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Proposed early in the 90ies, the detrended fluctuation analysis (DFA) can be used to estimate the Hurst exponent and has been proven relevant in various applications, from economics to biomedical. For the last years, variants have been proposed. They differ in the way to estimate the trend of the centered integrated signal. In this paper, we recall the main principles of some of these methods, provide explanations on the behaviours of the algorithms and analyze the relevance of new variants based on the Savitzky-Golay filter, also known as the LOESS approach, and the LOWESS. They bridge the gap between the DFA and the detrending moving average (DMA). We hence show that the LOESS-based method is a generalization of the DMA.

International audience; The detrended fluctuation analysis (DFA) and its higher-order variant make it possible to estimate the Hurst exponent and therefore to quantify the long-range dependence of a random process. These methods are popular and used in a wide range of applications where they have been proven to be discriminative to characterize or classify processes. Nevertheless, in practice, the signal may be short-memory. In addition, depending on the number of samples available, there is no guarantee that these methods provide the true value of the Hurst exponent, leading the user to draw erroneous conclusions on the long-range dependence of the signal under study. In this paper, using a matrix formulation and making no approximation, we first propose to analyze how the DFA and its higher-order variant behave with respect to the number of samples available. Illustrations dealing with short-memory data that can be modeled by a white noise, a moving-average process and a random process whose autocorrelation function exponentially decays are given. Finally, to avoid any wrong conclusions, we propose to derive abacuses linking the value provided by the DFA or its variant with the properties of the signal and the number of samples available.

A processing chain from the transmitter to the receiver dealing with a stepped frequency waveform combined with phase coding (PC) has been proposed in a recent paper. It consists in splitting the spectrum of a PC pulse into predetermined portions, and then transmitting the corresponding time-domain signals. At the receiver, a modified version of the frequency domain (FD) algorithm is used to process the received echoes. However, this processing chain could be improved. Indeed, alternative modulations could be considered to offer a degree of freedom to the practitioner. In addition, when the number of portions becomes large, the performance of the proposed FD algorithm degrades, the spectrum of the reconstructed waveform being distorted. Therefore, in this paper, the novelty stands in the following items: 1) at the transmitter, the non-linear frequency modulation (NLFM) can be considered as an alternative to PC $2)$ at the receiver, a novel time-domain waveform reconstruction (TWR) is proposed to process the received echoes in the time domain instead of operating in the frequency domain. Our simulations show that, unlike the modified FD algorithm, for any number of portions, the performance obtained using the TWR algorithm is the same at high signal-to-noise ratio (SNR), whereas at low SNR, the larger the number of portions used, the better the performance.

International audience; The non-linear frequency modulation (NLFM) waveform is one of the existing waveforms that can be used in high range resolution radar applications. However, a high sampling frequency and consequently an expensive ADC are required. To overcome this drawback while taking advantage of the features of the NLFM waveform, we suggest approximating the wideband NLFM waveform by a piecewise linear waveform and using it in a stepped frequency (SF) framework. Thus, a variable chirp rate SF-LFM waveform is proposed where SF is combined with a train of LFM pulses having different chirp rates, durations, and bandwidths. In this paper, these parameters are derived from a tangent-based NLFM waveform. At the receiver, a generalized version of the time domain (TD) algorithm is proposed to process the received echoes. Our purpose is to obtain the high range resolution profile (HRRP) whose properties are of the same magnitude orders as those obtained using a tangent-based NLFM waveform. These properties are the peak sidelobe ratio, the integrated sidelobe, and the range resolution. Toward this goal, a multi-objective optimization issue is addressed to deduce the parameters of the proposed waveform by using two types of approaches based on evolutionary algorithms. Their relevance is compared. Our analysis and simulations show that the proposed approaches attain the targeted performance goals with a smaller sampling frequency at the receiver.

International audience; The detrended fluctuation analysis (DFA) and its variants such as the detrended moving average (DMA) are widely used to estimate the Hurst exponent. These methods are very popular as they do not require advanced skills in the field of signal processing and statistics while providing accurate results. As a consequence, a great deal of interest has been paid to compare them and to better understand their behaviors from a mathematical point of view. In this paper, our contribution is threefold. Firstly, we propose another variant avoiding the discontinuities between consecutive local trends of the DFA by a priori constraining them to be continuous. Secondly, we show that, in all these approaches, the square of the fluctuation function can be presented in a similar matrix form. When the process is wide-sense stationary (w.s.s.), the latter can be seen as the power of the output of a linear filtering whose frequency response depends on the given method. In the general case, an interpretation of the square of the fluctuation function is also given by expressing it as the convolution between the 2D-Fourier transform of two matrices, one whose elements correspond to the instantaneous correlation function of the signal and the other which depends on the detrending method. To end up, an illustration is provided in the field of avionics for the detection of the visual tunneling, a deleterious cognitive state.

