38,196 research outputs found
Uncertainty Bounds for Spectral Estimation
The purpose of this paper is to study metrics suitable for assessing
uncertainty of power spectra when these are based on finite second-order
statistics. The family of power spectra which is consistent with a given range
of values for the estimated statistics represents the uncertainty set about the
"true" power spectrum. Our aim is to quantify the size of this uncertainty set
using suitable notions of distance, and in particular, to compute the diameter
of the set since this represents an upper bound on the distance between any
choice of a nominal element in the set and the "true" power spectrum. Since the
uncertainty set may contain power spectra with lines and discontinuities, it is
natural to quantify distances in the weak topology---the topology defined by
continuity of moments. We provide examples of such weakly-continuous metrics
and focus on particular metrics for which we can explicitly quantify spectral
uncertainty. We then consider certain high resolution techniques which utilize
filter-banks for pre-processing, and compute worst-case a priori uncertainty
bounds solely on the basis of the filter dynamics. This allows the a priori
tuning of the filter-banks for improved resolution over selected frequency
bands.Comment: 8 figure
Cooperative Radar and Communications Signaling: The Estimation and Information Theory Odd Couple
We investigate cooperative radar and communications signaling. While each
system typically considers the other system a source of interference, by
considering the radar and communications operations to be a single joint
system, the performance of both systems can, under certain conditions, be
improved by the existence of the other. As an initial demonstration, we focus
on the radar as relay scenario and present an approach denoted multiuser
detection radar (MUDR). A novel joint estimation and information theoretic
bound formulation is constructed for a receiver that observes communications
and radar return in the same frequency allocation. The joint performance bound
is presented in terms of the communication rate and the estimation rate of the
system.Comment: 6 pages, 2 figures, to be presented at 2014 IEEE Radar Conferenc
Heisenberg-style bounds for arbitrary estimates of shift parameters including prior information
A rigorous lower bound is obtained for the average resolution of any estimate
of a shift parameter, such as an optical phase shift or a spatial translation.
The bound has the asymptotic form k_I/ where G is the generator of the
shift (with an arbitrary discrete or continuous spectrum), and hence
establishes a universally applicable bound of the same form as the usual
Heisenberg limit. The scaling constant k_I depends on prior information about
the shift parameter. For example, in phase sensing regimes, where the phase
shift is confined to some small interval of length L, the relative resolution
\delta\hat{\Phi}/L has the strict lower bound (2\pi e^3)^{-1/2}/,
where m is the number of probes, each with generator G_1, and entangling joint
measurements are permitted. Generalisations using other resource measures and
including noise are briefly discussed. The results rely on the derivation of
general entropic uncertainty relations for continuous observables, which are of
interest in their own right.Comment: v2:new bound added for 'ignorance respecting estimates', some
clarification
Channel Uncertainty in Ultra Wideband Communication Systems
Wide band systems operating over multipath channels may spread their power
over bandwidth if they use duty cycle. Channel uncertainty limits the
achievable data rates of power constrained wide band systems; Duty cycle
transmission reduces the channel uncertainty because the receiver has to
estimate the channel only when transmission takes place. The optimal choice of
the fraction of time used for transmission depends on the spectral efficiency
of the signal modulation. The general principle is demonstrated by comparing
the channel conditions that allow different modulations to achieve the capacity
in the limit. Direct sequence spread spectrum and pulse position modulation
systems with duty cycle achieve the channel capacity, if the increase of the
number of channel paths with the bandwidth is not too rapid. The higher
spectral efficiency of the spread spectrum modulation lets it achieve the
channel capacity in the limit, in environments where pulse position modulation
with non-vanishing symbol time cannot be used because of the large number of
channel paths
The Theory and Practice of Estimating the Accuracy of Dynamic Flight-Determined Coefficients
Means of assessing the accuracy of maximum likelihood parameter estimates obtained from dynamic flight data are discussed. The most commonly used analytical predictors of accuracy are derived and compared from both statistical and simplified geometrics standpoints. The accuracy predictions are evaluated with real and simulated data, with an emphasis on practical considerations, such as modeling error. Improved computations of the Cramer-Rao bound to correct large discrepancies due to colored noise and modeling error are presented. The corrected Cramer-Rao bound is shown to be the best available analytical predictor of accuracy, and several practical examples of the use of the Cramer-Rao bound are given. Engineering judgement, aided by such analytical tools, is the final arbiter of accuracy estimation
- …