This paper is concerned with multi-modal data fusion (MMDF) under unexpected modality failures in nonlinear non-Gaussian dynamic processes. An efficient framework to tackle this problem is proposed. In particular, a notion termed modality "\emph{usefulness}", which takes a value of 1 or 0, is used for indicating whether the observation of this modality is useful or not. For $n$ modalities involved, $2^n$ combinations of their "\emph{usefulness}" values exist. Each combination defines one hypothetical model of the true data generative process. Then the problem of concern is formalized as a task of nonlinear non-Gaussian state filtering under model uncertainty, which is addressed by a dynamic model averaging (DMA) based particle filter (PF) algorithm. This DMA algorithm employs $2^n$ models, while all models share the same state-transition function and a unique set of particle values. That makes its computational complexity only slightly larger than a single model based PF algorithm, especially for scenarios in which $n$ is small. Experimental results show that the proposed solution outperforms remarkably state-of-the-art methods. Code and data are available at https://github.com/robinlau1981/fusion.