Even if they can be outperformed by other methods, the detrended fluctuation analysis (DFA) and the detrended moving average (DMA) are widely used to estimate the Hurst exponent because they are based on basic notions of signal processing. For the last years, a great deal of interest has been paid to compare them and to better understand their behaviors from a mathematical point of view. In this paper, our contribution is the following: we first propose to express the square of the so-called fluctuation function as a 2D Fourier transform (2D-FT) of the product of two matrices. The first one is defined from the instantaneous correlations of the signal while the second, called the weighting matrix, is representative of each method. Therefore, the 2D-FT of the weighting matrix is analyzed in each case. In this study, differences between the DFA and the DMA are pointed out when the approaches are applied on non-stationary processes.

The detrended fluctuation analysis (DFA) is widely used to estimate the Hurst exponent. Although it can be outperformed by wavelet based approaches, it remains popular because it does not require a strong expertise in signal processing. Recently, some studies were dedicated to its theoretical analysis and its limits. More particularly, some authors focused on the so-called fluctuation function by searching a relation with an estimation of the normalized covariance function under some assumptions. This paper is complementary to these works. We first show that the square of the fluctuation function can be expressed in a similar matrix form for the DFA and the variant we propose, called Continuous-DFA (CDFA), where the global trend is constrained to be continuous. Then, using the above representation for wide-sense-stationary processes, the statistical mean of the square of the fluctuation function can be expressed from the correlation function of the signal and consequently from its power spectral density, without any approximation. The differences between both methods can be highlighted. It also confirms that they can be seen as ad hocwavelet based techniques.

In this paper, we first propose to analyze the properties of the Kullback-Leibler divergence between wide-sense stationary random processes that can be modeled by ARMA or ARFIMA processes. This study makes it possible to introduce a new feature useful to compare two random processes and called "the asymptotic KL increment". The latter depends on various parameters such as the inverse filters associated to the random processes. An interpretation of "the asymptotic KL increment" is also given. Then, we propose to use it in order to compare the inter-beat intervals, which characterize the cardiac rhythm, when the subjects are either in a calm and soothing situation or under stress.

In multi-object tracking, some target groups can share a coordinated motion. They can for instance form a convoy or follow a road network. In any case, the target trajectories can be modeled by using the group motion characteristics and the self-properties of the targets. For this purpose, we introduce a new model: a hierarchical random finite set (RFS). A first RFS is considered to represent the target groups. Their numbers, their compositions and their common motion characteristics are assumed to be random. Each group is itself represented as an RFS for which the target number and the target states such as the position and velocity are random. We also propose a metric to compare two hierarchical RFSs taking into account all the sources of uncertainties (the cardinality of both the groups and the targets within the groups and the unknown motion parameters).

Comparing processes or models is of interest in various applications. Among the existing approaches, one of the most popular methods is to use the Kullback-Leibler (KL) divergence which is related to Shannon’s entropy. Similarly, the Renyi divergence of order α can be deduced from the Renyi entropy. When α tends to 1, it leads to the KL divergence. In this paper, our purpose is to derive the expression of the Renyi divergence between the probability density functions of k consecutive samples of two real first-order moving average (MA) processes by using the eigen-decompositions of their Toeplitz correlation matrices. The resulting expression is compared with the expressions of the Rao distance and the Jeffrey’s divergence (JD) based on the eigenvalues. The way these quantities evolve when k increases is then presented. When dealing with unit-zero MA processes, the derivate is infinite for the JD and finite for the others. The influence of α is also studied.

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 objects, organizing and rendering the objects accessible to students, disseminating the history of the telecommunications industry by using a website and quizzes and helping students see how the telecommunications industry and engineers have contributed to social and cultural evolution. This exhibit is particularly useful for the Minute Telecom, inspired from the Minute Physics, where the students are invited to create a video on theoretical concepts such as Shannon's theorem, mobile communication systems or the impact of innovation on user habits.

