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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.

A great deal of interest has been paid to enhance the radar range resolution for the last decades. One of the techniques is to construct a waveform combining inter-pulse and intra-pulse modulations. In this paper, stepped frequency (SF) waveform is used to represent the former, whereas phase coding (PC) is considered for the latter. To obtain the high-resolution range profile (HRRP) of a target induced by an SF waveform at the receiver, one of the approaches is the frequency domain (FD) algorithm. It has been successfully applied with SF linear frequency modulation waveforms. However, based on our investigations, processing the SFPC waveform with the FD algorithm does not lead to the performance, in terms of peak sidelobe ratio (PSLR) and integrated sidelobe ratio (ISLR), of the single-carrier phase coding (SCPC) waveform processed with a matched filter (MF). To overcome these drawbacks, we propose to split the spectrum of a phase coded pulse into a predetermined number of portions, and then to successively transmit the time-domain transformed versions of these various portions. The received echoes are then processed with a modified version of the FD algorithm. Our analysis and simulations show that the proposed waveform can be characterized by a PSLR and an ISLR close to those of the SCPC processed with MF in some scenarios.

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; Target classification can be of real interest for sea surveillance in both civil and military contexts. To address this issue, we present two approaches based on the Singer model. The latter has the advantage of covering a wide range of motions depending on the values of its parameters. Given noisy observations, the first method aims at estimating the motion model parameters by taking advantage of the properties of the correlation function of the estimated acceleration. It is based on a genetic algorithm. The second approach is on-line and consists in deriving a joint tracking and classification (JTC) method. Based on various simulations, we study their respective relevance in different operational settings. The proposed JTC corresponds to the best compromise in terms of performance and number of samples required.

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.

This paper proposes a new method for identifying ARMA models in the presence of additive white noise. The method operates with two main steps. First, the noisy ARMA model is approximated by the sum of an high-order AR model with an additive white noise. The parameters of the high-order AR model as well as the driving noise and the additive noise variances are estimated by using an errors-in-variables approach. Second, the coefficients of the ARMA model are extracted from those of the AR model previously identified by means of existing techniques. In particular, three different methods are considered and compared for solving the second step. The effectiveness of the described identification procedure has been tested by Monte Carlo simulations and compared with a prediction error method.

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.

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 representations corresponding to different values of the state-noise covariance matrix. In this framework, jointly estimating the state vector and the covariance matrix is a non-linear non-Gaussian problem. The inference is thus classically carried out using particle filtering techniques. In this case, the choice of the proposal distribution for the particles is of paramount importance regarding the estimation accuracy. A first contribution of this paper is to derive an approximation of the optimal proposal distribution of the particle filter when a DP prior is placed on the distribution of the state-noise covariance matrix. Then, an alternative DP-based formulation of the inference problem is proposed to reduce its dimensionality. It takes advantage that the possible functional forms of the state-noise covariance matrices are known up to a reduced number of time-switching hyperparameters in many applications. An approximation of the optimal proposal distribution is also derived. Finally, the relevance of both proposed approaches is analyzed in the framework of target tracking and a comparative study with existing methods is carried out. HighlightsWe address the joint estimations of the state vector and the state-noise covariance matrix.We use Bayesian non-parametric methods implemented by particle filtering.Two approaches are presented.In both cases, the optimal proposal distribution is derived.Both proposed algorithms are applied to target tracking.

In some multi-object tracking scenarios such as convoys or road constrained motions, it can be advantageous to track groups of targets sharing common motion characteristics, even if they are not necessarily close to each other. The objective is twofold: reducing the computational cost while increasing the accuracies of the individual trajectory estimates. In a previous communication, we introduced a generic model based on hierarchical random finite sets (RFSs) to represent these types of multigroup multi-target scenarios. A first RFS is used to represent the multi-group state: the number of groups, their common motion characteristics and their target compositions are assumed to be random variables. Then, for each group, a second layer of RFSs represents the multi-target state assuming that the number of targets inside a group and their trajectories are also random variables. The main contribution of this paper is to derive a filter dedicated to the state estimation of hierarchical RFSs from sequential sensor measurements. The proposed solution is based on the labeled multi-Bernoulli filter to estimate the group characteristics, which interacts with a bank of probability hypothesis density filters to address the multi-target layer.

