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In this paper, we derive the distributed observable state from first principles. In particular, we extend the estimation setup to a distributed framework where in addition to the state and sensing, we also have communication among the sensors. We consider that each sensor estimates the entire state-vector to recover its unobservability. Combining the estimates at all of the sensors we arrive at the...
We use the Gaussian information bottleneck (GIB) to investigate the optimal rate-information trade-off for signal compression in linear Gaussian models and we provide a novel interpretation of the GIB in terms of the eigendecomposition of the Wiener filter. We further study mean-square-error-optimal rate-distortion compression preceded by a linear filter. Choosing this filter as square root of the...
Recent results in compressed sensing have shown that a wide variety of structured signals can be recovered from undersampled and noisy linear observations. In this paper, we show that many of these signal structures can be modeled using an union of affine subspaces, and that the fundamental number of observations needed for stable recovery is given by the number of “free” values, i.e. the dimension...
We describe a generalization of the group testing problem termed symmetric group testing. Unlike in classical binary group testing, the roles played by the input symbols zero and one are “symmetric” while the outputs are drawn from a ternary alphabet. Using an information-theoretic approach, we derive sufficient and necessary conditions for the number of tests required for noise-free and noisy reconstructions...
The recently introduced network equivalence results are used to create bit-pipe models that can replace multi-terminal channels within a discrete memoryless network. The goal is to create a set of simple “components” or “blocks” that can be substituted for the channel in such a way that the resulting network is capable of emulating the operation of the original one. We develop general upper and lower...
Minimum mean square error (MMSE) estimation of block sparse signals from noisy linear measurements is considered. Unlike in the standard compressive sensing setup where the non-zero entries of the signal are independently and uniformly distributed across the vector of interest, the information bearing components appear here in large mutually dependent clusters. Using the replica method from statistical...
Despite its simplicity (two controllers and otherwise LQG), Witsenhausen's counterexample is one of the long-standing open problems in stochastic distributed control. Recently, it was proved that an asymptotic vector ??relaxation?? can be solved to within a constant factor of the optimal cost. A parallel result is shown here for the original scalar problem. Between linear strategies and explicit-signalling-based...
For target tracking in Interference Environments of cognitive radar problem, Extended Karman, Particle filter algorithms etc. are generally used to be regarded as usual solutions to state estimation. Many techniques have been developed to improve performance of target tracking. In this paper, we set the structure and key features of target's tracking design for cognitive radar, and newly propose cognitive...
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