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In this article, a study of state estimation for non-linear Markov jump systems (MJSs) with uncertain transition probabilities (TPs) is investigated. In the authors' method, the uncertainties of TPs are portrayed by intermediate stochastic variables depicted by truncated Gaussian probability density functions (TGPDFs). In order to incorporate the prior knowledge about uncertainties into the filtering process, a skew parameter is firstly inserted into TGPDF to yield skew truncated Gaussian probability density functions (STGPDFs) which contains the original one as a particular case. Then, the state estimation method is derived based on multiple model mechanism together with particle filter using confidence TPs that are obtained by normalising the expectations of STGPDFs. The proposed approach degenerates into the traditional interacting multiple model-particle filter (IMM-PF) when the standard deviations turn to zero. A meaningful example is presented to illustrate the effectiveness of the authors' method.