Jean-Marc Le Caillec

Nonlinear system identification using autoregressive quadratic models

In this paper, we study the identification of a special class of nonlinear systems, Quadratic AutoRegressive Moving Average systems, QARMA. In the first part, we discuss the relationship between this model and the Volterra models and also the property of stability of these systems. The second part is devoted to the derivation of the two equation sets needed for a possibly time-variant QARMA identification. The equation sets use higher-order moments and the first set is derived under the assumption of finite length correlation of the input data. The coefficients of this first system depend on a mixed set of third- and fourth-order moments. The second set of equations assumes only unskewed input data and the equation coefficients are a linear combination of moments from the third up to the sixth order with the system coefficients at previous lags. In order to validate the identification methods and to numerically verify the accuracy of the estimated coefficients for both equation sets, the QARMA methods were applied to the deconvolution of L-PAM symbols, the rate of good estimation of these symbols allowing a numerical comparison between the respective performances of both equation sets. Another application presented in this paper is a Second-Order Volterra Model (SOVM) identification although the QARMA model cannot be strictly equal to a SOVM.

Comparison of statistical indices using third order statistics for nonlinearity detection

In this paper we discuss the efficiency of nonlinearity indices based on higher order statistics in order to detect nonlinearities in an observed signal, the signal being the output of a transmission channel (possibly nonlinear) tile input of which is not accessible. Nonlinearity detection is the first step of nonlinearity analysis, this step being followed by nonlinearity location of the nonlinear components (in the Fourier domain) and quantification of these components. The main results reported in this paper are, first, a systematic survey of the robustness of hypothesis testing for each index and, second, the derivation of indices which neither involve the ratio of estimated quantities (such as bicoherence) nor phase unwrapping (such as the bicepstrum). The robustness of hypothesis testing is verified by calculating type II error probability (i.e. the error of declaring that the time series has been produced by a linear system while produced by a nonlinear one). To calculate this error, the observed time series is assumed to be the output of a second-order Volterra model driven by a Gaussian distributed noise. Obviously, the assumption of such a model might seem restrictive, but the results obtained allow us to draw some definitive conclusions about the robustness of the indices presented. The calculation is performed first from a theoretical spectrum and bispectrum and, second, from estimated indices. These indices are estimated from linear and nonlinear time series having the same spectrum. The estimation of the type II error probability on estimated indices allows the verification of the assumptions used to derive the theoretical index probability density function.

CPHD-DOA Tracking of Multiple Extended Sonar Targets in Impulsive Environments

In this paper, we propose a novel phased-array track before detect (TBD) filter for tracking multiple distributed (extended) targets from impulsive observations. Since the targets are angularly spread, we track the centroid Direction Of Arrival (DOA) of the target-generated (or backscattered) signal. The main challenge stems from the random target signals that, conditional to their respective states, constitute non-deterministic contributions to the system observation. The novelty of our approach is twofold. First, we develop a Cardinalized Probability Hypothesis Density (CPHD) filter for tracking multiple targets with non-deterministic contributions, more specifically, Spherically Invariant Random Vector (SIRV) processes. This is achieved by analytically integrating the SIRV and angularly distributed target signals in the update step. Thus, ensuring a more efficient implementation than existing solutions, that generally consider augmenting the target state with the target signal. Secondly, we provide an improved auxiliary particle CPHD filter and clustering methodology. The auxiliary step is carried out for persistent particles, while for newly birthed particles an adaptive importance distribution is given. This is in contrast with existing solutions that only consider the auxiliary step for birthed particles. Simulated data results showcase the improved performance of the proposed filter. Results on real sonar phased-array data are presented for underwater 3D image reconstruction applications.

Intensity-Based Block Matching Algorithm for Mosaicing Sonar Images

Registering sonar images to correctly describe seafloors and explain wide geological or biological phenomena is often achieved manually requiring significant human resources. This paper proposes an automatic intensity-based registration algorithm that relies on the optimization of a new similarity measure (SM), within a multiresolution block matching framework. Indeed, several SMs have been evaluated and ranked on real sidescan sonar data to determine the most relevant intensity dependencies between images for matching purposes. Correlation ratio (CR) and mutual information (MI) are then selected and because of their complementary behaviors, merged in a new SM (MI&CR), which performs better than CR or MI alone, to determine robust matching blocks between images. Thus, the proposed two-step registration algorithm uses MI&CR to match two sonar images: a single rigid translation globally matches the images, then a field of locally applied translations is computed for adjusting the final registration to remaining local distortions. Actual processing time can then be tuned according to the required registration accuracy. Due to a survey standard operating mode, only same-survey overlapping images are considered as candidates for matching. Moreover, building mosaics from registered images assumes a flat sea bottom as no global elevation information is provided by sidescan sonar images.

