Multi-modal Edge Cloud Computing (MECC) systems are proliferating in our daily lives. In general, the MECC data is often multi-modal and contains complex high-dimensional information. With tensor algebra tools, the Tensor Train Bayesian Filter (TTBF) framework for high-dimensional and multi-modal analysis is proposed. The framework combines the Tensor Train Decomposition (TTD) with the Bayesian filter, which can fully utilize the inherent structure information of high-dimensional data. Finally, some case studies are provided to demonstrate the application features of the proposed framework.