Recognizing and tracking the targets located behind walls through impulse radio ultra-wideband (IR-UWB) radar provides a significant advantage, as the characteristics of the IR-UWB radar signal enable it to penetrate obstacles. In this study, we design a through-wall radar system to estimate and track multiple targets behind a wall. The radar signal received through the wall experiences distortion, such as attenuation and delay, and the characteristics of the wall are estimated to compensate the distance error. In addition, unlike general cases, it is difficult to maintain a high detection rate and low false alarm rate in this through-wall radar application due to the attenuation and distortion caused by the wall. In particular, the generally used delay-and-sum algorithm is significantly affected by the motion of targets and distortion caused by the wall, rendering it difficult to obtain a good performance. Thus, we propose a novel method, which calculates the likelihood that a target exists in a certain location through a detection process. Unlike the delay-and-sum algorithm, this method does not use the radar signal directly. Simulations and experiments are conducted in different cases to show the validity of our through-wall radar system. The results obtained by using the proposed algorithm as well as delay-and-sum and trilateration are compared in terms of the detection rate, false alarm rate, and positioning error.