Ground fault detection in inverter-based microgrid (IBM) systems is challenging, particularly in a real-time setting, as the fault current deviates slightly from the nominal value. This difficulty is reinforced when there are partially decoupled disturbances and modeling uncertainties. The conventional solution of installing more relays to obtain additional measurements is costly and also increases the complexity of the system. In this brief, we propose a data-assisted diagnosis scheme based on an optimization-based fault detection filter with the output current as the only measurement. Modeling the microgrid dynamics and the diagnosis filter, we formulate the filter design as a quadratic programming (QP) problem that accounts for decoupling partial disturbances, robustness to nondecoupled disturbances and modeling uncertainties by training with data, and ensuring fault sensitivity simultaneously. To ease the computational effort, we also provide an approximate but analytical solution to this QP. Additionally, we use classical statistical results to provide a thresholding mechanism that enjoys probabilistic false-alarm guarantees. Finally, we implement the IBM system with Simulink and real-time digital simulator (RTDS) to verify the effectiveness of the proposed method through simulations.