In this thesis, an algorithm based on frequency-space domain MUSIC method is presented for estimating the propagation delay of a wireless multipath channel.For indoor geolocation systems, the time-of-arrival (TOA) is the most popular technique for accurate positioning system. The basic idea in TOA-based techniques is to accurately estimate the propagation delay of the radio signal arriving from the direct line-of-sight (DLOS) path. However, dense multipath environments may cause unresolved paths, and yield an error in the estimation of the DLOS path. UWB (Ultra-wideband) technology provides an excellent means for wireless positioning due to its high resolution capability in the time domain. Its ability to resolving multipath components makes it possible to obtain accurate location estimates. In this thesis, we investigate the use of UWB signals in positioning and combine frequency-domain MUSIC algorithm. At the same time, the structure of time-space-time method is studied. In addition, we propose a frequency-space domain MUSIC algorithm, called FSF-MUSIC algorithm, and use the spatial smoothing technique to improve the performance of the algorithm. For a two-multipath case, analysis and simulation results of multipath resolvability and the variance of estimation errors of signal arrival time are discussed.