Maximum Likelihood (ML) Direction-of-Arrival (DoA) estimation on the Vectorized Covariance Matrix Model (VCMM) exhibits improved performance in severe conditions compared to standard methods. Indeed, it benefits from the VCMM capacities summarized through the Virtual Array (VA) concept. Due to finite number of samples, the VCMM is corrupted by a coloured Gaussian noise. As a remedy, we previously introduced a pre-whitening noise transform converting the coloured noise into white Gaussian noise. Using the whitened model, we recently shown equivalence between sparse DoA estimators and the ML thereby enabling efficient implementation of ML DoA estimation under white Gaussian noise.In this work, the noise pre-whitening transform is shown to significantly improve the sparse problem conditioning by spatially decorrelating the dictionary vectors associated to sources directions thus simplifying the implementation of ML DoA estimation with a sparse representation. To this end, the expression of the spatial correlation coefficient after whitening is derived.Numerical simulations confirm the performance improvement of sparse DoA estimators after whitening for closely separated sources.

This paper proposes an unrolled Expectation Maximization (EM) algorithm tailored for robust radio interferometric imaging in the presence of non-Gaussian radio interferences . We introduce a compound Gaussian model for the observation noise and derive an unrolled neural architecture based on the EM algorithm to tackle the reconstruction problem in a robust manner. This innovative approach aims to enhance image reconstruction by simultaneously incorporating model information and generalization for the case of non-Gaussian heavy-tailed noise distribution, while leveraging the benefits of deep learning . Our experiments demonstrate significant improvements over state-of-the-art methods, highlighting the efficacy of our proposed scheme in handling the complexities of radiofrequency interference and improving image reconstruction accuracy.

Interferences and computational cost pose significant challenges in large-scale interferometric sensing, impacting the accuracy and numerical efficiency of imaging algorithms. In this letter, we introduce an imaging algorithm using antenna switching based on expectation-maximization (EM) to address both challenges. By leveraging the low-rank noise model, our approach effectively captures interferences in interferometric data. Additionally, the proposed switching strategy between different sub-arrays reduces significantly the computational complexity during image restoration. Through extensive experiments on simulated datasets, we demonstrate the superiority of the low-rank noise model over the Gaussian noise model in the presence of interferences. Furthermore, we show that the proposed switching approach yields similar imaging performance with fewer antennas compared to the full array configuration, thereby reducing computational complexity, while outperforming non-switching configurations with the same number of antennas.

This paper addresses the challenge of interference mitigation and reduction of computational cost in the context of radio interferometric imaging. We propose a novel maximum-likelihood-based methodology based on the antenna sub-array switching technique, which strikes a refined balance between imaging accuracy and computational efficiency. In addition, we tackle robustness regarding radio interference by modeling the additive noise as t-distributed. Through simulation results, we demonstrate the superiority of the t-distributed noise model over the conventional Gaussian noise model in scenarios involving interferences. We evidence that our proposed switching approach yields similar imaging performances with far fewer visibilities compared to the full array configuration, thus, diminishing the computational complexity.

On-grid based direction-of-arrival (DOA) estimation methods rely on the resolution of a difficult group-sparse optimization problem that involves the ℓ2,0pseudo-norm. In this work, we show that an exact relaxation of this problem can be obtained by replacing the ℓ2,0term with a group minimax concave penalty with suitable parameters. This relaxation is more amenable to non-convex optimization algorithms as it is continuous and admits less local (not global) minimizers than the initial ℓ2,0-regularized criteria. We then show on numerical simulations that the minimization of the proposed relaxation with an iteratively reweighted ℓ2,0algorithm leads to an improved performance over traditional approaches.

In sparse DOA estimation methods, the regularization parameter λ is generally empirically tuned. In this paper, we provide a statistical method allowing to estimate an admissible interval where λ must be chosen. This work is conducted in the case of an Uniform Circular Array, well known for its θ invariant performances, and vectorized covariance matrix observation. In the recent work [1], it is shown that the equivalence between the ℓ0-constrained problem and the corresponding regularized one is obtained for λ belonging to a given interval. This interval is conditional to an observation. The purpose of this work is to generalize this result for stochastic observations, providing so an interval I of λ valid in all scenarios for an UCA. This interval is not data dependent. Simulation results validate the proposed approach.

