For additive actuator and sensor faults, we propose a systematic method to design a state-space fault estimation filter directly from Markov parameters identified from fault-free data. We address this problem by parameterizing a system-inversion-based fault estimation filter with the identified Markov parameters. Even without building an explicit state-space plant model, our novel approach still allows the filter gain design for stabilization and H-2 estimation performance. This design freedom cannot be achieved by other existing data-driven fault estimation filter designs so far. Simulation results using a continuous stirred tank reactor illustrate the effectiveness of the proposed new method.