An illustrative example is given to demonstrate that the second algorithm outperforms the first one.