This paper investigates calibration of sensor arrays in the radio astronomy context. Current and future radio telescopes require computationally efficient algorithms to overcome the new technical challenges as large collecting area, wide field of view and huge data volume. Specifically, we study the calibration of radio interferometry stations with significant direction dependent distortions. We propose an iterative robust calibration algorithm based on a relaxed maximum likelihood estimator for a specific context: i) observations are affected by the presence of outliers and ii) parameters of interest have a specific structure depending on frequency. Variation of parameters across frequency is addressed through a distributed procedure, which is consistent with the new radio synthesis arrays where the full observing bandwidth is divided into multiple frequency channels. Numerical simulations reveal that the proposed robust distributed calibration estimator outperforms the conventional non-robust algorithm and/or the mono-frequency case.

In many deterministic estimation problems, the probability density function (p.d.f.) parameterized by unknown deterministic parameters results from the marginalization of a joint p.d.f. depending on additional random variables. Unfortunately, this marginalization is often mathematically intractable, which prevents from using standard maximum likelihood estimators (MLEs) or any standard lower bound on their mean squared error (MSE). To circumvent this problem, the use of joint MLEs of deterministic and random parameters are proposed as being a substitute. It is shown that, regarding the deterministic parameters: 1) the joint MLEs provide generally suboptimal estimates in any asymptotic regions of operation yielding unbiased efficient estimates, 2) any representative of the two general classes of lower bounds, respectively the Small-Error bounds and the Large-Error bounds, has a “non-standard” version lower bounding the MSE of the deterministic parameters estimate.

This paper investigates parametric direction-of-arrival (DOA) estimation in a particular context: i) each sensor is characterized by an unknown complex gain and ii) the array consists of a collection of subarrays which are substantially separated from each other leading ] to a structured noise covariance matrix. We propose two iterative algorithms based on the maximum likelihood (ML) estimation method adapted to the context of joint array calibration and DOA estimation. Numerical simulations reveal that the two proposed schemes, the iterative ML (IML) and the modified iterative ML (MIML) algorithms for joint array calibration and DOA estimation, outperform the state of the art methods and the MIML algorithm reaches the Cramer-Rao bound for a low number of iterations.

Bayesian hierarchical modelling is a well-established branch of Bayesian inference. In this letter, we derive and study the estimation performance for the Bayesian hierarchical linear model (BHLM). Specifically, we consider a linear model with hierarchical priors for the involved amplitude and noise vectors. We provide closed-form expressions of the Bayesian Cramér-Rao bound (BCRB) for the following settings: (i) an arbitrary prior and hyperprior and (ii) a Gaussian-Y prior for the amplitudes, while the prior of noise is a Gaussian-X in both cases. Gaussian-X means that the conditional prior given the hyperparameter is Gaussian and X is the hyperprior. For the hierarchical distribution associated with spherical invariant random variables, the BCRB has a compact closed-form expression and enjoys several interesting properties that are discussed. Finally, we provide a theoretical analysis of the statistical efficiency of the linear minimum mean square error (MMSE) estimator in the low- and high-noise variance regimes when the hyperparameters are stochastically dominant.

This paper addresses the direct geolocation of sources in one step via a multi-base (or multi-array) context. The 1-step methods such as DPD and LOST are working on a global array composed of all the sensors of each base. However, even if these algorithms introduce a narrowband decomposition (unfortunately imperfect), these recent powerful algorithms can be disturbed by the residual broadband effect due to the partial coherence of signals (even incoherent signals) between stations. The main contribution of this work is to study the DPD performance in presence of a residual array-broadband effect.

In the literature of direct blind geolocalization algorithms, two algorithms are mainly concurrent: DPD and LOST. The first one appears to be very sensitive to the spectral contents and the second, although presenting wide scope of scenarii with better performance than DPD, does not exploit the TDoA. This last algorithm could therefore be again improved. The purpose of this paper is to propose a new algorithm LOST-FIND which exploits (for non monochromatic sources) the structured TDoA between stations thanks to a spectral estimation of sources. The proposed algorithm is an iterative extension of LOST algorithm initially designed for monochromatic sources. Simulations confirm the expected improvements versus DPD and LOST.

