Abstract: The Kalman filter is an important method in the field of state estimation and data denoising. Because of the high complexity of modern dynamical systems and assumptions' limitation of the traditional Kalman filtering theory, the conventional Kalman filtering methods su er diculty to meet the increasing demand for high-precision data analysis. Firstly, motivated by the analysis on the properties of the conventional Kalman filter, the research of the existing Kalman filtering method is summarized according to di erent system types and noise characterization ways. Secondly, the existing adaptive Kalman filtering system is deeply discussed through di erent adaptive ways based on the fact of the mismatch between model and the real system. Then, the engineering usability analysis of the Kalman filtering is shown for practical systems based on the current research, and some important research development are introduced on observability, observable degree and engineering intelligent Kalman filter theory. Finally, several important research directions are given for smart Kalman filtering.