A novel localization framework is presented based on ultra-wideband (UWB) channel sounding, employing a triangulation method using the geometrical properties of propagation paths, such as time delay of arrival, angle of departure, angle of arrival, and their estimated variances. In order to extract these parameters from the UWB sounding data, an extension to the high-resolution RiMAX algorithm was developed, facilitating the analysis of these frequency-dependent multipath parameters. This framework was then tested by performing indoor measurements with a vector network analyzer and virtual antenna arrays. The estimated means and variances of these geometrical parameters were utilized to generate multiple sample sets of input values for our localization framework. Next to that, we consider the existence of multiple possible target locations, which were subsequently clustered using a Kim-Parks algorithm, resulting in a more robust estimation of each target node. Measurements reveal that our newly proposed technique achieves an average accuracy of 0.26, 0.28, and 0.90 m in line-of-sight (LoS), obstructed-LoS, and non-LoS scenarios, respectively, and this with only one single beacon node. Moreover, utilizing the estimated variances of the multipath parameters proved to enhance the location estimation significantly compared to only utilizing their estimated mean values.