To tackle the inherent high nonlinearity of motion equation and observation equation of radiation source, a GS (Gaussian-sum) based 5CKF (5th-order cubature Kalman filter) tracking algorithm, referred to as GS-5CKF, was proposed. It consists of multiple parallel 5CKFs, which were initialized through partitioning the candidate source positions determined by the time difference of arrival measurement at the beginning of the tracking process with respect to the source latitude. The linear combination of filter outputs was conducted to estimate the motion state of radiation source. A new nonlinearity measure was advocated, on the basis of which a filtering splitting and merging procedure was developed to further enhance the performance of GS-5CKF while keeping its computational complexity fixed. Simulation results show that: compared with the tracking algorithms using the single 5CKF and the GS-3CKF, the newly proposed GS-5CKF technique exhibits higher source geolocation accuracy.