In statistical signal processing, hybrid parameter estimation refers to the case where the parameters vector to estimate contains both non-random and random parameters. Numerous works have shown the versatility of deterministic constrained Cramér-Rao bound for estimation performance analysis and design of a system of measurement. However in many systems both random and non-random parameters may occur simultaneously. In this communication, we propose a constrained hybrid lower bound which take into account of equality constraint on deterministic parameters. The usefulness of the proposed bound is illustrated with an application to radar Doppler estimation

This letter investigates hybrid lower bounds on the mean square error in order to predict the so-called threshold effect. A new family of tighter hybrid large error bounds based on linear transformations (discrete or integral) of a mixture of the McAulay-Seidman bound and the Weiss-Weinstein bound is provided in multivariate parameters case with multiple test points. For use in applications, we give a closed-form expression of the proposed bound for a set of Gaussian observation models with parameterized mean, including tones estimation which exemplifies the threshold prediction capability of the proposed bound.

In statistical signal processing, hybrid parameter estimation refers to the case where the parameters vector to estimate contains both non-random and random parameters. As a contribution to the hybrid estimation framework, we introduce a recursive hybrid Cramér–Rao lower bound for discrete-time Markovian dynamic systems depending on unknown deterministic parameters. Additionally, the regularity conditions required for its existence and its use are clarified.

The purpose of this paper is to give a closed form expression of the RMS (Root Mean Square) error of the estimated DOA (Direction Of Arrival) for multi-parametric MUSIC in presence of a modeling error. The multi-parametric MUSIC approach, [1] firstly introduced by [2] in polarization diversity context, estimates with a subspace approach the sources DOAs jointly to the nuisance parameters such as the polarization vector. The results are based on a second order approximation of the multi-parametric criterion with respect to modeling errors. DOA estimation errors is then an Hermitian form of multi-variate complex random variables. Theoretical results are validated by simulations in the context of coherent multi-paths in polarizations diversity.

In statistical signal processing, hybrid parameter estimation refers to the case where the parameters vector to estimate contains both non-random and random parameters. In this communication, we propose a new hybrid lower bound which, for the first time, includes the Ziv-Zakaï bound well known for its tightness in the Bayesian context (random parameters only). For the general case of parameterized mean model with Gaussian noise, closed-form expressions of the proposed bound are provided.

This article investigates hybrid lower bounds in order to predict the estimators mean square error threshold effect. A tractable and computationally efficient form is derived. This form combines the Barankin and the Weiss-Weinstein bounds. This bound is applied to a frequency estimation problem for which a closed-form expression is provided. A comparison with results on the hybrid Barankin bound shows the superiority of this new bound to predict the mean square error threshold.

The CRB is a lower bound of great interest for system analysis and design in the asymptotic region (high SNR and/or large number of snapshots), as it is simple to calculate and it is usually possible to obtain closed form expressions. It is from this perspective that the paper highlights, by means of a classical radar estimation problem, two results useful for system analysis and design: a reparameterization inequality and the equivalence between reparameterization and equality constraints.

The problem of passive localization is commonly solved by independently measuring intermediate parameters (such as angles of arrival (AOA), times of arrival (TOA)…) on several multiple sensors base stations in a first step. In a second step, the transmitted parameters are then used to estimate the position. Recently, studies proposed new promising one step algorithms based on stacked multiple station observations vectors gathering all received signals of all base stations. This strategy leads naturally to a wideband estimation problem, solved in this paper by an alternative space-time processing. The proposed algorithm is compared to existing techniques and the corresponding Cramer-rao bound.

