In this study, an interval extension method of a bi-iterative is proposed to determine a moving source. This method is developed by utilising the time difference of arrival and frequency difference of arrival measurements of a signals received from several receivers. Unlike the standard Gaussian noise model, the time difference of arrival - frequency difference of arrival measurements are obtained by interval enclosing, which avoids convergence and initialisation problems in the conventional Taylor-series method. Using the bi-iterative strategy, the algorithm can alternately calculate the position and velocity of the moving source in interval vector form. Simulation results indicate that the proposed scheme significantly outperforms other methods, and approaches the Cramer-Rao lower bound at a sufficiently high noise level before the threshold effect occurs. Moreover, the interval widths of the results provide the confidence degree of the estimate.