Spectral inversion of second order Volterra models based on the blind identification of Wiener models

In this paper, we develop two main results. The first one is a theorem proving that a second order Wiener model can be blindly identified, i.e. using only the mean, the third and fourth order cumulants of the output data. The second result is the application of this theorem to spectral inversion (i.e. the recovering of the power spectrum density) of the input signal of a second order Volterra model to which usual inversion schemes cannot be applied, in particular when the linear kernel has a strong attenuation in frequency range. Numerical results are discussed with respect to the nonlinear energy amount of the output, the time series length and the SNR values.

Model-Based Adaptive 3D Sonar Reconstruction in Reverberating Environments

In this paper, we propose a novel model-based approach for 3D underwater scene reconstruction, i.e., bathymetry, for side scan sonar arrays in complex and highly reverberating environments like shallow water areas. The presence of multipath echoes and volume reverberation generates false depth estimates. To improve the resulting bathymetry, this paper proposes and develops an adaptive filter, based on several original geometrical models. This multimodel approach makes it possible to track and separate the direction of arrival trajectories of multiple echoes impinging the array. Echo tracking is perceived as a model-based processing stage, incorporating prior information on the temporal evolution of echoes in order to reject cluttered observations generated by interfering echoes. The results of the proposed filter on simulated and real sonar data showcase the clutter-free and regularized bathymetric reconstruction. Model validation is carried out with goodness of fit tests, and demonstrates the importance of model-based processing for bathymetry reconstruction.

A Methodology to Evaluate Important Dimensions of Information Quality in Systems

Assessing the quality of the information proposed by an information system has become one of the major research topics in the last two decades. A quick literature survey shows that a significant number of information quality frameworks are proposed in different domains of application: management information systems, web information systems, information fusion systems, and so forth. Unfortunately, they do not provide a feasible methodology that is both simple and intuitive to be implemented in practice. In order to address this need, we present in this article a new information quality methodology. Our methodology makes use of existing frameworks and proposes a three-step process capable of tracking the quality changes through the system. In the first step and as a novelty compared to existing studies, we propose decomposing the information system into its elementary modules. Having access to each module allows us to locally define the information quality. Then, in the second step, we model each processing module by a quality transfer function, capturing the module’s influence over the information quality. In the third step, we make use of the previous two steps in order to estimate the quality of the entire information system. Thus, our methodology allows informing the end-user on both output quality and local quality. The proof of concept of our methodology has been carried out considering two applications: an automatic target recognition system and a diagnosis coding support system.

3-D bathymetric reconstruction in multi-path and reverberant underwater environments

In this paper a 3-D reconstruction method is proposed of sea bottom topography, i.e. bathymetry, for sonar data in highly reverberant and multi-path underwater environments. Recent publications showcase the negative impact of waves involving sea surface reflections on the sea bottom imaging process. The novelty of our proposal is twofold: firstly it relies on the use of Markovian-model based processors for bahymetric reconstruction and involves data association filters. Secondly, we propose a nearest neighbor version of the Integrated Probabilistic Data Association filter, capable of filtering several echo trajectories in the presence of clutter with a relatively reduced complexity compared to other existent methods.

Enhanced sonar bathymetry tracking in multi-path environment

In this paper we address DOA estimation for the side scan sonar in the presence of multiple interfering echoes. We illustrate the potential usage of high resolution methods and tracking algorithms. The proposed tracking algorithm is based on a apriori information on the sea-floor DOA angle. Because of the non-linearity of the model and non-Gaussian behavior of the observed 4600 data, the implementation of the proposed algorithm is based on the particle filter. The proposed tracking algorithm is shown to be able to resolve the multi-path interference problem. The heavy-tailed/non-Gaussian character of the data is noted and the Laplace distribution is shown to better characterize the tails of the observed data. The multivariate Laplace distribution is derived for the observed data and the particle filter coupled with the multivariate Laplace distribution is shown to provide better estimates than with the Gaussian assumption.

Subsurface soil modeling based on geological database for simulation of electromagnetic wave propagation

In this paper the application of geological databases for electromagnetic subsurface soil modeling is discussed. Firstly the basic information about the soil classifications are presented as well as description of the data available into geological databases. Secondly the soil dielectric models are presented as a function of frequency, moisture content and soil texture (i.e., percentage of clay, silt, sand, and bulk density). Finally data from the SPADE/2 database are applied for calculation the soil dielectric model. The results of subsurface soil modeling for ground penetrating radar (GPR) are presented and discussed.