The constant gain Kalman filter (CGKF) is always a good choice for applications with limited computational power. The traditional CGKF for nonlinear systems is usually designed using the local linearization at the operation point of the system, which cannot guarantee the stability and performance globally and is even unsuitable for the system without operation points. To globally ensure the performance, this paper presents a novel CGKF design framework for general nonlinear systems, the key of which includes the single-domain nonlinear filtering and segmentation over domain of interest (DOI). The estimation error system is firstly transformed into a polytopic system through a global linearization procedure, such that the CGKF is formulated by linear matrix inequalities (LMIs). The prior polytopic linearization of the given nonlinear system is obtained by tensor product (TP) techniques, which is capable of manipulating the polytopic linearization for the conservativeness reduction. Because it is too conservative to share a common filter gain over the whole DOI, the clustering technique is applied to segment the DOI so that the filter can be finalized with multiple gains, each of which corresponds to one specific sub-domain. Finally, the effectiveness of the CGKF is verified by the detailed design example.