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The problem of offset in acoustic pulse reflectometry
Acoustic pulse reflectometry has become established as a useful non-invasive technique for measuring a variety of duct properties. A sound pulse is injected into the duct under investigation and the resultant reflections are recorded. Suitable analysis of the reflections yields the input impulse response of the duct, from which both its input impedance and its internal dimensions can be calculated. However, an input impulse response measurement made using acoustic pulse reflectometry generally contains an offset. Unless this offset is removed, the application of a bore reconstruction algorithm results in a calculated duct profile which expands or contracts spuriously.
In this paper, the offset in an input impulse response measurement is shown to consist of both constant and time-varying components. Methods of preventing or removing these DC and time-varying offsets are proposed and subsequent improvements to the bore reconstruction accuracy are demonstrated
Compressive Identification of Active OFDM Subcarriers in Presence of Timing Offset
In this paper we study the problem of identifying active subcarriers in an
OFDM signal from compressive measurements sampled at sub-Nyquist rate. The
problem is of importance in Cognitive Radio systems when secondary users (SUs)
are looking for available spectrum opportunities to communicate over them while
sensing at Nyquist rate sampling can be costly or even impractical in case of
very wide bandwidth. We first study the effect of timing offset and derive the
necessary and sufficient conditions for signal recovery in the oracle-assisted
case when the true active sub-carriers are assumed known. Then we propose an
Orthogonal Matching Pursuit (OMP)-based joint sparse recovery method for
identifying active subcarriers when the timing offset is known. Finally we
extend the problem to the case of unknown timing offset and develop a joint
dictionary learning and sparse approximation algorithm, where in the dictionary
learning phase the timing offset is estimated and in the sparse approximation
phase active subcarriers are identified. The obtained results demonstrate that
active subcarrier identification can be carried out reliably, by using the
developed framework.Comment: To appear in the proceedings of the IEEE Global Communications
Conference (GLOBECOM) 201
Time-varying Clock Offset Estimation in Two-way Timing Message Exchange in Wireless Sensor Networks Using Factor Graphs
The problem of clock offset estimation in a two-way timing exchange regime is
considered when the likelihood function of the observation time stamps is
exponentially distributed. In order to capture the imperfections in node
oscillators, which render a time-varying nature to the clock offset, a novel
Bayesian approach to the clock offset estimation is proposed using a factor
graph representation of the posterior density. Message passing using the
max-product algorithm yields a closed form expression for the Bayesian
inference problem.Comment: 4 pages, 2 figures, ICASSP 201
Stability of Curvature Measures
We address the problem of curvature estimation from sampled compact sets. The
main contribution is a stability result: we show that the gaussian, mean or
anisotropic curvature measures of the offset of a compact set K with positive
-reach can be estimated by the same curvature measures of the offset of a
compact set K' close to K in the Hausdorff sense. We show how these curvature
measures can be computed for finite unions of balls. The curvature measures of
the offset of a compact set with positive -reach can thus be approximated
by the curvature measures of the offset of a point-cloud sample. These results
can also be interpreted as a framework for an effective and robust notion of
curvature
Deconstructing Approximate Offsets
We consider the offset-deconstruction problem: Given a polygonal shape Q with
n vertices, can it be expressed, up to a tolerance \eps in Hausdorff distance,
as the Minkowski sum of another polygonal shape P with a disk of fixed radius?
If it does, we also seek a preferably simple-looking solution P; then, P's
offset constitutes an accurate, vertex-reduced, and smoothened approximation of
Q. We give an O(n log n)-time exact decision algorithm that handles any
polygonal shape, assuming the real-RAM model of computation. A variant of the
algorithm, which we have implemented using CGAL, is based on rational
arithmetic and answers the same deconstruction problem up to an uncertainty
parameter \delta; its running time additionally depends on \delta. If the input
shape is found to be approximable, this algorithm also computes an approximate
solution for the problem. It also allows us to solve parameter-optimization
problems induced by the offset-deconstruction problem. For convex shapes, the
complexity of the exact decision algorithm drops to O(n), which is also the
time required to compute a solution P with at most one more vertex than a
vertex-minimal one.Comment: 18 pages, 11 figures, previous version accepted at SoCG 2011,
submitted to DC
On control of discrete-time state-dependent jump linear systems with probabilistic constraints: A receding horizon approach
In this article, we consider a receding horizon control of discrete-time
state-dependent jump linear systems, particular kind of stochastic switching
systems, subject to possibly unbounded random disturbances and probabilistic
state constraints. Due to a nature of the dynamical system and the constraints,
we consider a one-step receding horizon. Using inverse cumulative distribution
function, we convert the probabilistic state constraints to deterministic
constraints, and obtain a tractable deterministic receding horizon control
problem. We consider the receding control law to have a linear state-feedback
and an admissible offset term. We ensure mean square boundedness of the state
variable via solving linear matrix inequalities off-line, and solve the
receding horizon control problem on-line with control offset terms. We
illustrate the overall approach applied on a macroeconomic system
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