Henri Clergeot

Some properties of ordered eigenvalues of a Wishart matrix: application in detection test and model order selection

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.

Estimation of the number of signals from features of the covariance matrix: a supervised approach

The purpose of this paper is to provide a fast and simplified detection test for use in the presence of a small number of sources (from 0-2), which is able to accommodate correlated paths and nonwhite noise; conventional eigenvalue-based criteria are unable to do so. For a uniform linear array, using common sense arguments, a small set of significant features of the covariance matrix are used as inputs to a neural net. The nonlinear transfer function of the neural net is adjusted by supervised training to provide the discriminant functions for order selection in its outputs. Results from the net are then compared with conventional criteria and demonstrate superior performance, in particular, for correlated sources and small sample sizes. Training may be introduced for known nonwhite noise, which serves to maintain high performance for reasonable correlation lengths.

A maximum likelihood approach for the passive identification of time-varying multipath channels

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.

Performance study of a generalized subspace-based method for scattered sources

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.

Adaptive maximum likelihood algorithms for the blind tracking of time-varying multipath channels

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 non-stationary context, the channel model has to be updated by periodically sending the training sequence, thus reducing the transmission rate. We address herein the problem of blind identification, which does not require such a sequence and allows a higher transmission rate. We have first proposed a two-stage algorithm (see Reference 2) for the blind identification of multipath channel. We investigate here the maximum-likelihood approach for the blind estimation of channel parameters. In order to track non-stationary 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. Furthermore, the proposed method can easily cope with a model including Doppler shift, which is not directly possible with more common methods. Monte-Carlo simulations confirm the expected results and demonstrate the performance.

A new parametric approach for wind profiling with Doppler Radar

In this paper, we propose a new approach for wind profile extraction with Doppler radar. To perform this, we first focus on the analysis and modeling of VHF or UHF waves backscattered by clear-air turbulence. A physical description of the backscattered wave is given. This description involves a spectral model that includes a parametric profile of the Doppler spectrum. A parametric approach of the wind profile can be easily generated. The sounding volume is divided into slabs whose thickness is consistent with that of the expected homogeneous turbulent layer. The echo spectrum of each slab is supposed Gaussian. Thus, for the range gate, the backscattered spectrum is a priori non-Gaussian, since it is weighted by a nonconstant reflectivity. This represents a more realistic assumption than the classical ones. The realistic temporal model thereby obtained can be used in simulation, which provides a valable tool for testing the extraction algorithm. An original recursive fitting, in terms of maximum likelihood, between the experimentally recorded spectrum and the parametric candidate spectrum is described and implemented as a second-order, steepest-descent algorithm. This optimization problem is solved in a weighted fashion on the entire gate simultaneously. The regularized parametric method, described in this paper, is a way to minimize some of the drawbacks encountered with traditional methods. Simulations reveal good statistical performance compared with traditional methods. The algorithm is then tested on real data. To achieve this, original methods are proposed for noise suppression and clutter removal.

Design of neural estimators for multisensors: second order backpropagation, initialization and generalization

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.<<ETX>>

A dual isometric transformation for the determination of ambiguities in bearing estimation

Abstract Linear dependence in the array antenna manifold (“steering vectors”) leads to a failure of subspace-based methods (e.g. “MUSIC”) in identifying source locations. These manifold ambiguities provide parasitic peaks in the spatial spectrum. In this paper, we present a method for determining the manifold ambiguities for a linear array based on isometric polygon transformations in the complex plane. For rank-two ambiguities, we demonstrate that the array can be split into two subarrays. This step reduces the problem to a determination of rank-one ambiguities for just one of these subarrays. We then generalize these results for rank- n ambiguities. The geometrical construct presented enables an exhaustive determination of any-rank ambiguity for the array under consideration. Examples are used to illustrate the proposed method.

A two dimensional laser rangefinder for robot vision and autonomy

The authors have designed a double modulation laser telemeter in their laboratory. The performance achieved makes this telemeter a true instrumentation device (relative precision 0.5*10/sup -4/), with reasonable dimensions and a high measurement rate ability (maximum 50 kHz). Its coaxial design makes scanning an easier task than for triangulation type devices. They report the performances obtained with the telemeter as well as those obtained by the scanning system. They point out the fact that the light power returned is very important for target recognition, and the need for specific processing tools for range data exploitation with some basic primitives implemented is analysed.<<ETX>>

Spectral analysis for Doppler radar: a parametric model for regularisation

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.