Alain Y. Kibangou

Wiener-Hammerstein systems modeling using diagonal Volterra kernels coefficients

In this letter, we first present explicit relations between block-oriented nonlinear representations and Volterra models. For an identification purpose, we show that the estimation of the diagonal coefficients of the Volterra kernels associated with the considered block-oriented nonlinear structures is sufficient to recover the overall model. An alternating least squares-type algorithm is provided to carry out this model identification.

Graph Laplacian based matrix design for finite-time distributed average consensus

In this paper, we consider the problem of finding a linear iteration scheme that yields distributed average consensus in a finite number of steps D. By modeling interactions between the nodes in the network by means of a time-invariant undirected graph, the problem is solved by deriving a set of D Laplacian based consensus matrices. We show that the number of steps is given by the number of nonzero distinct eigenvalues of the graph Laplacian matrix. Moreover the inverse of these eigenvalues constitute the step-sizes of the involved Laplacian based consensus matrices. When communications are made through an additive white Gaussian noise channel, based on an ensemble averaging method, we show how average consensus can be asymptotically reached. Performance analysis of the suggested protocol is given along with comparisons with other methods in the literature.

Finite-time average consensus based protocol for distributed estimation over AWGN channels

This paper studies the problem of distributed estimation of a static parameter with sensors communicating through an additive white Gaussian noise (AWGN) channel. In the noiseless case, we first introduce the concept of finite-time average consensus, in which nodes can compute exactly the average in a finite number of steps for an arbitrary graph, provided the topology is time-invariant. In fact, finite-time consensus is achieved owing to joint diagonalizable matrices. By considering a linear iterations scheme, we derive closed form expressions for such matrices. Then, based on an ensemble averaging method we show how average consensus can be asymptotically reached over AWGN channels. Performance analysis of the suggested protocol is given along with comparisons with other methods in the literature.

Selection of generalized orthonormal bases for second-order Volterra filters

Volterra models are very useful for signal and system representation due to their general nonlinear structure and their property of linearity with respect to their parameters, the kernel coefficients. However, when using Volterra models we are confronted with a complexity problem that results from the very large number of parameters required by such models. Expanding the kernels on a generalized orthonormal basis allows to significantly reduce this parametric complexity. In the present paper, a new constructive procedure is described for selecting such a generalized orthonormal basis in the case of second-order Volterra systems. A pruning method is also proposed for eliminating the least significant terms in the kernel expansions.

Laguerre-Volterra Filters Optimization Based on Laguerre Spectra

New batch and adaptive methods are proposed to optimize the Volterra kernels expansions on a set of Laguerre functions. Each kernel is expanded on an independent Laguerre basis. The expansion coefficients, also called Fourier coefficients, are estimated in the MMSE sense or by applying the gradient technique. An analytical solution to Laguerre poles optimization is provided using the knowledge of the Fourier coefficients associated with an arbitrary Laguerre basis. The proposed methods allow optimization of both the Fourier coefficients and the Laguerre poles.

Graph constrained-CTM observer design for the Grenoble south ring

Abstract An important problem in traffic estimation, forecasting, and control is the reconstruction of densities in portions of the road links not equipped with sensors. In this paper, and based on ideas from Morarescu and Canudas-de Wit [2011], we use a deterministic constrained model that reduces the number of possible affine dynamics of the system and preserves the number of vehicles in the network. In particular we reformulate the idea in Morarescu and Canudas-de Wit [2011] with the correct number of feasible modes, and introduce the concept of graph constrained-CTM observer, which is used to reconstruct the densities from the Grenoble south ring use case that contains 45 cells organized in 9 links, and is simulated using a calibrated AISUM micro-simulator. This work is performed in connection with HYCON2 traffic show case (www.hycon2.eu), and with the Grenoble Traffic Lab (GTL) (http://necs.inrialpes.fr/pages/reseach/gtl.php).

Blind equalization of nonlinear channels using a tensor decomposition with code/space/time diversities

In this paper, we consider the blind equalization problem for nonlinear channels represented by means of a Volterra model. We first suggest a precoding scheme inducing a three-dimensional (3-D) structure for the received data due to code, space, and time diversities. The tensor of received data admits a PARAFAC (parallel factors) decomposition with finite alphabet and Vandermonde structure constraints. We derive a uniqueness result taking such constraints into account. When one of the matrix factors, the code matrix, is known or belongs to a known finite set of matrices, we give new uniqueness results and three equalization algorithms are proposed. The performances of these algorithms are illustrated by means of simulation results.

Identification of Parallel-Cascade Wiener Systems Using Joint Diagonalization of Third-Order Volterra Kernel Slices

This letter is concerned with the parameter estimation of linear and nonlinear subsystems of parallel-cascade Wiener systems (PCWS). We first present the relationship between a PCWS and its associated Volterra model. We show that the coefficients of the linear subsystems can be obtained using a joint diagonalization of the third-order Volterra kernel slices. Then, the coefficients of the nonlinear subsystems are estimated using the least square algorithm. The proposed parameter estimation method is illustrated by means of simulation results.

Adaptive Kalman filtering for multi-step ahead traffic flow prediction

Given the importance of continuous traffic flow forecasting in most of Intelligent Transportation Systems (ITS) applications, where every new traffic data become available in every few minutes or seconds, the main objective of this study is to perform a multi-step ahead traffic flow forecasting that can meet a trade-off between accuracy, low computational load, and limited memory capacity. To this aim, based on adaptive Kalman filtering theory, two forecasting approaches are proposed. We suggest solving a multi-step ahead prediction problem as a filtering one by considering pseudo-observations coming from the averaged historical flow or the output of other predictors in the literature. For taking into account the stochastic modeling of the process and the current measurements we resort to an adaptive scheme. The proposed forecasting methods are evaluated by using measurements of the Grenoble south ring.

Decentralized Laplacian Eigenvalues Estimation and Collaborative Network Topology Identification

In this paper we first study observability conditions on networks. Based on spectral properties of graphs, we state new sufficient or necessary conditions for observability. These conditions are based on properties of the Khatri-Rao product of matrices. Then we consider the problem of estimating the eigenvalues of the Laplacian matrix associated with the graph modeling the interconnections between the nodes of a given network. Eventually, we extend the study to the identification of the network topology by estimating both eigenvalues and eigenvectors of the network matrix. In addition, we show how computing, in finite-time, some linear functionals of the state initial condition, including average consensus. Specifically, based on properties of the observability matrix, we show that Laplacian eigenvalues can be recovered by solving a local eigenvalue decomposition on an appropriately constructed matrix of observed data. Unlike FFT based methods recently proposed in the literature, in the approach considered herein, we are also able to estimate the multiplicities of the eigenvalues. Then, for identifying the network topology, the eigenvectors are estimated by means of a consensus-based least squares method.