We consider tracking a moving target in a wireless communication system that is based on the radio signal. Considering a bounded workspace with many unknown obstacles, we handle tracking a non-cooperative transmitter using multiple signal receivers. Here, a non-cooperative transmitter is a transmitter whose signal emission time is not known in advance. We consider a time difference of arrival (TDOA) location problem, which locates the transmitter by processing the signal measurement time at multiple receivers. In tracking a non-cooperative transmitter, non-line-of-sight (NLOS) errors occur if obstacles block the LOS line connecting the receiver and the moving transmitter. Our article addresses how to track a moving transmitter while decreasing the NLOS error in TDOA-only measurements. We propose an algorithm to localize a transmitter while decreasing the NLOS error in TDOA measurements. For tracking a moving transmitter in real time, we integrate the proposed localization algorithm and the interacting multiple model Kalman filter (IMM KF). As far as we know, our article is novel in tracking a moving transmitter based on TDOA-only measurements in an unknown mixed LOS/NLOS workspace. We show that the proposed filter considerably decreases the NLOS errors in TDOA-only measurements while running fast. Therefore, the proposed tracking scheme is suitable for tracking a moving transmitter in real time. Through MATLAB simulations, we show that the proposed filter outperforms other state-of-the-art TDOA filters, considering both time efficiency and tracking accuracy.