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 parameter on it. More particularly, we show that the ratios between the variance of the additive white noise and the variance of the AR-process driving process on the one hand, and the sum of the ratios between the SCE process power and the AR-process PSD at the normalized angular frequencies on the other hand, has a strong impact on the JD. The 2-norm of the AR-parameter has also an influence. Illustrations confirm the theoretical part.

Time series models play a key-role in many applications from biomedical signal analysis to applied econometric. The purpose of this paper is to compare 1 st -order moving-average (MA) models by using dissimilarity measures such as the Jeffrey's divergence (JD), which is the symmetric version of the Kullback-Leibler divergence (KL). The MA models can be real or complex. They can also be disturbed by additive white noises or not. Analytical expressions are first proposed and analyzed. Then, the JD is used to compare more than two 1 st -order MA models in order to extract MA model subsets. In the latter case, we suggest analyzing the higher-order singular values of a tensor defined from the JDs between models over time to deduce the number of subsets and their cardinals. Simulation results illustrate the theoretical analysis. HighlightsAnalytical Jeffrey's Divergence expressions are provided for 1st-order MA models.Real or complex, noise-free or noisy 1st-order MA model cases are studied.Time evolution of the Jeffrey's Divergence depends on the 1st-order MA parameters.Comparative study with other dissimilarity measures (Rao distance, etc.) is done.Two methods are proposed to compare more than two 1st-order MA models.

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 transient period, the JD between both models is incremented by a constant value that depends on the model parameters while k is incremented by 1. The JD is hence characterized by this increment and it is not necessary to consider a lot of samples.

International audience; This paper deals with digital post-distortion for radio frequency (RF) power amplifiers (PAs) used in cognitive radio (CR) systems. This technique is based on a new approach modelling the PA behavior. The latter characterizes not only the PA non-linearities and memory effects but also its highly-varying behavior with carrier frequency in CR context. Given this modelling, a Kalman algorithm based post-distortion and detection is used to compensate the CR-PA non-linear effect and restore the input signal. This method is suitable for uplink communications in CR context because it saves the consumed power at the transmitter. Finally, this on-line technique does not require known test signals to estimate the PA model parameters.

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, the symmetric Itakura-Saito divergence, the log-spectral distance or Jeffrey's divergence (JD), which corresponds to the symmetric version of the Kullback-Leibler divergence. These matrices are then transformed to get the same properties as correlation matrices. Eigenvalue decompositions are performed to get the number of AR-model subsets and the estimations of their cardinals. Finally, K-means are used for classification. A comparative study points out the relevance of the JD-based method. Illustrations with sea radar clutter are also provided.

This paper deals with a phase-coded waveform which combines two binary phase codes, each impacting on specific properties of the radar receiving channel. After giving a detailed analysis of the expression of the received signal after processing when the Gaussian clutter is modeled by a pth-order autoregressive process, we focus our attention on the choice of the two phase codes: one aims at increasing the unambiguous range whereas the other is chosen by taking into account several criteria such as the detection performance. For this purpose, we suggest determining the Pareto fronts of 1st, 2nd and 3rd orders by means of an exhaustive search. Given the three Pareto fronts for different types of clutters simulated by making the AR parameters vary, we provide an automatic way to determine, before embedding it, the most robust phase codes using a fuzzy logic operator.

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 possible to derive the variances of both the driving process and the additive white noise. The method is based on the Frisch scheme. One of the main difficulties in this case is to evaluate the minimal AR-process order that must be considered to have a 'good' approximation of the MA process. To this end, we propose a way based on K-means method. Simulation results of the proposed method are presented and compared to existing MA-parameter estimation approaches.

Optimal filters such as Kalman filters are used in a wide range of applications from speech enhancement to biomedical applications. They are based on an a priori state-space model describing a dynamic system. If this model is not well-suited, the accuracy of the state vector may be poor. Therefore, several estimators based on different models can be combined. However, state-space models that are dissimilar enough must be chosen. To our knowledge, there are no guidelines to select them, we hence address this issue in this paper. Given an initial model set, our aim is to determine subsets of similar models by using Jeffrey?s divergence between the distributions of the state-vector time paths based on the different models. Our approach operates with the following steps: the so-called dissimilarity matrix composed of Jeffrey?s divergences between model pairs is created. Then, this matrix is transformed to get the same properties as a correlation matrix and an eigenvalue decomposition is performed. Subsequently, we propose an interpretation of the predominant eigenvalues which is then used to deduce the number of model subsets and their cardinals. A classification algorithm can then be considered to determine which models belong to which subsets. HighlightsWe propose to compare two state models by using the Jeffrey's divergence (JD).We generalize the above approach to determine subsets in an initial model set.The eigenvalues decomposition is then interpreted to deduce the number of model subsets.Then, a classification algorithm can be used to determine which model belongs to which subset.The method is more particularly applied to a toy example and to tracking.