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).

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 used. The principle is to consider different target classes depending on their maneuvrability, each of them being associated to a set of motion models. In this context, additional information such as a target length extent measurement can improve both classification and trajectory estimation. Therefore, we propose a multiple-model Bernoulli filter to perform JTC. To jointly estimate the trajectory and the target length which is constant, a Rao-Blackwellized approach is considered. Another contribution is that a bank of probabilistic data association filters is run instead of Kalman filters to account for false detections.

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.

When dealing with time-frequency analysis, each distribution belonging to the Cohen class (CC) is defined by its kernel. It introduces a time-frequency smoothing which impacts on the time-frequency resolution and the cross-term disappearance. Depending on the application, the practitioner has to find the ''best'' compromise. In this paper, we suggest combining several CC time-frequency representations (TFRs), corresponding to coarse-to-fine scales of smoothing. Taking advantage of this diversity, our approach consists in differentiating the signal, assumed to be characterized by 2-D near-linear stable trajectories in the time-frequency plane, and the cross-terms, assumed to be geometrically unstructured. For this purpose, a ''confidence map'' for each TFR is deduced from a local variational analysis of the time-frequency distribution. The set of confidence maps is then used to combine the different TFRs in order to obtain an ''enhanced'' TFR. Our approach is compared with various conventional TFRs by using synthetic data. Despite a comparatively higher computational cost, the resulting enhanced TFR exhibits a high time-frequency resolution while having limited cross-terms. As simulation results confirm the effectiveness of our method, it is then applied in the field of inverse synthetic aperture radar (ISAR) processing.

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 account the target extent measurements for single-target tracking. In this paper, we extend this work to multi-target tracking (MTT) by using probability hypothesis density (PHD) filters. More precisely, assuming that each target class is characterized by its own kinematic-model set, a multiple-model (MM) PHD filter is used for each class. State estimates from each class are then combined by using class probabilities. Finally, the proposed approach, namely a multiclass MM-GMPHD, is applied to maritime-target tracking and simulation results show the relevance of the proposed approach regarding the tracking of various types of targets.

This paper deals with the identification of a nonlinear SISO system modelled by a second-order Volterra series expansion when both the input and the output are disturbed by additive white Gaussian noises. Two methods are proposed. Firstly, we present an unbiased on-line approach based on the LMS. It includes a bias correction scheme which requires the variance of the input additive noise. Secondly, we suggest solving the identification problem as an errors-in-variables issue, by means of the so-called Frisch scheme. Although its computational cost is high, this approach has the advantage of estimating the Volterra kernels and the variances of both the additive noises and the input signal, even if the signal-to-noise ratios at the input and the output are low.

A great deal of interest has been paid to autoregressive parameter estimation in the noise-free case or when the observation data are disturbed by random noise. Tracking time-varying autoregressive (TVAR) parameters has been also discussed, but few papers deal with this issue when there is an additive zero-mean white Gaussian measurement noise. In this paper, one considers deterministic regression methods (or evolutive methods) where the TVAR parameters are assumed to be weighted combinations of basis functions. However, the additive white measurement noise leads to a weight-estimation bias when standard least squares methods are used. Therefore, we propose two alternative blind off-line methods that allow both the variance of the additive noise and the weights to be estimated. The first one is based on the errors-in-variable issue whereas the second consists in viewing the estimation issue as a generalized eigenvalue problem. A comparative study with other existing methods confirms the effectiveness of the proposed methods.

