  This paper presents a data-driven receding horizon fault estimation method
for additive actuator and sensor faults in unknown linear time-invariant
systems, with enhanced robustness to stochastic identification errors.
State-of-the-art methods construct fault estimators with identified state-space
models or Markov parameters, but they do not compensate for identification
errors. Motivated by this limitation, we first propose a receding horizon fault
estimator parameterized by predictor Markov parameters. This estimator provides
(asymptotically) unbiased fault estimates as long as the subsystem from faults
to outputs has no unstable transmission zeros. When the identified Markov
parameters are used to construct the above fault estimator, zero-mean
stochastic identification errors appear as model uncertainty multiplied with
unknown fault signals and online system inputs/outputs (I/O). Based on this
fault estimation error analysis, we formulate a mixed-norm problem for the
offline robust design that regards online I/O data as unknown. An alternative
online mixed-norm problem is also proposed that can further reduce estimation
errors when the online I/O data have large amplitudes, at the cost of increased
computational burden. Based on a geometrical interpretation of the two proposed
mixed-norm problems, systematic methods to tune the user-defined parameters
therein are given to achieve desired performance trade-offs. Simulation
examples illustrate the benefits of our proposed methods compared to recent
literature.
