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 faultfree data. We address this problem by parameterizing a systeminversion-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 suboptimal H2 performance. This design freedom cannot be achieved by other existing data-driven fault estimation filter designs so far. Another benefit of our proposed design is the convenience of determining the state order: a higher state order of the filter leads to better estimation performance, at the cost of heavier computational burden. In contrast, order determination is cumbersome when using an identified statespace plant model for the filter design, because of the complicated propagation of the model mismatch into the fault estimation errors. Simulations using an unstable aircraft system illustrate the effectiveness of the proposed new method.