We propose a new estimation method for the characterization of the Hodgkin-Huxley formalism. This method is an alternative technique to the classical estimation methods associated with voltage clamp measurements. It uses voltage clamp type recordings, but is based on the differential evolution algorithm. The parameters of an ionic channel are estimated simultaneously, such that the usual approximations of classical methods are avoided and all the parameters of the model, including the time constant, can be correctly optimized. In a second step, this new estimation technique is applied to the automated tuning of neuromimetic analog integrated circuits designed by our research group. We present a tuning example of a fast spiking neuron, which reproduces the frequency-current characteristics of the reference data, as well as the membrane voltage behavior. The final goal of this tuning is to interconnect neuromimetic chips as neural networks, with specific cellular properties, for future theoretical studies in neuroscience.

This paper deals with the joint estimation of Rayleigh fading channels and symbols in a MC-DS-CDMA system. Formerly, particle filtering has been introduced as a set of promising methods to solve communication problems. PF consists in simulating possible values of the unkwnown parameters and selecting the most likely candidates with regard to the received signal. Here, the Rao-Blackwellized particle filter (RBPF) is used to significantly decrease the variance of the channel/symbol estimates. Our contribution is twofold. Firstly, sinusoidal stochastic models have been shown to better represent the statistical properties of Rayleigh channels than classical autoregressive models. Therefore, the proposed RBPF estimator is based on these models which are expressed as the sum of two sinusoids in quadrature at the maximum Doppler frequency with autoregressive processes as amplitudes. The model parameters are unknown and need to be estimated. Since PFs are not well-suited to recover non-varying parameters, we propose to cross-couple the RBPF with a Kalman filter which makes use of the RBPF ouputs to sequentially update the parameters. Secondly, the choice of an efficient proposal distribution to simulate the particles is crucial for PF performance. We suggest using a suboptimal distribution which simulates likely values of the symbols at a reasonable computational cost.

This paper deals with the joint signal and parameter estimation for linear state-space models. An efficient solution to this problem can be obtained by using a recursive instrumental variable technique based on two dual Kalman filters. In that case, the driving process and the observation noise in the state-space representation for each filter must be white with known variances. These conditions, however, are too strong to be always satisfied in real cases. To relax them, we propose a new approach based on two dual Hinfin filters. Once a new observation of the disturbed signal is available, the first Hinfin algorithm uses the latest estimated parameters to estimate the signal, while the second Hinfin algorithm uses the estimated signal to update the parameters. In addition, as the Hinfin filter behavior depends on the choice of various weights, we present a way to recursively tune them. This approach is then studied in the following cases: (1) consistent estimation of the AR parameters from noisy observations and (2) speech enhancement, where no a priori model of the additive noise is required for the proposed approach. In each case, a comparative study with existing methods is carried out to analyze the relevance of our solution.

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 in different classes. In each class, the SSRs are characterized by a known functional form but differ by a reduced set of unknown hyperparameters. To use this information, we thus propose a new hierarchical model for the SLDM wherein a discrete variable indicates the SSR class. Conditionally to this class, the distributions of the hyperparameters are modeled by DPs. The estimation problem is solved by using a Rao-Blackwellized particle filter. Simulation results show that our model outperforms existing methods in the field of target tracking.

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 inversion and an inverse DFT. In comparison with the initial approach, the algorithm proposed in this article reduces by two the set of parameters required to obtain the INL. This new method is validated on experimental data from the 12-bit ADC12D800RF converter run at 800MHz.

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.

This paper deals with the identification of an autoregressive (AR) process disturbed by an additive moving-average (MA) noise. Our approach operates as follows: Firstly, the AR parameters are estimated by using the overdetermined high-order Yule–Walker equations. The variance of the AR process driving process can be deduced by means of an orthogonal projection between two types of estimates of AR process correlation vectors. Then, the correlation sequence of the MA noise is estimated. Secondly, the MA parameters are obtained by using inner–outer factorization. To study the relevance of the resulting method, we compare it with existing algorithms, and we analyze the identifiability limits. The identification approach is then combined with Kalman filtering for channel estimation in mobile communication systems.

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.

