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Particle filters (PF), as a kind of non-linear/non-Gaussian estimation method, are suffering from two problems in large-dimensional cases, namely particle impoverishment and sample size dependency. Previous studies from the authors have proposed a novel PF algorithm that incorporates ant colony optimisation (PFACO), to alleviate these problems. In this paper the authors will provide a theoretical foundation of this new algorithm; two theorems are introduced to validate that the PFACO introduces smaller Kullback-Leibler divergence (K-L divergence) between the proposal distribution and the optimal one compared to those produced by the generic PF. In addition, with the same threshold level, the PFACO has a higher probability than the generic PF to achieve a certain K-L divergence. A mobile robot localisation experiment is applied to examine the performance between various PF schemes.