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This paper presents a novel data-driven, direct filtering approach forunknown linear time-invariant systems affected by unknown-but-boundedmeasurement noise. The proposed technique combines independent multistepprediction models, identified resorting to the Set Membership framework, torefine a set that is guaranteed to contain the true system output. The filteredoutput is then computed as the central value in such a set. By doing so, themethod achieves an accurate output filtering and provides tight and minimalerror bounds with respect to the true system output. To attain these results,the online solution of linear programs is required. A modified filteringapproach with lower online computational cost is also presented, obtained bymoving the solution of the optimization problems to an offline preliminaryphase, at the cost of larger accuracy bounds. The performance of the proposedapproaches are evaluated and compared with those of standard model-basedfiltering techniques in a numerical example.

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