This paper deals with a system combining orthogonal frequency di- vision multiplexing (OFDM) and interleave-division multiple access (IDMA). OFDM makes the system robust against intersymbol inter- ference, whereas IDMA combats the multiple access interference. Nevertheless, unwanted phenomena must be taken into account: 1/ carrier frequency offset (CFO) must be estimated/corrected to guarantee the orthogonality between subcarriers and hence the sym- bol detection in the system. 2/ the conventional iterative IDMA receiver, initially proposed by Ping et al., requires a priori knowl- edge of the multipath channel. Therefore, the CFO and the multipath channel must be estimated "accurately" in an OFDM-IDMA system. Our contribution is to propose a new scheme where a CFO correc- tion is no longer necessary, unlike common OFDM approaches. We show that without a CFO correction, the symbols transmitted by the different users can be recovered by modifying the conventional iterative architecture of the IDMA receiver. When considering an OFDM-IDMA network over different Rayleigh fading channels, simulation results clearly show the efficiency of the proposed algorithm in terms of estimation accuracy and bit error rate.

National audience; In the STAP domain, modeling the interferences as an autoregressive (AR) process with the detector called Parametric Adaptive Matched Filter (PAMF), provides an estimation of the clutter-rejection filter with few training data. The main difficulty of this approach is the estimation of the AR matrices by using the training data. Thus, we propose an on-line estimation based on the Kalman filter and its variants. A comparative study is carried out and illustrates the relevance of such approaches with data provided by the DGA.

In radar processing, coloured transmission aims at improving the detection of targets that appear as fast as they disappear. It consists in simultaneously transmitting different waveforms using a wide beam. To differentiate the transmitted waveforms, various orthogonal coding schemes such as phase and frequency coding have been considered. In this paper, we suggest using in the MIMO radar case the so-called multicarrier phase coded signals (MCPC) initially introduced in SISO radar processing. This approach has the advantage of having better performances than phase coding based schemes. In addition, it has a lower computational cost than the frequency coding system.

Whereas lecturing is the most widely used mode of instruction, we have explored small-group learning projects to make signal processing more appealing at the University and in Engineering schools in Bordeaux (France). The projects cover a wide range of applications, from audio processing to mobile communication system analysis and can be based on problems suggested by industrial partners. After a state of the art in the area, the students develop signal processing algorithms and usually deliver new softwares. At the end of the semester, they provide a final 8-page report and present their work during a one-day workshop. The projects enable the students to experience cooperative works, which is mostly done in industry. In addition, they help the students to see more easily the links between the courses they follow, including project managing. The students are hence involved in dialog inside their own group, in writing English reports as well as in problem solving, analysis and synthesis. This paper presents four examples dealing with speech processing, spectral analysis, Universal Mobile Telecommunications System (UMTS) mobile positioning and orthogonal frequency division multiple access (OFDMA) synchronization.

on line depuis novembre 2008; International audience; This paper deals with the on-line estimation of time-varying frequency-flat Rayleigh fading channels based on training sequences and using H∞ filtering. When the fading channel is approximated by an autoregressive (AR) process, the AR model parameters must be estimated. As their direct estimations from the available noisy observations at the receiver may yield biased values, the joint estimation of both the channel and its AR parameters must be addressed. Among the existing solutions to this joint estimation issue, Expectation Maximization (EM) algorithm or crosscoupled filter based approaches can be considered. They usually require Kalman filtering which is optimal in the H2 sense provided that the initial state, the driving process and measurement noise are independent, white and Gaussian. However, in real cases, these assumptions may not be satisfied. In addition, the state-space matrices and the noise variances are not necessarily accurately estimated. To take into account the above problem,we propose to use two crosscoupled H∞ filters. This method makes it possible to provide robust estimation of the fading channel and its AR parameters.

