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

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

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

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