Remote State Estimation over Packet Dropping Links in the Presence of an Eavesdropper

Leong, Alex S.; Quevedo, Daniel E.; Dolz, Daniel; Dey, Subhrakanti

doi:10.48550/arxiv.1702.02785

Cited by 1 publication

(11 citation statements)

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“…• The codes achieve unbounded eavesdropper's error almost surely, while the user's estimation performance is optimal. This supersedes the results in [21], [22] where unbounded eavesdropper's error is achieved only in expectation and the user's performance is degraded. • The condition for perfect secrecy is remarkably minimal, requiring just a single occurrence of the critical event.…”

Section: Dynamical Systemsupporting

confidence: 55%

“…A control-theoretic approach was recently employed in [21], [22], where the performance metric of both the user and the eavesdropper is minimum mean square error (mmse). This framework does not use any encoding.…”

Section: Dynamical Systemmentioning

confidence: 99%

“…This framework does not use any encoding. Instead, a secrecy mechanism is employed, which withholds information, either randomly [21] or deterministically [22]. In the case of unstable systems, under certain conditions, the eavesdropper's expected error can grow to infinity while the user's expected error remains bounded.…”

Section: Dynamical Systemmentioning

confidence: 99%

“…We consider two scenarios. In the first one, we contrast the performance achieved by the State-Secrecy Codes with the one achieved by the mechanisms in [21], [22]. The comparison is made assuming direct state measurements.…”

Section: Simulationsmentioning

confidence: 99%

“…In the first scenario, with direct state information (C = I, R = 0), we assume that the channel outcomes have the probabilities p 11 = 0.54, p 00 = 0.04, p 01 = 0.06 and p 10 = 0.36 and initial state error covariance matrix Σ 0 = Q. We compare the performance of our code with the one of the mechanisms in [21] and [22]-see Figure 4. The comparison is made for the same sequence of channel outcomes, with respect to the user's and eavesdropper's estimation errors (tr (P u,k ) State-Secrecy Code Mechanism in [21] Mechanism in [22] Fig.…”

Section: Simulationsmentioning

confidence: 99%

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State-Secrecy Codes for Networked Linear Systems

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Gatsis

Pappas

2020

IEEE Trans. Automat. Contr.

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In this paper, we study the problem of remote state estimation, in the presence of a passive eavesdropper. An authorized user estimates the state of an unstable linear plant, based on the packets received from a sensor, while the packets may also be intercepted by the eavesdropper. Our goal is to design a coding scheme at the sensor, which encodes the state information, in order to impair the eavesdropper's estimation performance, while enabling the user to successfully decode the sent messages. We introduce a novel class of codes, termed State-Secrecy Codes, which use acknowledgment signals from the user and apply linear time-varying transformations to the current and previously received states. By exploiting the properties of the system's process noise, the channel physical model and the dynamics, these codes manage to be fast, efficient and, thus, suitable for real-time dynamical systems. We prove that under minimal conditions, State-Secrecy Codes achieve perfect secrecy, namely the eavesdropper's estimation error grows unbounded almost surely, while the user's estimation performance is optimal. These conditions only require that at least once, the user receives the corresponding packet while the eavesdropper fails to intercept it. Even one occurrence of this event renders the eavesdropper's error unbounded with asymptotically optimal rate of increase. State-Secrecy Codes are provided and studied for two cases, i) when direct state measurements are available, and ii) when we only have output measurements. The theoretical results are illustrated in simulations.the definition (7) of P k and equation (35), we have P k = Cov {x k |J k (s 0:k )} in C. There exist two cases: Case I: s k = 0. In this case, by the definition (33), we have J k (s 0:k ) = J k (s 0:k−1 ). Therefore:where the third equality follows from (35). Case II: s k = 1. Here, by (35):where z k (s 0:k ) is defined in (33). Since all variables are Gaussian, we can compute the posterior estimation error using the Schur complement formula applied to the covariance matrix of x k and z k (s 0:k ) given J k (s 0:k−1 ) (see [28]). By (35), in C we haveHence, by the Schur's complement formula, we have P k = Σ xx − Σ xz (Σ zz ) † Σ zx in C, when s k = 1.We can describe both cases with one equation:since s k = γ k in C. But this holds for any event C = {g 0:k = s 0:k }. Thus, the result holds everywhere, since the events {g 0:k = s}, s ∈ {0, 1} 2k+1 are a partition of the probability space.

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Section: Dynamical Systemsupporting

confidence: 55%

Section: Dynamical Systemmentioning

confidence: 99%