The integrate-and-dump filter is a core component of satellite navigation receivers, enabling the tracking of navigation satellite signals and significantly influencing receiver performance. Currently, satellite navigation receivers, particularly onboard unmanned aerial vehicles (UAVs), are vulnerable to spoofing. Whether counterfeit signals can successfully hijack a receiver depends critically on how these signals alter the integrate-and-dump filter output. Existing research on satellite navigation spoofing often uses an output signal model for the integrate-and-dump filter derived from continuous-time integration. However, this model deviates from practical implementation because most modern navigation receivers are built on digital circuits that approximate continuous-time integration through discrete-time accumulation. Consequently, the discrete-time nature of actual hardware introduces errors that are not captured by the conventional continuous-time model. In this study, a mathematical model for the output signal of an integrate-and-dump filter was implemented via discrete-time accumulation. The accuracy of the proposed model was verified through simulations, and a comparative analysis with the traditional continuous-time integration model was conducted to highlight the impact of discretization errors.