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This paper presents a method for positioning using ultra-wideband impulse radio (UWB-IR) signals that is robust in indoor environments characterized by dense multipath channel with path overlapping. Path overlapping effects arising from multipath in dense cluttered environments decrease the direct path resolution in time domain, and hence induce time-of-arrival (TOA) and angle-of-arrival (AOA) based positioning inaccuracy. To mitigate this problem, system design that is capable of resolving the closely-spaced multipath at low cost is of value. Our method yields the least-squares estimation of joint TOA and AOA with low computational cost. It is based on the spectral observation of beam forming, in which the path overlapping effect is mitigated using multipath-aided acquisition. The computational cost is reduced using in-band power spectrum and accurate initial estimations. The performance is verified both in IEEE 802.15.4a CM3 channel model and in a real environment. Simulation results in CM3 channel model show that the TOA and AOA estimation improvements on average are 2.4cm and 13.1° in the dense multipath scenario. Measurement in an indoor open hall environment shows that the AOA error decreases from 10.6° to 7.2°, and the TOA error decreases from 2.1cm to 1.9cm when the path overlapping effects are mitigated in the range of 21m.