This paper deals with the estimation of rapidly time- varying Rayleigh fading channels in synchronous multi-carrier direct-sequence code division multiple access (MC-DS-CDMA) systems. When the fading channel is approximated by an autoregressive (AR) process, it can be estimated by means of Kalman filtering for instance. Nevertheless, this requires the a priori estimation of the AR parameters. One standard solution consists in first fitting the AR process autocorrelation function to the Jakes one and then solving the resulting Yule-Walker equations (YWE). However, due to the band-limited nature of the Jakes Doppler spectrum, severely ill-conditioned YWE are unavoidable for all but very small AR model orders. Therefore, previous studies focused only on 1st and 2nd order AR models. To overcome the ill-conditioning problem, a very small positive bias can be added to the main diagonal of the autocorrelation matrix in the YWE. Even if the resulting process is not band-limited and corresponds to an AR process+noise model, the approximation can be of interest. Indeed, according to our simulation results, high-order AR models+noise yield significant results in terms of spectrum approximation and bit error rate (BER). However, to reduce the computational cost, a 5th order AR model can be considered.

The paper deals with the design of a receiver for synchronous multi-carrier direct-sequence code division multiple access (MC-DS-CDMA) systems, in time-varying frequency selective fading channels. We consider a structure operating in two steps; after channel compensation and time alignment along each carrier, the resulting signals are combined and define the input of the blind adaptive multiuser detector. Our contribution is twofold. First, we propose a generalization of the blind least mean squares (LMS) algorithm on the basis of multiple delayed input signal vectors, which has the advantage of improving the convergence features in a high multiple access interference (MAI) environment and time-varying fading scenario. In addition, we carry out a comparative study between the proposed algorithm and previously published blind LMS and blind Kalman filter algorithms. Simulation results show that the proposed algorithm can trade-off performance with complexity. In other words, it can have a better performance than the existing blind LMS algorithm and less computational complexity than the blind Kalman filter algorithm.

In the framework of speech enhancement, many approaches have been developed when the speech signal is only corrupted by additive noise. However, in an auditorium, when echoes appear, spatial transformations between the sources and the microphones must be considered. For this reason, we propose to deal with speech contaminated by both convolutive and additive coloured noise. The two-microphone based noise canceller we present operates as follows: firstly, a prewhitening step is carried out. Secondly, the blind deconvolution method we use makes it possible to estimate the finite impulse responses (FIR), their orders and the variances of the additive noise, which is a great advantage. Then, the filtered versions of speech, estimated by means of a subspace method, are used to retrieve the original speech.

When a single sequence of noisy observations is available, the autoregressive (AR)-model based methods using Kalman-filter make it possible to enhance speech. However, the estimation of the AR parameters is required, but is still a challenging problem as the signal is corrupted by an additive noise. In this paper, we propose to both estimate the signal and the AR parameters by developing a recursive instrumental variable-based approach. Avoiding a non linear approach such as the EKF, this method involves two conditionally linked Kalman filters running in parallel. Once a new observation is available, the first filter uses the latest estimated AR parameters to estimate the signal, while the second filter uses the estimated signal to update the AR parameters. A comparative study between existing speech enhancement methods is completed.

In the framework of speech enhancement, many approaches have been developed when the speech signal is embedded in an additive noise, white or coloured. In this paper, we focus our attention on speech contaminated both by convolutive and additive noise. This happens for instance in audio conferences or in an auditorium when echoes appear. The approach we propose here makes it possible to retrieve speech by using a two-microphone based device. It operates as follows: first, one performs the blind estimation of the variances of the additive noises and the finite impulse responses (FIR), which represent the spatial transformations between the sources and the microphones. Then, the filtered versions of speech, estimated by means of subspace methods, are used to retrieve the source speech. This approach has the advantage of not using a Voice Activity Detector (VAD), which is usually required to estimate the noise variances. In addition, the method can be easily extended to the additive coloured noise by introducing a pre-whitening step, in each "channel".

This paper deals with Kalman filter-based enhancement of a speech signal contaminated by a white noise, using a single microphone system. Such a problem can be stated as a realization issue in the framework of identification. For such a purpose we propose to identify the state space model by using subspace non-iterative algorithms based on orthogonal projections. Unlike estimate-maximize (EM)-based algorithms, this approach provides, in a single iteration from noisy observations, the matrices related to state space model and the covariance matrices that are necessary to perform Kalman filtering. In addition no voice activity detector is required unlike existing methods. Both methods proposed here are compared with classical approaches.

