This article studies static state estimation in multisensor settings, with a caveat that an unknown subset of the sensors are compromised by an adversary, whose measurements can be manipulated arbitrarily. The attacker is able to compromise q out of m sensors. A new performance metric, which quantifies the asymptotic decay rate for the probability of having an estimation error larger than delta, is proposed. We develop an optimal estimator for the new performance metric with a fixed delta, which is the Cheby-shev center of a union of ellipsoids. We further provide an estimator that is optimal for every delta, for the special case where the sensors are homogeneous. Numerical examples are given to elaborate the results.

In this paper, we consider a secure distributed filtering problem for linear time-invariant systems with bounded noises and unstable dynamics under compromised observations. A malicious attacker is able to compromise a subset of the agents and manipulate the observations arbitrarily. We first propose a recursive distributed filter consisting of two parts at each time. The first part employs a saturation like scheme, which gives a small gain if the innovation is too large. The second part is a consensus operation of state estimates among neighboring agents. A sufficient condition is then established for the boundedness of estimation error, which is with respect to network topology, system structure, and the maximal compromised agent subset. We further provide an equivalent statement, which connects to 2s-sparse observability in the centralized framework in certain scenarios, such that the sufficient condition is feasible. Numerical simulations are finally provided to illustrate the developed results.

This paper studies how to deploy sensors in the context of detection in adversarial environments. A fusion center is performing a binary hypothesis testing based on measurements from remotely deployed heterogeneous sensors. An attacker may compromise some of the deployed sensors, which send arbitrary measurements to the fusion center. The problems of interest are: to characterize the performance of the system under attack and, thus, develop a performance metric; and to deploy sensors within a cost budget, such that the proposed performance metric is maximized. In this paper, we first present a performance metric by formulating the detection in adversarial environments in a game theoretic way. A Nash equilibrium pair of the detection algorithm and attack strategy, with the deployed sensors given, is provided and the corresponding detection performance is adopted as the performance metric. We then show that the optimal sensor deployment can be determined approximately by solving a group of unbounded knapsack problems. We also show that the performance metric gap between the optimal sensor deployment and the optimal one with sensors being identical is within a fixed constant for any cost budget. The main results are illustrated by numerical examples.

This paper studies static state estimation based on measurements from a set of sensors, a subset of which can be compromised by an attacker. The measurements from a compromised sensor can be manipulated arbitrarily by the adversary. A new notion is adopted to indicate the performance of an estimator, that is, the asymptotic exponential rate, with which the worst-case probability of estimate lying outside certain ball centered at the true underlying state goes to zero. An optimal estimator, which computes Chebyshev centers and only utilizes the information contained in the averaged measurements, is proposed. Numerical examples are given to elaborate the results.