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This work proposes an algorithmic method to verify differential privacy forestimation mechanisms with performance guarantees. Differential privacy makesit hard to distinguish outputs of a mechanism produced by adjacent inputs.While obtaining theoretical conditions that guarantee differential privacy maybe possible, evaluating these conditions in practice can be hard. This isespecially true for estimation mechanisms that take values in continuousspaces, as this requires checking for an infinite set of inequalities. Instead,our verification approach consists of testing the differential privacycondition for a suitably chosen finite collection of events at the expense ofsome information loss. More precisely, our data-driven, test framework forcontinuous range mechanisms first finds a highly-likely, compact event set, aswell as a partition of this event, and then evaluates differential privacy wrtthis partition. This results into a type of differential privacy with highconfidence, which we are able to quantify precisely. This approach is then usedto evaluate the differential-privacy properties of the recently proposed $W_2$Moving Horizon Estimator. We confirm its properties, while comparing itsperformance with alternative approaches in simulation.

A Numerical Verification Framework for Differential Privacy in Estimation