Data-driven filtering for linear systems using Set Membership multistep predictors

This paper presents a novel data-driven, direct filtering approach for unknown linear time-invariant systems affected by unknown-but-bounded measurement noise. The proposed technique combines independent multistep prediction models, identified resorting to the Set Membership framework, to refine a set that is guaranteed to contain the true system output. The filtered output is then computed as the central value in such a set. By doing so, the method achieves an accurate output filtering and provides tight and minimal error bounds with respect to the true system output. To attain these results, the online solution of linear programs is required. A modified filtering approach with lower online computational cost is also presented, obtained by moving the solution of the optimization problems to an offline preliminary phase, at the cost of larger accuracy bounds. The performance of the proposed approaches are evaluated and compared with those of standard model-based filtering techniques in a numerical example.