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Resilient Sensor Placement for Kalman Filtering in Networked Systems Complexity and Algorithms

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Document pages: 11 pages

Abstract: Given a linear dynamical system affected by noise, we study the problem ofoptimally placing sensors (at design-time) subject to a sensor placement budgetconstraint in order to minimize the trace of the steady-state error covarianceof the corresponding Kalman filter. While this problem is NP-hard in general,we consider the underlying graph associated with the system dynamics matrix,and focus on the case when there is a single input at one of the nodes in thegraph. We provide an optimal strategy (computed in polynomial-time) to placethe sensors over the network. Next, we consider the problem of attacking (i.e.,removing) the placed sensors under a sensor attack budget constraint in orderto maximize the trace of the steady-state error covariance of the resultingKalman filter. Using the insights obtained for the sensor placement problem, weprovide an optimal strategy (computed in polynomial-time) to attack the placedsensors. Finally, we consider the scenario where a system designer places thesensors under a sensor placement budget constraint, and an adversary thenattacks the placed sensors subject to a sensor attack budget constraint. Theresilient sensor placement problem is to find a sensor placement strategy tominimize the trace of the steady-state error covariance of the Kalman filtercorresponding to the sensors that survive the attack. We show that this problemis NP-hard, and provide a pseudo-polynomial-time algorithm to solve it.

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