150 research outputs found
Adaptive Quantizers for Estimation
In this paper, adaptive estimation based on noisy quantized observations is
studied. A low complexity adaptive algorithm using a quantizer with adjustable
input gain and offset is presented. Three possible scalar models for the
parameter to be estimated are considered: constant, Wiener process and Wiener
process with deterministic drift. After showing that the algorithm is
asymptotically unbiased for estimating a constant, it is shown, in the three
cases, that the asymptotic mean squared error depends on the Fisher information
for the quantized measurements. It is also shown that the loss of performance
due to quantization depends approximately on the ratio of the Fisher
information for quantized and continuous measurements. At the end of the paper
the theoretical results are validated through simulation under two different
classes of noise, generalized Gaussian noise and Student's-t noise
Optimal Asymmetric Binary Quantization for Estimation Under Symmetrically Distributed Noise
Estimation of a location parameter based on noisy and binary quantized
measurements is considered in this letter. We study the behavior of the
Cramer-Rao bound as a function of the quantizer threshold for different
symmetric unimodal noise distributions. We show that, in some cases, the
intuitive choice of threshold position given by the symmetry of the problem,
placing the threshold on the true parameter value, can lead to locally worst
estimation performance.Comment: 4 pages, 5 figure
Adjustable Quantizers for Joint Estimation of Location and Scale Parameters
Poster SessionInternational audienceAn adaptive algorithm to estimate jointly unknown location and scale parameters of a sequence of symmetrically distributed independent and identically distributed random variables using quantized measurements from a quantizer with adjustable input gain and input offset is presented. The asymptotic variance of estimation is obtained, simulations under Cauchy and Gaussian distributions are presented to validate the asymptotic results and they are compared to the continuous optimal estimator performance
Quantification asymétrique optimale pour l'estimation d'un paramètre de centrage dans un bruit de loi symétrique
Présentation oraleNational audienceNous traitons de l'estimation d'un paramètre de centrage à partir d'observations bruitées quantifiées sur deux niveaux. Le comportement de la BCR (Borne de Cramér-Rao) est étudié en fonction du centrage du quantifieur pour différentes distributions symétriques de bruit. Nous montrons que, contrairement à ce qui est mentionné dans la littérature, l'emplacement optimal du centrage du quantifieur dépend radicalement de la loi de bruit et que son emplacement sur le paramètre de centrage, un choix intuitif vu la symétrie du problème, peut donner la performance d'estimation localement la plus mauvaise
Asymptotic Approximation of Optimal Quantizers for Estimation
Poster SessionInternational audienceIn this paper, the asymptotic approximation of the Fisher information for the estimation of a scalar parameter based on quantized measurements is studied. As the number of quantization intervals tends to infinity, it is shown that the loss of Fisher information due to quantization decreases exponentially as a function of the number of quantization bits. The optimal quantization interval density and the corresponding maximum Fisher information are obtained. Comparison between optimal nonuniform and uniform quantization for the location estimation problem indicates that nonuniform quantization is slightly better. At the end of the paper, an adaptive algorithm for jointly estimating and setting the thresholds is used to show that the theoretical results can be approximately obtained in practice
2D Time-frequency interference modelling using stochastic geometry for performance evaluation in Low-Power Wide-Area Networks
In wireless networks, interferences between trans- missions are modelled
either in time or frequency domain. In this article, we jointly analyze
interferences in the time- frequency domain using a stochastic geometry model
assuming the total time-frequency resources to be a two-dimensional plane and
transmissions from Internet of Things (IoT) devices time- frequency patterns on
this plane. To evaluate the interference, we quantify the overlap between the
information packets: provided that the overlap is not too strong, the packets
are not necessarily lost due to capture effect. This flexible model can be used
for multiple medium access scenarios and is especially adapted to the random
time-frequency access schemes used in Low-Power Wide-Area Networks (LPWANs). By
characterizing the outage probability and throughput, our approach permits to
evaluate the performance of two representative LPWA technologies
Sigfox{\textsuperscript \textregistered} and LoRaWA{\textsuperscript
\textregistered}
A Fusion Center Approach for Estimation Using Quantized Measurements
Rapport interne de GIPSA-labA fusion center approach to estimate a constant location parameter using quantized noisy measurements from multiple sensors is presented. The asymptotic estimation performance is obtained and simulations for different numbers of sensors under Gaussian and Cauchy noise are used for validation. A performance comparison under constrained communication bandwidth between a fusion center approach with two low resolution sensors and a high resolution single sensor approach is presented to motivate the use of low resolution sensor networks
When Analytic Calculus Cracks AdaBoost Code
The principle of boosting in supervised learning involves combining multiple
weak classifiers to obtain a stronger classifier. AdaBoost has the reputation
to be a perfect example of this approach. We have previously shown that
AdaBoost is not truly an optimization algorithm. This paper shows that AdaBoost
is an algorithm in name only, as the resulting combination of weak classifiers
can be explicitly calculated using a truth table. This study is carried out by
considering a problem with two classes and is illustrated by the particular
case of three binary classifiers and presents results in comparison with those
from the implementation of AdaBoost algorithm of the Python library
scikit-learn.Comment: 8 pages, 1 figur
3-D Mobile-to-Mobile channel tracking with first-order autoregressive model-based Kalman filter
International audienceThis paper deals with channel estimation in Mobile-to-Mobile communication assuming three-dimensional scattering environment. It approximates the channel by a first-order autoregressive (AR(1)) model and tracks it by a Kalman filter. The common method used in the literature to estimate the parameter of AR(1) model is based on a correlation matching criterion. We propose another criterion based on the Minimization of the Asymptotic Variance of the Kalman filter, and we justify why it is more appropriate for slow fading variations. This paper provides the closed-form expression of the optimal AR(1) parameter under minimum asymptotic variance criterion and the approximated expression of the estimation variance in output of the Kalman filter, both for Fixed-to-Mobile and Mobile-to-Mobile communication channels
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