Given a linear system in a real or complex domain, linear regression aims to recover the model parameters from a set of observations. Recent studies in compressive sensing have successfully shown that under certain conditions, a linear program, namely, 1 -minimization, guarantees recovery of sparse parameter signals even when the system is underdetermined. In this paper, we consider a more challenging problem: when the phase of the output measurements from a linear system is omitted. Using a lifting technique, we show that even though the phase information is missing, the sparse signal can be recovered exactly by solving a simple semidefinite program when the sampling rate is sufficiently high, albeit the exact solutions to both sparse signal recovery and phase retrieval are combinatorial. The results extend the type of applications that compressive sensing can be applied to those where only output magnitudes can be observed. We demonstrate the accuracy of the algorithms through theoretical analysis, extensive simulations and a practical experiment.
We introduce a model for the operational costs of an electric distribution utility. The model focuses on two of the new services that are enabled by the Advanced Metering Infrastructure (AMI): (1) the fine-grained anomaly detection that is possible thanks to the frequent smart meter sampling rates (e.g., 15 minute sampling intervals of some smart meter deployments versus monthlyreadings from old meters), and (2) the ability to shape the load thanks to advanced demand-response mechanisms that leverage AMI networks, such as direct-load control.We then study two security problems in this context. (1) In the first part of the paper we formulate the problem of electricity theft detection (one of the use-cases of anomaly detection) as a game between the electric utility and the electricity thief. The goal of the electricity thief is to steal a predefined amount of electricity while minimizing the likelihood of being detected, while the electric utility wants to maximize the probability of detection and the degree of operational cost it will incur for managing this anomaly detection mechanism. (2) In the second part of the paper we formulate the problem of privacy-preserving demand response as a control theory problem, and show how to select the maximum sampling interval for smart meters in order to protect the privacy of consumers while maintaining the desired load shaping properties of demand-response programs. II. IFor most electric distribution utilities, creating a business case for improving computer security and supporting long-term security research is a difficult task because of the lack of risk models that capture the effects of security and privacy in their revenue and profit margins.We consider the point of view of an electric distribution utility that needs to create a business case for improving their security posture by introducing an electricity-theft anomaly detection mechanism and a privacy-preserving demand response program.We model the electricity-theft anomaly detection case as a game played between the utility and fraudulent consumers, and characterize the Nash equilibrium of the game.In the second part of the paper we consider the privacy-preserving demand-response problem and using realistic values of a direct-load control example, we show how the peak shaving goal of the demand-response program depends on the privacy (sampling interval) of the Advanced Metering Infrastructure (AMI). III. B M A. Electricity TheftEnergy theft in emerging economies has been a widespread practice. A World Bank report [1] found that up to 50% of electricity in developing countries is acquired via theft. Electricity theft can be caused by physical and cyber attacks. Physical security considerations range from defaulting on payments to directly connecting loads to the electricity distribution lines. A cyber attack against smart meters is also possible (and the focus of this paper). While some basic protective measures have been developed (tamper-evident seals, secure link communication...
Despite growing attention in autonomy, there are still many open problems, including how autonomous vehicles will interact and communicate with other agents, such as human drivers and pedestrians. Unlike most approaches that focus on pedestrian detection and planning for collision avoidance, this paper considers modeling the interaction between human drivers and pedestrians and how it might influence map estimation, as a proxy for detection. We take a mapping inspired approach and incorporate people as sensors into mapping frameworks. By taking advantage of other agents' actions, we demonstrate how we can impute portions of the map that would otherwise be occluded. We evaluate our framework in human driving experiments and on real-world data, using occupancy grids and landmark-based mapping approaches. Our approach significantly improves overall environment awareness and outperforms standard mapping techniques.
In order to develop provably safe human-in-the-loop systems, accurate and precise models of human behavior must be developed. In the case of intelligent vehicles, one can imagine the need for predicting driver behavior to develop minimally invasive active safety systems or to safely interact with other vehicles on the road. We present a optimization based method for approximating the stochastic reachable set for human-inthe-loop systems. This method identifies the most precise subset of states that a human driven vehicle may enter, given some dataset of observed trajectories. We phrase this problem as a mixed integer linear program, which can be solved using branch and bound methods. The resulting model uncovers the most representative subset that encapsulates the likely trajectories, up to some probability threshold, by optimally rejects outliers in the dataset. This tool provides set predictions consisting of trajectories observed from the nonlinear dynamics and behaviors of the human driven car, and can account for modes of behavior, like the driver state or intent. This allows us to predict driving behavior over long time horizons with high accuracy. By using this realistic data and flexible algorithm, a precise and accurate driver model can be developed to capture likely behaviors. The resulting prediction can be tailored to an individual for use in semi-autonomous frameworks or generally applied for autonomous planning in interactive maneuvers.
Large-scale sensing and actuation infrastructures have allowed buildings to achieve significant energy savings; at the same time, these technologies introduce significant privacy risks that must be addressed. In this paper, we present a framework for modeling the trade-off between improved control performance and increased privacy risks due to occupancy sensing. More specifically, we consider occupancybased HVAC control as the control objective and the location traces of individual occupants as the private variables. Previous studies have shown that individual location information can be inferred from occupancy measurements. To ensure privacy, we design an architecture that distorts the occupancy data in order to hide individual occupant location information while maintaining HVAC performance. Using mutual information between the individual's location trace and the reported occupancy measurement as a privacy metric, we are able to optimally design a scheme to minimize privacy risk subject to a control performance guarantee. We evaluate our framework using real-world occupancy data: first, we verify that our privacy metric accurately assesses the adversary's ability to infer private variables from the distorted sensor measurements; then, we show that control performance is maintained through simulations of building operations using these distorted occupancy readings.
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