  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
suboptimal $\mathcal{H}_2$ 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 state-space 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.
