Nonlinear Compressive Particle Filtering

Many systems for which compressive sensing is used today are dynamical. The common approach is to neglect the dynamics and see the problem as a sequence of independent problems. This approach has two disadvantages. Firstly, the temporal dependency in the state could be used to improve the accuracy of the state estimates. Secondly, having an estimate for the state and its support could be used to reduce the computational load of the subsequent step. In the linear Gaussian setting, compressive sensing was recently combined with the Kalman filter to mitigate above disadvantages. In the nonlinear dynamical case, compressive sensing can not be used and, if the state dimension is high, the particle filter would perform poorly. In this paper we combine one of the most novel developments in compressive sensing, nonlinear compressive sensing, with the particle filter. We show that the marriage of the two is essential and that neither the particle filter or nonlinear compressive sensing alone gives a satisfying solution.Comment: Accepted to CDC 201

Compressively characterizing high-dimensional entangled states with complementary, random filtering

The resources needed to conventionally characterize a quantum system are overwhelmingly large for high- dimensional systems. This obstacle may be overcome by abandoning traditional cornerstones of quantum measurement, such as general quantum states, strong projective measurement, and assumption-free characterization. Following this reasoning, we demonstrate an efficient technique for characterizing high-dimensional, spatial entanglement with one set of measurements. We recover sharp distributions with local, random filtering of the same ensemble in momentum followed by position---something the uncertainty principle forbids for projective measurements. Exploiting the expectation that entangled signals are highly correlated, we use fewer than 5,000 measurements to characterize a 65, 536-dimensional state. Finally, we use entropic inequalities to witness entanglement without a density matrix. Our method represents the sea change unfolding in quantum measurement where methods influenced by the information theory and signal-processing communities replace unscalable, brute-force techniques---a progression previously followed by classical sensing.Comment: 13 pages, 7 figure

Device-free Localization using Received Signal Strength Measurements in Radio Frequency Network

Device-free localization (DFL) based on the received signal strength (RSS) measurements of radio frequency (RF)links is the method using RSS variation due to the presence of the target to localize the target without attaching any device. The majority of DFL methods utilize the fact the link will experience great attenuation when obstructed. Thus that localization accuracy depends on the model which describes the relationship between RSS loss caused by obstruction and the position of the target. The existing models is too rough to explain some phenomenon observed in the experiment measurements. In this paper, we propose a new model based on diffraction theory in which the target is modeled as a cylinder instead of a point mass. The proposed model can will greatly fits the experiment measurements and well explain the cases like link crossing and walking along the link line. Because the measurement model is nonlinear, particle filtering tracing is used to recursively give the approximate Bayesian estimation of the position. The posterior Cramer-Rao lower bound (PCRLB) of proposed tracking method is also derived. The results of field experiments with 8 radio sensors and a monitored area of 3.5m 3.5m show that the tracking error of proposed model is improved by at least 36 percent in the single target case and 25 percent in the two targets case compared to other models.Comment: This paper has been withdrawn by the author due to some mistake

Tunable Vibrational Band Gaps in One-Dimensional Diatomic Granular Crystals with Three-Particle Unit Cells

We investigate the tunable vibration filtering properties of one-dimensional diatomic granular crystals composed of arrays of stainless steel spheres and cylinders interacting via Hertzian contact. The arrays consist of periodically repeated three-particle unit cells (steel-cylinder-sphere) in which the length of the cylinder is varied systematically. We apply static compression to linearize the dynamic response of the crystals and characterize their linear frequency spectrum. We find good agreement between theoretical dispersion relation analysis (for infinite systems), state-space analysis (for finite systems), and experiments. We report the observation of up to three distinct pass bands and two finite band gaps and show their tunability for variations in cylinder length and static compression