The estimation of the parameters of an autoregressive process (AR) from noisy observations is still a challenging problem. In this paper, we propose to sequentially estimate both the signal and the parameters, avoiding a non-linear approach such as the extended Kalman filter. The method is based on 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. This approach can be viewed as a recursive instrumental variable-based method and hence has the advantage of providing consistent estimates of the parameters from noisy observations. A comparative study with existing algorithms illustrates the performances of the proposed method when the additive noise is either white or coloured.

One of the most important challenges when applying multiple-model approaches is model-set design. However, to our knowledge, there are not general rules to choose models. For this purpose, we recently proposed an approach based on the Jeffrey's divergence to characterize dissimilarities between two state models. In this paper, our contribution is to use the Jeffrey's divergence to classify at least two models into subsets. Our approach consists in creating a dissimilarity matrix composed of Jeffrey's divergences between model pairs. Then, we transform this matrix to get a correlation-like matrix and an eigenvalue decomposition is computed. We propose an interpretation of the predominant eigenvalues and use it to deduce the number of model subsets and their cardinals. Finally, a classification algorithm can be considered to determine which models belong to which subsets. Among the applications, we focus on target tracking.

In current airborne radars, detection and identification are done with two distinct waveforms. However, while the radar switches from one function to another, the target scene can change. In this paper, we propose a hybrid waveform combining intra and interpulse phase codes. This waveform is first processed in a low-resolution “channel”. Then, if a target is detected, the received signal is reprocessed in a high-resolution “channel”. Given the above scenario and assuming that the received data are disturbed by a colored Gaussian clutter, we address the optimization of the phase codes by searching the Pareto front of a multi-objective optimization problem. Finally, we aim at analyzing the sensitivity of the Pareto front to the clutter properties. For this purpose, we study whether a first-order autoregressive (AR) modelling for the clutter in the high-resolution case is relevant or not.

In Cognitive Radio (CR) systems, spectrum sensing plays a key role to determine the free frequency bands. However, when the primary-user (PU) signal spectrum exhibits localized fading, PU detection cannot be guaranteed. In addition, as the CR may use the PU faded frequencies, the PU spectrum can be disturbed by a narrow-band interference (NBI) and synchronization algorithms used for the PU carrier frequency offset (CFO) estimation suffer degradations. In this paper, we propose a new scheme that jointly allows the CR-NBI to be detected and the PU-CFOs and the channels to be estimated in an orthogonal frequency division multiple access (OFDMA) system. It combines a sigma point Kalman filter and a test aiming at detecting a variation of the measurement-noise covariance matrix. Simulation results confirm that the proposed algorithm can accurately detect the CR-NBI and estimate the PU-CFOs.

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.

Space time adaptive processing (STAP) is useful in radar processing to detect a target by filtering the clutter and the additive thermal noise. A derived version based on a multichannel autoregressive (M-AR) model of the clutter has the advantage of reducing the computational cost. Nevertheless, the estimation of the AR matrix parameters is a key issue because the clutter is not Gaussian in real cases. When dealing with an off-line solution, the multichannel least squares method (MLS) can be considered, but the estimation of the disturbance covariance matrix is required. In this paper, we suggest using the so-called fixed point method since it has “matrix- and texture-constant false alarm rate” property (matrix-CFAR and texture-CFAR) and it provides an unbiased and consistent estimate in a non-Gaussian case. A comparative study is then carried out between off-line M-AR based STAP methods and it points out the relevance of the solution we propose.

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 the channel and its AR parameters must be addressed. Existing solutions to this dual estimation issue require Kalman filtering. This kind of filtering is optimal in the H2 sense provided that the underlying state-space model is accurate. Moreover, the initial state, the driving process and the measurement noise must be independent, white and Gaussian. However, in real cases, these assumptions may no longer be satisfied. To relax them, we propose to consider a structure based on two cross-coupled H2 filters. This method makes it possible to provide robust estimation of the fading channel and its AR parameters.

