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We derive Concentration of Measure (CoM) inequalities for randomized Toeplitz matrices. These inequalities show that the norm of a high-dimensional signal mapped by a Toeplitz matrix to a low-dimensional space concentrates around its mean with a tail probability bound that decays exponentially in the dimension of the range space divided by a quantity which(More)
— Recovering or estimating the initial state of a high-dimensional system can require a potentially large number of measurements. In this paper, we explain how this burden can be significantly reduced for certain linear systems when randomized measurement operators are employed. Our work builds upon recent results from the field of Compressive Sensing (CS),(More)
The thermal storage potential of Thermostatically Controlled Loads (TCLs) is a tremendous flexible resource for providing various ancillary services to the grid. In this work, we study aggregate modeling, characterization, and control of TCLs for frequency regulation service provision. We propose a generalized battery model for aggregating flexibility of a(More)
— In this paper, we consider topology identification of large-scale interconnected dynamical systems. The system topology under study has the structure of a directed graph. Each edge of the directed network graph represents a Finite Impulse Response (FIR) filter with a possible transport delay. Each node is a summer, whose inputs are the signals from the(More)
ÐA method is developed to analyze the accuracy of the relative head-to-object position and orientation (pose) in augmented reality systems with head-mounted displays. From probabilistic estimates of the errors in optical tracking sensors, the uncertainty in head-to-object pose can be computed in the form of a covariance matrix. The positional uncertainty(More)
In augmented reality (AR) systems using head-mounted displays (HMD's), it is important to accurately sense the position and orientation (pose) of the user's head with respect to the world, in order that graphical overlays are drawn correctly aligned with real world objects. It is desired to maintain registration dynamically (while the person is moving their(More)
— In this paper, we consider the problem of identifying the exact topology of an interconnected dynamical network from a limited number of measurements of the individual nodes. Within the network graph, we assume that interconnected nodes are coupled by a discrete-time convolution process, and we explain how, given observations of the node outputs, the(More)