Compact torus (CT) injection is one of the most promising methods for the central fuelling of next-generation reactor-grade fusion devices due to its high density, high velocity, and self-contained magnetised structure. A newly compact torus injector (CTI) device in Keda Torus eXperiment (KTX), named KTX-CTI, was successfully developed and tested at the University of Science and Technology in China. In this study, first, we briefly introduce the basic principles and structure of KTX-CTI, and then, present an accurate circuit model that relies on nonlinear regression analysis (NRA) for studying the current waveform of the formation region. The current waveform, displacement, and velocity of CT plasma in the acceleration region are calculated using this NRA-based one-dimensional point model. The agreement between the model results and the experimental results is better than in the previous general model results estimated by the device dimensions in previous. The next-step upgrading reference scheme of the KTX-CTI device is preliminarily investigated using this NRA-based point model. This research can provide insights for the development of experiments and future upgrades of the device.