AR modeling is used in a wide range of applications from speech processing to Rayleigh fading channel simulation. When the observations are disturbed by an additive white noise, the standard Least Squares estimation of the AR parameters is biased. Some authors of this paper recently reformulated this problem as an errors-in-variables (EIV) issue and proposed an off-line solution, which outperforms other existing methods. Nevertheless, its computational cost may be high. In this paper, we present a blind recursive EIV method that can be implemented for real-time applications. It has the advantage of converging faster than the noise-compensated LMS based solutions. In addition, unlike EKF or Sigma Point Kalman filter, it does not require a priori knowledge such as the variances of the driving process and the additive noise. The approach is first tested with synthetic data; then, its relevance is illustrated in the field of radar sea clutter rejection.

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.

In various applications from radar processing to mobile communication systems based on CDMA or OFDM, M-AR multichannel processes are often considered and may be combined with Kalman filtering. However, the estimations of the M-AR parameter matrices and the autocorrelation matrices of the additive noise and the driving process from noisy observations are key problems to be addressed. In this paper, we suggest solving them as an errors-in-variables issue. In that case, the noisy-observation autocorrelation matrix compensated by a specific diagonal block matrix and whose kernel is defined by the M-AR parameter matrices must be positive semi-definite. Hence, the parameter estimation consists in searching every diagonal block matrix that satisfies this property, in reiterating this search for a higher model order and then in extracting the solution that belongs to both sets. A comparative study is then carried out with existing methods including those based on the Extended Kalman Filter (EKF) and the Sigma-Point Kalman Filters (SPKF). It illustrates the relevance and advantages of the proposed approaches.

In 1952 Hodgkin and Huxley introduced the voltage--clamp technique to extract the parameters of the ionic channel model of a neuron. Although this method is widely used today, it has a lot of disadvantages. In this paper, we propose an alternative approach to the estimation method of the voltage--clamp technique using metaheuristics such as Simulated Annealing, Genetic Algorithms and Differential Evolution. This method avoids approximations of the original technique by simultaneously estimating all the parameters of a single ionic channel with a single fitness function. To compare the different methods, we apply them on measurements from a neuromimetic integrated circuit. This circuit, due to its analog behavior, provides us noisy data like a biological system. Therefore we can validate the efficiency of our method on experimental-like data.

This paper deals with the estimation of time-varying Multi-Carrier Direct-Sequence Code DivisionMultiple Access (MC-DS-CDMA) fading channels using a training-aided scheme. Our approach consists in using an optimal filtering based on a linear state-space model of the fading channel system. In that case, two issues have to be investigated: 1) what kind of optimal filtering can be used? 2) how to estimate the state-space matrices?

This paper deals with the identification of time-varying frequency-flat Rayleigh fading channels disturbed by an additive white Gaussian noise, using a training sequence based approach. When the channel is modeled by an Autoregressive (AR) process, it can be estimated by using a Kalman filter. However, this solution requires the preliminary unbiased estimations of the AR parameters and the variances of both the additive noise and the driving process in the state space representation of the system. Instead of using the existing noise compensated approaches which usually require a long observation window and do not necessarily provide reliable estimates when the signal to noise ratio is low, we propose an alternative approach using recent results developed for the Errors-In-Variables (EIV) issue. This method consists in estimating the kernel of specific autocorrelation matrices and has the advantage of providing both the noise variances and the channel AR parameters. Moreover, the maximum Doppler frequency can be also deduced.

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.

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.

Kalman algorithms have been widely applied, for instance in single-channel speech enhancement. However, when carrying out Kalman smoothing, computational cost and data storage requirements are two specific problems. A dual-filter-based smoother is proposed and used in the framework of speech enhancement. Our approach comprises a forward-in-time Kalman filter and a backward-in-time Kalman filter. Both filters are based on their respective forward-in-time linear prediction (LP) model and backward-in-time LP model. This method does not require as large a storage space as a standard Kalman smoother does. The algorithm is evaluated by considering a speech signal embedded in a white Gaussian noise. Simulation results show that the proposed algorithm provides a higher improvement of signal-to-noise ratio (SNR) than Kalman filtering.

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.