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Range-based localisation and tracking methods use the time-of-arrival (TOA) between the mobile station and several base stations, but the multipath propagation of non-line-of-sight channels complicates the estimation and processing. For channel modelling, the Gaussian scatterer distribution model has been reported to have a reasonable match between its TOA probability density distribution (PDF) and measured TOA data. In this study, this TOA PDF is adapted, along with selection from multiple motion models of the mobile station, for a new location and tracking algorithm. Since the TOA PDF is non-Gaussian and is a non-linear function of the position of the mobile, particle filtering is used which increases the complexity of the algorithm. The focus is on the tracking performance, and this is evaluated by simulation using idealised statistical channels, allowing direct comparison between different location algorithms. In this context, the presented algorithm is more accurate than the benchmarks of extended Kalman filter tracking, and positioning using least squares.