In operational systems (Radar, communication, sonar,‥), for practical considerations the MUSIC pseudo spectrum optimization must be conducted after removing the outliers. When the number of sources is known, this work considers the influence of the statistical rejection of dominating outliers. Strictly speaking, we calculate, in presence of modeling errors, the MUSIC performances (bias and variance) conditionally to the fact that, in the pseudo spectrum, outliers are not dominating the true DOAs. We also provide the probability that dominating outliers occur. These theoretical investigations lead us to propose a outliers-robust MUSIC based on pseudo-spectrum thresholding to remove outliers. We then calculate the performances of the proposed algorithm. These performances prediction is a key tool for operational system design.

Bayesian recursive inference of phase in additive Gaussian noise environments is studied. A tractable conjugate system is established using a von Mises distribution. Its shaping parameter, re, is studied, to reveal the link with classical phase estimation via matched transforms. Uncertainty quantifiers involve a modified Bessel function kernel. The optimal predictor of data is derived in the presence of phase uncertainty. The theory is applied in phase synchronization for a digital receiver, where phase is distributed as a mixture of von Mises. A fully Bayesian treatment of the decoding problem for phase-uncertain carriers results. Simulation results provide evidence for the improvement in accuracy over a certainty-equivalent-based prediction.

In this paper, we study the impact of modeling error on the receiver of a MIMO radar. Following other works on classical array processing, we derive closed-form expressions of the Cramér-Rao bounds for an observation model of a widely spaced MIMO radar affected by modeling error. We show that, as the signal-to-noise ratio increases, the Cramér-Rao bound and the mean square error of the maximum likelihood estimator of the angle-of-arrival do not fall to zero (contrary to the classical case without error modeling) and converge to a fixed limit for which we give a closed-form expression. Moreover, we give a simple closed-form expression of the critical value of the signal-to-noise ratio where this limitation of performance appears.

It is well known that in non-linear estimation problems the ML estimator exhibits a threshold effect, i.e. a rapid deterioration of estimation accuracy below a certain SNR or number of snapshots. This effect is caused by outliers and is not captured by standard tools such as the Cramer-Rao bound (CRB). The search of the SNR threshold value can be achieved with the help of approximations of the Barankin bound (BB) proposed by many authors. These approximations result from a linear transformation (discrete or integral) of the uniform unbiasness constraint introduced by Barankin. Nevertheless, non-linear transformations can be used as well for some class of p.d.f. including the Gaussian case. The benefit is their combination with existing linear transformation to get tighter lower bounds improving the SNR threshold prediction.

Under Gaussian assumptions, the sample covariance matrix (SCM) is encountered in many covariance based processing algorithms. In case of impulsive noise, this estimate is no more appropriate. This is the reason why when the noise is modeled by spherically invariant random vectors (SIRV), a natural extension of the SCM is extensively used in the literature: the well-known normalized sample covariance matrix (NSCM), which estimates the covariance of SIRV. Indeed, this estimate gets rid of a fluctuating noise power and is widely used in radar applications. The aim of this paper is to derive closed-form expressions of the first- and second-order moments of the NSCM

A wide variety of processing incorporates a binary detection test that restricts the set of observations available for parameter estimation and requires to take this statistical conditioning into account to compute the Cramer-Rao bound (CRB). Therefore, we propose a derivation of the CRB for the deterministic signal model conditioned by the energy detector widely used in signal processing applications. This derivation has lead us to introduce novel identities on some conditional expectations of complex circular Gaussian random vectors that may be useful for other derivations.

The search for an easily computable but tight approximation of the Barankin bound (BB) is important for the prediction of the signal-to-noise ratio (SNR) value where the Cramer-Rao bound (CRB) becomes unreliable for prediction of maximum likelihood estimators (MLE) variance. In this paper we propose a method for the derivation of a general class of BB approximations which has the advantage of a clear interpretation. This method suggests a new practical BB approximation, whose computational complexity does not exceed that of the CRB but which seems tighter than existing approximations

This paper deals with lower bound on the mean square error (MSE). In the Bayesian framework, we present a new bound which is derived from a constrained optimization problem. This bound is found to be tighter than the Bayesian Bhattacharyya bound, the Reuven-Messer bound, the Bobrovsky-Zakai bound, and the Bayesian Cramer-Rao bound

This paper presents a detailed theoretical analysis of a recently introduced covariance matrix estimator, called the fixed point estimate (FPE). It plays a significant role in radar detection applications. This estimate is provided by the maximum likelihood estimation (MLE) theory when the non-Gaussian noise is modelled as a spherically invariant random process (SIRP). We study in details its properties: existence, uniqueness, unbiasedness, consistency and asymptotic distribution. We propose also an algorithm for its computation and prove the convergence of this numerical procedure. These results allow us to study the performance analysis of the adaptive CFAR radar detectors (GLRT-LQ, BORD, ...).

