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Like other divergences, Jeffrey's divergence (JD) is used for change detection, for model comparison, etc. Recently, a great deal of interest has been paid to this symmetric version of the Kullback-Leibler (KL) divergence. This led to analytical expressions of the JD between autoregressive (AR) processes, moving-average (MA) processes, either noise-free or disturbed by additive white noises, as well...
Various works have been carried out about the Jeffrey's divergence (JD) which is the symmetric version of the Kullback-Leibler (KL) divergence. An expression of the JD for Gaussian processes can be deduced from the definition of the KL divergence and the expression of the Gaussian-multivariate distributions of k-dimensional random vectors. It depends on the k × k Toeplitz covariance matrices of the...
This paper deals with the analysis of the Jeffrey's divergence (JD) between an autoregressive process (AR) and a sum of complex exponentials (SCE), whose magnitudes are Gaussian random values, which is then disturbed by an additive white noise. As interpreting the value of the JD may not be necessarily an easy task, we propose to give an expression of the JD and to analyze the influence of each process...
In this article, we share our positive experience about the creation of a Telecom showcase in our engineering school, which is an exhibition of old technology to help students learn about previous habits and think about some of the consequences of rapid innovation. This project was done in collaboration with industrial partners such as Thales and Orange. It includes the following steps: collecting...
This paper deals with model comparison based on the Jeffrey's divergence (JD). More particularly, after providing the JD between the joint distributions of k consecutive values of a white noise and the ones of a real moving-average or autoregressive model, the JD between real 1st-order MA and real 1st-order AR models is studied. Except when the 1st MA parameter is equal to 1, we show that, after a...
In this paper, single-target tracking using radar measurements is addressed. Recently, algorithms based on Bernoulli random finite sets have proved efficient in a cluttered environment. However, in Bayesian approaches, the choice of the motion model impacts the trajectory estimation accuracy. To select an appropriate set of motion models, a joint tracking and classification (JTC) algorithm can be...
When using Bayesian estimation techniques, the algorithm is strongly sensitive to the system evolution model and more particularly to the setting of the state-noise covariance matrix. Recently, Bayesian non-parametric models and in particular Dirichlet processes (DPs) have been proposed as a scalable solution to this issue. They assume that the system can switch between an infinite number of state-space...
The autoregressive models (AR) and moving-average models (MA) are regularly used in signal processing. Previous works have been done on dissimilarity measures between AR models by using a Riemannian distance, the Jeffrey's divergence (JD) and the spectral distances such as the Itakura-Saito divergence. In this paper, we compare the Rao distance and the JD for MA models and more particularly in the...
For a high-resolution radar, an extended target is characterized by a few main scatterers spread over several range gates not necessarily consecutive. The joint detections and localizations of these scatterers are of particular interest in order to estimate the range profile and identify the target. In this paper, we study a detector based on the Generalized Likelihood Ratio Test considering the unknown...
When using Bayesian estimation techniques for target tracking, the algorithm accuracy is induced by the choice of the system evolution model. Information on the type of target and its maneuver capability can then be helpful to choose relevant motion models. Joint tracking and classification (JTC) methods based on target features have thus been introduced. Among them, we recently proposed to take into...
In this paper, our purpose is to estimate time-varying Rayleigh fading channels in Orthogonal Frequency Division Multiplexing (OFDM) mobile systems. When the fading channel is approximated by an AutoRegressive (AR) process, the direct estimation of the model parameters from the noisy observations available at the receiver may yield biased values. To avoid this drawback, the joint estimation of both...
A great deal of interest has been paid to target tracking for the last decades. When using Bayesian estimation algorithms, choosing relevant motion models is crucial for accurate localization. Information on the type of target and its maneuver capability can be helpful in the motion model design. Thus, joint tracking and classification (JTC) methods based on target features have been recently developed...
This study deals with an interweave cognitive-radio (CR) system, where an uplink orthogonal frequency-division multiple access system is considered for the primary users (PUs). Our purpose is to estimate the PU carrier frequency offsets (PU-CFOs) as well as the channels to estimate the transmitted symbols. However, in wideband wireless communications, the PU received-signal spectrum usually exhibits...
Dirichlet process (DP) mixtures were recently introduced to deal with switching linear dynamical models (SLDM). They assume the system can switch between an a priori infinite number of state-space representations (SSR) whose parameters are on-line inferred. The estimation problem can thus be of high dimension when the SSR matrices are unknown. Nevertheless, in many applications, the SSRs can be categorized...
This work aims at improving the power amplifier (PA) efficiency in uplink OFDM-based cognitive radio (CR) communications. Unlike the traditional approaches, we suggest transmitting a non-linearily ampliied signal without any il-tering and addressing the OFDM sample estimation from the distorted signal at the receiver. The proposed post-distortion and detection technique is based on a Volterra model...
In this paper, we propose to address the moving average (MA) parameters estimation issue based only on noisy observations and without any knowledge on the variance of the additive stationary white Gaussian measurement noise. For this purpose, the MA process is approximated by a high-order AR process and its parameters are estimated by using an errors-in-variables (EIV) approach, which also makes it...
Autoregressive (AR) models are used in various applications, from speech processing to radar signal analysis. In this paper, our purpose is to extract different model subsets from a set of two or more AR models. The approach operates with the following steps: firstly the matrix composed of dissimilarity measures between AR-model pairs are created. This can be based on the symmetric Itakura divergence,...
This paper deals with our positive experience about project-based pedagogy with the help of industrial partners to teach signal and image processing. During one semester, students are working in small groups of 6 to 8 students, supervised by two teachers or engineers working in a small or a big com pany. Various topics are proposed each year such as radar pro cessing, mobile communication system or...
This paper presents a spectrum-based method to estimate the integral non-linearity (INL) of an analog-to-digital converter. It relies on a previous work published in the literature that consists in expanding in Fourier series the analytical expression of a converter distorted signal output. The INL estimation process is then reduced to three operations: a discrete Fourier transform (DFT), a matrix...
In the field of cognitive radio (CR), radio frequency (RF) transceivers must be efficient to save the terminal battery autonomy. Therefore, when designing the CR power amplifier (CR-PA), an obvious objective is to optimize efficiency over a large bandwidth. As a consequence, the CR-PA operates in its non-linear region and then frequency-dependent distortions are generated. This issue is all the more...
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