In order to improve tracking performance of the single-observer infrared search and tracking (IRST) system, an algorithm called the robust improved Gaussian-sum cubature Kalman filter (RIGSCKF) was proposed. For the initial value fuzzy problem, the cubature Kalman filter framework was firstly divided into a set of weighted sub-filters, each with a different initial value, where the weights were determined by the likelihood function. In the measurement update, the predictive density was split in the direction of the maximum eigenvector and was merged according to sub-filters when nonlinear degree exceeded a threshold. It is certified that the method makes the tracking more accurate. Furthermore, to deal with the contaminated Gaussian noise in the measurements, the weights of outliers were reduced according to equivalent weight function which could improve the innovation covariance efficiently. Simulations show shat the RIGSCKF performs superior accuracy when there are no outliers. On the contrary, when outliers appear, the performance of conventional algorithms degrades rapidly, but that of the RIGSCKF is still accurate and robust.