This paper provides an asymptotic (in the number of snapshots) closed form expression of the bias and RMS (root mean square) error of the estimated DOA (direction of arrival) for the algorithm recently introduced in Ferreol et al. (2004). This algorithm provides a 1D DOA estimation in a multi-parameter context where the DOA have to be estimated with some separable nuisance parameters. Results are based on a second order approximation of the criterion. DOA estimation errors are then expressed as a ratio of Hermitian forms of multivariate complex random variables. Theoretical results are validated by simulations in a self-calibration context.

This paper studies the performance of the frequency maximum likelihood (ML) estimator of a single tone in Gaussian noise. Two mean-square error (MSE) approximations are first applied and then compared in the case of a known phase offset. The first is proposed by Van Trees and corresponds to the method of interval errors (MIE). The second MSE approximation is proposed by Rife and Boorstyn in . The problem is formulated in the data-aided frequency synchronization frame.

In array processing, the far-field assumption of planar wavefronts is widely used by direction of arrival (DOA) estimators but not always satisfied. In this letter, we introduce a new method for bearing-range estimation, which extends classical subspace-based bearing estimators to a curved wavefront context. The bearing estimation is provided by a one-dimensional procedure, and ranges are simply analytically deduced from the bearing estimates. The proposed approach is illustrated by the introduction of the music curved wavefront (MCW) algorithm.

Estimation of the direction of arrival of a signal source by means of a monopulse antenna is one of the oldest and most widely used high resolution techniques. Although the statistical performance of this estimation technique has been extensively investigated, it has never been analyzed from the viewpoint of a two-sensor system. This deficiency is responsible for the form of the common solution (detector/estimator) which restricts the accessible performance. Applying the optimal detection theory to this problem, when a Raleigh-type signal source is present, shows that changing the detector is necessary to optimize the overall performance. The analytical performance of the new solution has been established , thus complementing the existing characterization of the common solution.

In estimation theory, the asymptotic efficiency of the maximum likelihood (ML) method for independent identically distributed observations and when the number of observations, T, tends to infinity is a well known result. In some scenarios, the number of snapshots may be small, making this result inapplicable. In the array processing framework, for Gaussian emitted signals, we fill this lack at high signal-to-noise ratio (SNR). In this situation, we show that the ML estimation is asymptotically (with respect to SNR) inefficient and non Gaussian.

The signal-to-noise ratio (SNR) threshold behavior is studied in the frame of data-aided carrier synchronization in additive white Gaussian noise. The closed form expression of the Chapman-Robbins bound, relative to the carrier frequency offset estimation is first established then used to derive an indicator of the SNR threshold. For a given sequence of pilot symbols, the threshold region is localized at the departure of the Chapman-Robbins bound from the Cramer-Rao bound. The data-aided maximum likelihood estimator is considered to examine the derived indicator usefulness.

The purpose of this letter is to investigate, in the deterministic case, the nonasymptotic behavior of beamforming estimation of the direction of arrival of a single source impinging on a uniform linear array. We derive an approximate analytical expression of the maximum-likelihood mean-squared error that is valid for all SNR ranges and number of snapshots. Computer simulations confirm the validity of the theoretical investigations.

This letter is devoted to the analysis of the nonasymptotic behavior of beamforming for the bearing estimation of a single stochastic source impinging on an uniform linear array. An analytic expression of the maximum-likelihood mean-squared error is derived. This general expression is valid at any SNR and for any number of snapshots. Simulation results verify the analytically predicted performances.

