330,766 research outputs found
How well can we estimate a sparse vector?
The estimation of a sparse vector in the linear model is a fundamental
problem in signal processing, statistics, and compressive sensing. This paper
establishes a lower bound on the mean-squared error, which holds regardless of
the sensing/design matrix being used and regardless of the estimation
procedure. This lower bound very nearly matches the known upper bound one gets
by taking a random projection of the sparse vector followed by an
estimation procedure such as the Dantzig selector. In this sense, compressive
sensing techniques cannot essentially be improved
Energy Efficient Spectrum Sensing for State Estimation over A Wireless Channel
The performance of remote estimation over wireless channel is strongly
affected by sensor data losses due to interference. Although the impact of
interference can be alleviated by performing spectrum sensing and then
transmitting only when the channel is clear, the introduction of spectrum
sensing also incurs extra energy expenditure. In this paper, we investigate the
problem of energy efficient spectrum sensing for state estimation of a general
linear dynamic system, and formulate an optimization problem which minimizes
the total sensor energy consumption while guaranteeing a desired level of
estimation performance. The optimal solution is evaluated through both
analytical and simulation results.Comment: 4 pages, 6 figures, accepted to IEEE GlobalSIP 201
Adaptive Sensing for Estimation of Structured Sparse Signals
In many practical settings one can sequentially and adaptively guide the
collection of future data, based on information extracted from data collected
previously. These sequential data collection procedures are known by different
names, such as sequential experimental design, active learning or adaptive
sensing/sampling. The intricate relation between data analysis and acquisition
in adaptive sensing paradigms can be extremely powerful, and often allows for
reliable signal estimation and detection in situations where non-adaptive
sensing would fail dramatically.
In this work we investigate the problem of estimating the support of a
structured sparse signal from coordinate-wise observations under the adaptive
sensing paradigm. We present a general procedure for support set estimation
that is optimal in a variety of cases and shows that through the use of
adaptive sensing one can: (i) mitigate the effect of observation noise when
compared to non-adaptive sensing and, (ii) capitalize on structural information
to a much larger extent than possible with non-adaptive sensing. In addition to
a general procedure to perform adaptive sensing in structured settings we
present both performance upper bounds, and corresponding lower bounds for both
sensing paradigms
Compressive Time Delay Estimation Using Interpolation
Time delay estimation has long been an active area of research. In this work,
we show that compressive sensing with interpolation may be used to achieve good
estimation precision while lowering the sampling frequency. We propose an
Interpolating Band-Excluded Orthogonal Matching Pursuit algorithm that uses one
of two interpolation functions to estimate the time delay parameter. The
numerical results show that interpolation improves estimation precision and
that compressive sensing provides an elegant tradeoff that may lower the
required sampling frequency while still attaining a desired estimation
performance.Comment: 5 pages, 2 figures, technical report supporting 1 page submission for
GlobalSIP 201
Optimal Remote State Estimation for Self-Propelled Particle Models
We investigate the design of a remote state estimation system for a
self-propelled particle (SPP). Our framework consists of a sensing unit that
accesses the full state of the SPP and an estimator that is remotely located
from the sensing unit. The sensing unit must pay a cost when it chooses to
transmit information on the state of the SPP to the estimator; and the
estimator computes the best estimate of the state of the SPP based on received
information. In this paper, we provide methods to design transmission policies
and estimation rules for the sensing unit and estimator, respectively, that are
optimal for a given cost functional that combines state estimation distortion
and communication costs. We consider two notions of optimality: joint
optimality and person-by-person optimality. Our main results show the existence
of a jointly optimal solution and describe an iterative procedure to find a
person-by-person optimal solution. In addition, we explain how the remote
estimation scheme can be applied to tracking of animal movements over a costly
communication link. We also provide experimental results to show the
effectiveness of the scheme.Comment: a part of the article was submitted to IEEE Conference on Decision
and Control 201
Distributed quantum sensing enhanced by continuous-variable error correction
A distributed sensing protocol uses a network of local sensing nodes to estimate a global feature of the network, such as a weighted average of locally detectable parameters. In the noiseless case, continuous-variable (CV) multipartite entanglement shared by the nodes can improve the precision of parameter estimation relative to the precision attainable by a network without shared entanglement; for an entangled protocol, the root mean square estimation error scales like 1/M with the number M of sensing nodes, the so-called Heisenberg scaling, while for protocols without entanglement, the error scales like 1√M. However, in the presence of loss and other noise sources, although multipartite entanglement still has some advantages for sensing displacements and phases, the scaling of the precision with M is less favorable. In this paper, we show that using CV error correction codes can enhance the robustness of sensing protocols against imperfections and reinstate Heisenberg scaling up to moderate values of M. Furthermore, while previous distributed sensing protocols could measure only a single quadrature, we construct a protocol in which both quadratures can be sensed simultaneously. Our work demonstrates the value of CV error correction codes in realistic sensing scenarios
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