In this work we present a novel approach for describing radio signal spaces for localization algorithms.We first introduce a new metric, the Discretely Distributed Log-H ¨older Metric(DDLHM). The DDLHM is designed to characterize the type and degree of signal distortion relative to lognormal signal-to-distance path models. We first show how the DDLHM can describe and discriminate distortions in an exhaustive set of synthetic signal spaces.We then determine a reduced set of maximally diagnostic distortion parameters. Using only 4% of the maximal set of DDLHMs, we found the reduced set matches with an acceptable degree of error 95% of the time. Using the synthetic reduced set, we characterized a variety of wireless localization algorithms’ behaviors to attenuation, bias,and multipath. We found algorithms made much different tradeoffs between best case and average case error. We then use the DDLHM to identify distortion types in three different physical environments using measured 802.11 signal strengths, and predict the positioning performance of several localization algorithms. Our approach predicts average localization error to within 2 meters of the observed average error. In this work we present a novel approach for describing radio signal spaces for localization algorithms. We first introduce a new metric, the Discretely Distributed Log-H ¨older Metric (DDLHM). The DDLHM is designed to characterize the type and degree of signal distortion Relative to lognormal signal-to-distance path models. We first show how the DDLHM can describe and discriminate distortions in an exhaustive set of synthetic signal spaces.We then determine a reduced set of maximally diagnostic distortion parameters. Using only 4% of the maximal set of DDLHMs, we found the reduced set matches with an acceptable degree of error 95% of the time. Using the synthetic reduced set, we characterized a variety of wireless localization algorithms’ behaviors to attenuation, bias, and multipath. We found algorithms made much then tradeoffs between best case and average case error. We then use the DDLHM to identify distortion types in three different physical environments using measured 802.11 signal strengths, and predict the positioning performance of several localization algorithms. Our approach predicts average localization error to within 2 meters of the observed average error.