A filter based on characteristic functions is developed in this paper, to fit to a class of non-Gaussian dynamical systems, which state models and measurement models are all nonlinear and multi-dimensional. The new filter overcomes limitations and expands the application of this kind of filter, which is proved to just fit to one special kind of systems with multi-dimensional linear state models and one-dimensional nonlinear measurement models. Firstly, the filter using characteristic function is introduced and its limitation is analysed. Then, we design the new filter to fit to nonlinear states and multi-dimensional measurements. Thirdly, the matrix format of performance index is presented to match to the new filter gain, and the weighting function vector is given to ensure the uniform boundedness of such a performance index. Finally, the new filter gain can be obtained by minimizing this performance index, and the process of filtering design is accomplished. Simulation examples are given to illustrate the effectiveness of the proposed filter design scheme. (C) 2017 Elsevier Ltd. All rights reserved.