Although particle filters are extremely effective algorithms for object tracking, one of their limitations is a reliance on an accurate model for the object dynamics and observation mechanism. The limitation is circumvented to some extent by the incorporation of parameterized models in the filter, with simultaneous on-line learning of model parameters, but frequently, identification of an appropriate parametric model is extremely difficult. This paper addresses this problem, describing an algorithm that combines Kernel Recursive Least Squares and particle filtering to learn a functional approximation for the measurement mechanism whilst generating state estimates. The paper focuses on the specific scenario when a training period exists during which supplementary measurements are available from a source that can be accurately modelled. Simulation results indicate that the proposed algorithm, which requires very little information about the true measurement mechanism, can approach the performance of a particle filter equipped with the correct observation model.