Specification and tuning of errors from dynamical models are important issues in data assimilation. In this work, we propose an iterative expectation-maximisation (EM) algorithm to estimate the model error covariances using classical extended and ensemble versions of the Kalman smoother. We show that, for additive model errors, the estimate of the error covariance converges. We also investigate other forms of model error, such as parametric or multiplicative errors. We show that additive Gaussian model error is able to compensate for non additive sources of error in the algorithms wepropose. We also demonstrate the limitations of the extended version of the algorithm and recommend the use of the more robust and flexible ensemble version. This article is a proof of concept of the methodology with the Lorenz-63 attractor. We developed an open-source Python library to enable future users to apply the algorithm to their own nonlinear dynamical models.

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In order to improve the resolution of seismic images, a blind deconvolution of seismic traces is necessary, since the source wavelet is not known and cannot be considered as a stationary signal. The reflectivity sequence is modeled as a Gaussian mixture, depending on three parameters (high and low reflector variances and reflector density), on the wavelet impulse response, and on the observation noise variance. These parameters are unknown and must be estimated from the recorded trace, which is the reflectivity convolved with the wavelet, plus noise. Two methods are compared in this paper for the parameter estimation. Since we are considering an incomplete data problem, we first consider maximum likelihood estimation by means of a stochastic expectation maximization (SEM) method. Alternatively, proper prior distributions can be specified for all unknown quantities. Then, a Bayesian strategy is applied, based on a Monte Carlo Markov Chain (MCMC) method. Having estimated the parameters, one can proceed to the deconvolution. A maximum posterior mode (MPM) criterion is optimized by means of an MCMC method. The deconvolution capability of these procedures is checked first on synthetic signals and then on the seismic data of the IFREMER ESSR4 campaign, where the wavelet duration blurs the reflectivity, and on the SMAVH high-resolution marine seismic data.

International audienceThe aim of this paper is to study the bit-loading and power allocation problem in the presence of interference (Inter-carrier Interference (ICI) and Inter-Symbol Interference (ISI)) in Orthogonal Frequency Division Multiplexing (OFDM) systems. ISI and ICI significantly degrade the performance of OFDM systems and make the resource management optimized without the assumption of interference less efficient. To solve this problem, an initial solution based on the greedy approach is proposed in this paper. Then, several reduced complexity approaches, which yield a little degradation compared to the initial solution, have been developed. Simulation results presented in the context of Power Line Communication (PLC) show that the performance of proposed algorithms is tight with their upper bound. Moreover, these algorithms efficiently improve the system performance as compared to the constant power water-filling allocation algorithm as well as maximum power allocation algorithm

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We consider the cumulative residual entropy (CRE) a recently introduced measure of entropy. While in previous works distributions with positive support are considered, we generalize the definition of CRE to the case of distributions with general support. We show that several interesting properties of the earlier CRE remain valid and supply further properties and insight to problems such as maximum CRE power moment problems. In addition, we show that this generalized CRE can be used as an alternative to differential entropy to derive information-based optimization criteria for system identification purpose.

International audienceIn 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 RandomVector (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