It is well known that the stochastic maximum-likelihood (SML) method yields Gaussian and efficient estimates when the number of independent identically distributed samples tends to infinity. This letter investigates the behavior of SML bearing estimation for a single source impinging on an antenna array when the SNR tends to infinity for a fixed number of samples. We prove that, rather surprisingly, the bearing estimates are not efficient and are asymptotically distributed according to a Student law. Simulation results confirm theoretical analysis.

The purpose of this work is the estimation of Doppler echoes spectral moments. In case of strong overlapping, Fourier-like techniques provide poor results because of the lack of resolution. We propose the use of stochastic maximum-likelihood (SML) and subspace-based methods (WPSF algorithm) for a joint estimation of spectral moments. The statistical performances (theoretical and empirical by Monte Carlo simulations) of estimators are compared with the Cramer-Rao lower bound. The results of tests performed on very high frequency (VHF) times series obtained during Thunderstorm, Arecibo, PR during September and October 1998 validate the model and algorithms and confirm the interest of both approaches.

We have revisited and solved the problem of establishing lower bounds for the estimation of deterministic parameters by means of a constrained optimization problem. We show that these various bounds (Cramer-Rao, Barankin, Battacharyya) can be easily obtained as the result of an optimization by impozing the bias of the estimator. Simulations results are presented in spectral analysis.

The EXtended Invariance Principle (EXIP) has been recently applied to the structured covariance estimation of a zero mean Gaussian vector [1–2]: the resulting method was named COMET (COvariance Matching Estimation Techniques) [3]. We present in this paper an asymptotically efficient Approximate Maximum Likelihood Method for the joint estimation of the structured mean and covariance of a Gaussian vector. We call the obtained criterion MCOMET (Mean and COvariance Matching Estimation Techniques). It is shown to be separable with respect to mean and covariance parameters and composed of the COMET criterion and a new additional term MMET. Moreover this criterion can be optimized in a computationally efficient way through the use of embedded estimators. It is finally applied to array processing problems.

Signal array processing appears today as a good means to improve the wireless network, as it could permit a better estimation of the propagation channel parameters. Now, this paper focuses on high resolution bearing estimation, when scatterers local to the emitter engender diffuse paths deteriorating the performances of conventional algorithms. S. Valaee and B. Champagne (see IEEE Trans. on Signal Processing, vol.43, no.9, p.2144-53, 1995) introduced a subspace-based algorithm for the characterization of so-called scattered sources. This article extends this previous work and studies the performance of the algorithm in the case of two extreme propagation conditions. The theoretical variances and the Cramer Rao bounds are derived and compared to the Monte Carlo simulations in the case of a Gaussian shape of the angular power density.

The radio electrical transmissions often have multiple paths due to reflections on physical objects or due to the inhomogeneity of the propagation medium for example the ionospheric layers in a HF communication. This work presents a new algorithm for the blind estimation of the physical parameters in a multipath channel (direction of arrival, time delay and fading). The results exposed are useful for tactical applications such as HF radio-localization, or for radio communication systems, to combat the degradations due to the channel. The present study is based on the recent work done on blind deconvolution which estimates the channels impulse responses. Based on a physical path parametric model, a spatio-temporal parametric blind identification of the front wave is performed. These parameters are direction of arrival: DOA /spl theta/, relative time delay /spl tau/ and complex gain /spl phi/ (fading).

In signal subspace parameter estimation techniques, like MUSIC, degradations may occur due to parasite peaks in the spectrum, which may be connected to high sidelobes in the beam pattern or to ambiguities themselves. This paper studies the presence of ambiguities in an array of given planar geometry. We propose a general framework for the analysis and thus we obtain a generalisation of results published by Lo and Marple (1992) and by Proukakis and Manikas (see Proc. ICASSP'94, vol.4, p.549-52, 1994) for rank one and two ambiguities. For rank k/spl ges/3 ambiguities the study is restricted to linear arrays, for which we derive original and synthetic results. We present a geometrical construction that is able to determine all the ambiguous directions which can appear for a given linear array. The method allows determination of any rank ambiguities and for each ambiguous direction set, the rank of ambiguity is obtained. The search is exhaustive. Application of the method requires no assumption for the linear array and is easy to implement. An example is detailed for a non-uniform linear array.