Recent studies in human health assume a causal link between the complexity of psychophysiological control systems and the complexity of their resulting biosignals. This PhD illustrates the aforementioned principle by relying on an interdisciplinary approach, combining physiology, psychology and signal processing. The dynamics of human output physiological signals are studied in response to induced stress in individual or collective situations. The objective is to extract individual signatures depicting the central and autonomic regulations at rest or in different experimental situations. Since stress is a multifactorial process depending on the individual perception and interpretation of a situation, the study of physiological signals is combined with the evaluation of psychological contextual and dispositional characteristics. We focus our attention on cardiac regulations which are analysed from the time series defined by the successive durations of the RR intervals. Statistical signal processing methods, either temporal, frequency or non-linear, are used to study the adaptive capacities of individuals facing different situations of cognitive tasks associated or not with stressors. A particular interest is given to multiscale entropy to assess the complexity of signals, which makes it possible to consider the interconnections existing between cortical, subcortical structures and autonomic cardiac regulations. The probability density functions of recorded cardiac signals along each different experimental situation are compared two by two by using the Kullback-Leibler divergence, and in particular the estimate of the asymptotic increment of the divergence of Kullback-Leibler. The results show that studying cardiac signals allows to discriminate the psychophysiological state of an individual when facing either cognitive tasks or stressful situations. Psychophysiological state differences emerge during stress, not only at an individual level, but also at a collective one, for which the subject is not directly confronted with stressful stimuli. The stress is therefore empathic. Two experimental applications are carried out from our results. First, we show that the cardiac complexity, which is altered in people stressed at work, can be improved by cardiac coherence biofeedback training. Second, signal processing methods are also used to the study of postural regulation. Overall, our results strengthen the interest of human monitoring in health.; Les études récentes en santé humaine supposent un lien de causalité entre la complexité des systèmes de contrôle psychophysiologique et la complexité des biosignaux qu’ils émettent. Le travail mené dans le cadre de cette thèse illustre ce principe en s’appuyant sur une démarche interdisciplinaire, combinant physiologie, psychologie et traitement du signal. Il vise à étudier les dynamiques des signaux physiologiques émis par l’Homme, en réponse à un stress induit en situation individuelle ou collective. Le stress étant un processus multifactoriel qui dépend de la perception et de l’interprétation d’une situation donnée par un individu, l’étude des signaux physiologiques est combinée à l’évaluation de caractéristiques psychologiques contextuelles et dispositionnelles. En particulier, nous nous intéressons aux régulations cardiaques qui sont analysées à partir des séries temporelles définies par les durées successives des intervalles RR. Des approches statistiques temporelles, fréquentielles ou non-linéaires sont utilisées afin d’étudier les capacités d’adaptation des individus confrontés à différentes situations de tâches cognitives associées ou non à des facteurs stressants. Il s’agit d’extraire des signatures caractéristiques des régulations centrales et autonomes, au repos ou dans différentes situations expérimentales. Dans ce travail, un intérêt particulier est accordé à l’entropie multi-échelles afin d’évaluer la complexité des signaux, une complexité induite par les interconnexions existant entre structures corticales, sous-corticales et régulations autonomes cardiaques. Nous proposons également d’analyser les signaux collectés durant les différentes situations expérimentales, en comparant deux à deux leurs densités de probabilité à partir de la divergence de Kullback-Leibler, et en particulier d’une estimation de l'incrément asymptotique de la divergence de Kullback-Leibler. Les résultats obtenus mettent en évidence que l’étude des signaux cardiaques peut permettre d’appréhender l’état psychophysiologique d’un individu lorsqu’il est confronté à des situations de tâches cognitives et de stress. Des différences d’états apparaissent non seulement à l’échelle individuelle, mais également à l’échelle collective, lorsque l’individu n’est pas directement confronté aux stimuli stressants mais que le stress est de nature empathique. Enfin, deux applications sont réalisées. Nous montrons que la complexité des signaux cardiaques, altérée chez des personnes stressées au travail, peut être améliorée par un entraînement à la cohérence cardiaque. Nous appliquons également les méthodes de traitement du signal à l’étude de la régulation posturale. L’ensemble de nos résultats renforcent l’intérêt du monitoring de l’humain en matière de santé.

Estimating the autoregressive parameters from noisy observations has been addressed by various authors for the last decades. Although several on-line or off-line approaches have been proposed when the additive noise is white, few papers deal with the additive moving average noise. In this paper, we suggest estimating the model parameters by using the prediction error method. Despite its high computational cost, the method has the advantage of being efficient in the Gaussian case. A comparative study with existing methods is then carried out and points out the efficiency of our approach especially when the number of samples is small.