Accurate and robust positioning in multipath environments can enable many applications, such as search-and-rescue and asset tracking. For this problem, ultra-wideband (UWB) technology can provide the most accurate range estimates, which are required for range-based positioning. However, UWB still faces a problem with non-line-of-sight (NLOS) measurements, in which the range estimates based on time-of-arrival (TOA) will typically be positively biased. There are many techniques that address this problem, mainly based on NLOS identification and NLOS error mitigation algorithms. However, these techniques do not exploit all available information in the UWB channel impulse response. Kernel-based machine learning methods, such as Gaussian Process Regression (GPR), are able to make use of all information, but they may be too complex in their original form. In this paper, we propose novel ranging methods based on kernel principal component analysis (kPCA), in which the selected channel parameters are projected onto a nonlinear orthogonal high-dimensional space, and a subset of these projections is then used as an input for ranging. We evaluate the proposed methods using real UWB measurements obtained in a basement tunnel, and found that one of the proposed methods is able to outperform state-of-the-art, even if little training samples are available.