In this paper, we focus on the application of Compressive Sensing (CS) techniques to Impulse Radio (IR) Ultra-WideBand (UWB) positioning systems under indoor propagation environments. Direct Position Estimation (DPE) approaches can potentially improve the position estimation accuracy of conventional two-step techniques by directly estimating the position coordinates from the observed signal in a single step. Furthermore, DPE does not require a threshold selection upon which accuracy of two-step approaches depend on. Although in the presence of multipath the actual gains are not straight forward, recent evaluation of DPE positioning in IR-UWB system proved accurate positioning estimate gains. However it comes at a cost of higher computational complexity. This paper exploits the sparseness of the problem to reduce the computational load of the positioning estimation process and relax the requirements of the Analog to Digital Converter (ADC) when sampling UWB signals. Based on the fact that the number of unknown targets is small in the discrete spatial domain, this paper incorporates the multiple location hypotheses into an overcomplete basis, which highlights the sparseness of the spatial domain. This fact motivates the use of CS-based sampling and sparsity-based reconstruction techniques to jointly evaluate all possible hypotheses, thus avoiding the traditional position-by-position scanning where the multiple location hypotheses are evaluated independently. In so doing, we not only achieve a significant reduction in computational time but also we relax the sampling requirements.