Accurate positioning in harsh environments can enable many application, such as search-and-rescue in emergency situations. For this problem, ultra-wideband (UWB) technology can provide the most accurate range estimates, which are required for range-based positioning. However, it still faces a problem in non-line-of-sight (NLOS) environments, in which range estimates based on time-of-arrival (TOA) are positively biased. There are many techniques that try to address this problem, mainly based on NLOS identification and NLOS error mitigation. However, these techniques do not exploit all available information from the UWB channel impulse response. In this paper, we propose a novel ranging technique based on kernel principal component analysis (kPCA), in which the selected channel parameters are projected onto nonlinear orthogonal high-dimensional space, and a subset of these projections is then used for ranging. We tested this technique using UWB measurements obtained in a basement tunnel of Linköping university, and found that it provides much better ranging performance comparing with standard techniques based on PCA and TOA.