The problem of linear interpolation of nonstationary multidimensional processes with stationary increments is studied. The expressions for the interpolation filters and for the estimation error are derived, which generalize the results of the interpolation theory for stationary processes. Both finite and infinite extent interpolation are considered. An application to the interpolation of an underwater depth map is presented.

Transmissions through multipath channels suffer from Rayleigh fading and intersymbol interference. This can be overcome by sending a (known) training sequence and identifying the channel (active identification). However, in a nonstationary context, the channel model has to be updated by periodically sending the training sequence, thus reducing the transmission rate. We address the problem of blind identification, which does not require such a sequence and allows a higher transmission rate. In order to track nonstationary channels, we have derived an adaptive (Kalman) algorithm which directly estimates the entire set of characteristic parameters. An original adaptive estimation of the noise model has been proposed for this investigation. Monte-Carlo simulations confirm the expected results and demonstrate the performance.

The authors propose a new spectral analysis technique for Doppler radar. They present some limitations of classical methods which motivate their study. Particularly they insist on bias introduced on the wind speed profile in the case of wind shear and strong variations of the reflectivity. In order to improve this behaviour, they introduce a realistic backscattered wave modeling based on stratification of the range gate. Regularisation is necessary to compensate observation limitation specially for some range gates where the SNR is poor. For this purpose they introduce a parametric wind speed profile, to take into account spatio-temporal continuity. They propose a second order steepest descent algorithm which recursively fits the parametric spectrum to the observation. Simulation results demonstrate the expected improvement. The algorithm is also tested on real data.

High resolution methods for estimation of parameters in signal processing (bearing angles in array processing or frequencies in spectral analysis for example) can suffer from a bad selection of the model order. This paper proposes an algorithm based on the properties of the eigenvalues of the covariance matrix. In the noise only case, this matrix is a Wishart matrix. For white noise the profile of ordered eigenvalues fits an exponential law. The proposed algorithm uses this property and looks for a mismatch between the observed profile and the model in order to detect the presence of a signal. Under estimation may result from the occurrence of small signal eigenvalues. Performances is greatly improved by the use of deflation for recursive detection-estimation test. Results of simulations are provided in order to show the capabilities of the algorithm.

This paper presents identifiability and treatment relative to bearing estimation in presence of modelling errors. It introduces the general case of direction-dependent modelling errors. The classical direction-independent case is only a particular case which takes into account a prior knowledge. This general case introduces the important issue of simultaneous sources and perturbation identifiability which is analysed. A new self-calibration technique based on MUSIC algorithm and which is able to treat direction-dependent errors is also proposed. For the purpose of regularization, a "cost term" is introduced in this algorithm. It confers good robustness to the algorithm which usually fails in the presence of great gap between the model and reality. After reduction of the new multidimensional "increased function", values of azimuths are easily obtained on a monodimensional spectrum. Some simulations support results and verify the improvements expected from the theory.

The static networks as multilayer perceptrons (MLP) are able to implement boolean logic functions, to partition the pattern space for classification problems and to approximate nonlinear functions. The present goal is to study their capabilities when used to effect a parametric estimation without an explicit model (supervised estimation). One can also consider varying parameters. The paper focuses on the combined use of second order backpropagation and performant initial values of the weights. The authors also study the effects of noise introduction into training sets in robustness and generalization faculties. These results are then applied to the extraction of parameters from real multisensor signals. They show a drastic reduction in training time, improved robustness against local minima and better generalization.>

Maximum-likelihood (ML) and approximate ML may be considered as the upper state of the art in high-resolution methods, but they suffer from initialization of the sources' number and position. Starting from a crude initialization with a low-resolution method, the authors propose a time recursive method for simultaneous update of the sources' number and location. For the current estimate of the sources' number the algorithm computes the best ML position estimate over the past observations. The corresponding signal is subtracted from the observations, and the residue is tested for the noise-only hypothesis. If the test fails, the sources' number is incremented, a new initialization is provided, and ML estimation proceeds. Emphasis is on the stationary case.>