We consider deterministic parameter estimation and the situation where the probability density function (p.d.f.) parameterized by unknown deterministic parameters results from the marginalization of a joint p.d.f. depending on random variables as well. Unfortunately, in the general case, this marginalization is mathematically intractable, which prevents from using the known standard deterministic lower bounds (LBs) on the mean squared error (MSE). Actually the general case can be tackled by embedding the initial observation space in a hybrid one where any standard LB can be transformed into a modified one fitted to nonstandard deterministic estimation, at the expense of tightness however. Furthermore, these modified LBs (MLBs) appears to include the submatrix of hybrid LBs which is an LB for the deterministic parameters.Moreover, since in the nonstandard estimation, maximum likelihood estimators (MLEs) can be no longer derived, suboptimal nonstandard MLEs (NSMLEs) are proposed as being a substitute. We show that any standard LB on the MSE of MLEs has a nonstandard version lower bounding the MSE of NSMLEs. We provide an analysis of the relative performance of the NSMLEs, as well as a comparison with the MLBs for a large class of estimation problems. Last, the general approach introduced is exemplified, among other things, with a new look at the well-known Gaussian complex observation models.

Multisymbol receiver is an effective method to demodulate noncoherent sequences. However it is necessary to correlate an important number of symbols in a noncoherent scheme to reach the performances carried out by optimal coherent Maximum a Posteriori (MAP) detectors such as BCJR. In this paper, we propose an advanced multisymbol receiver by adding some memory to the decision process. The advanced receiver, called here Multisymbol With Memory (MWM) takes into account the cumulative phase information unlike multisymbol algorithm and thus it can be seen as a truncated BCJR. An exact mathematical derivation is performed for this truncated BCJR. Then an implementation of the MWM detector applied to a continuous phase frequency shift keying modulation is presented. Finally an asymptotic analysis is carried out based on the achievable Symmetric Mutual Information rate. The proposed system exhibits good performances compared to classical multisymbol receivers at the expense of increased complexity and can approach the performances of a coherent receiver.

In this paper, we present a new data-aided carrier-recovery method for Continuous Phase Modulation (CPM) signals over frequency-selective channels. We first present a linear model of the received signal based on Mengali representation over selective channels and show how to use it to perform joint channel and carrier-frequency estimation. We also derive a low-complexity version of the estimator. Simulation results show that this method performs better than the optimal method suited to the Additive White Gaussian Noise (AWGN) channels.

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 introduces a hierarchical Bayesian model for the reconstruction of hyperspectral images using compressed sensing measurements. This model exploits known properties of natural images, promoting the recovered image to be sparse on a selected basis and smooth in the image domain. The posterior distribution of this model is too complex to derive closed form expressions for the estimators of its parameters. Therefore, an MCMC method is investigated to sample this posterior distribution. The resulting samples are used to estimate the unknown model parameters and hyperparameters in an unsupervised framework. The results obtained onrealdataillustratetheimprovementinreconstructionquality when compared to some existing techniques.

Thepurposeofthispaperistoderivenewasymptoticpropertiesoftherobustadaptivenormalizedmatchedfilter(ANMF). More precisely, the ANMF built with Tyler estimator (TyEANMF) is analyzed under the framework of complex elliptically symmetric (CES) distributions. We show that the distribution of TyE-ANMF can be accurately approximated by the well-known distribution of the ANMF built with the sample covariance matrix (SCM-ANMF) under the Gaussian assumption. To that end, the asymptotic properties of the difference between both ANMF detectors are derived. By comparison with the state of the art, the asymptotic properties of the TyE-ANMF are shown to be better approximated by the SCM-ANMF rather than using the NMF (test built with the true CM). Some Monte-Carlo simulations support that claim and demonstrate the interest of this theoretical result.

This paper derives lower bounds for the mean square errors of parameter estimators in the case of Poisson distributed data subjected to multiple abrupt changes. Since both change locations (discrete parameters) and parameters of the Poisson distribution (continuous parameters) are unknown, it is appropriate to consider a mixed Cramér-Rao/Weiss-Weinstein bound for which we derive closed-form expressions and illustrate its tightness by numerical simulations.

The several progress of the free-accessible global navigation satellites system (GNSS) is not without major hurdles and challenges in it course of application in urban setting. Several error sources in these environments such as multipath and non-line-of-sight (NLOS) reception, signal masking and poor constellation geometry hinder the required positioning accuracy by GNSS signals. Facing this pressing need for performance enhancement in NLOS conditions, a new trend of approaches seek a constructive use of these degraded signals by correcting ranging measurements, using a 3D GNSS simulator for instance. However, this approach may engender a great risk of deteriorating PR measurements instead of correcting them if the compensation term is not accurate enough. Therefore, we propose in this paper to address the influence of PR bias estimation on the performances of this positioning method based on the correction of PR measurement. This original study permits us defining the maximum level of inaccuracy on bias estimation that any 3D GNSS simulator, or other tools, mustn’t exceed. A detailed study on this most acceptable level of inaccuracy on the PR bias estimation is performed using real GNSS data in Toulouse and encompass analysis by type of environment (Urban, Peri-urban and rural environments) and by type of GNSS signals.

Recent work has shown that existing powerful Bayesian hyperspectral unmixing algorithms can be significantly improved by incorporating the inherent local spatial correlations between pixel class labels via the use of Markov random fields. We here propose a new Bayesian approach to joint hyperspectral unmixing and image classification such that the previous assumption of stochastic abundance vectors is relaxed to a formulation whereby a common abundance vector is assumed for pixels in each class. This allows us to avoid stochastic reparameterizations and, instead, we propose a symmetric Dirichlet distribution model with adjustable parameters for the common abundance vector of each class. Inference over the proposed model is achieved via a hybrid Gibbs sampler, and in particular, simulated annealing is introduced for the label estimation in order to avoid the local- trap problem. Experiments on a synthetic image and a popular, publicly available real data set indicate the proposed model is faster than and outperforms the existing approach quantitatively and qualitatively. Moreover, for appropriate choices of the Dirichlet parameter, it is shown that the proposed approach has the capability to induce sparsity in the inferred abundance vectors. It is demonstrated that this offers increased robustness in cases where the preprocessing endmember extraction algorithms overestimate the number of active endmembers present in a given scene.

This paper deals with EEG source localization. The aim is to perform spatially coherent focal localization and recover temporal EEG waveforms, which can be useful in certain clinical applications. A new hierarchical Bayesian model is proposed with a multivariate Bernoulli Laplacian structured sparsity prior for brain activity. This distribution approximates a mixed ℓ20 pseudo norm regularization in a Bayesian framework. A partially collapsed Gibbs sampler is proposed to draw samples asymptotically distributed according to the posterior of the proposed Bayesian model. The generated samples are used to estimate the brain activity and the model hyperparameters jointly in an unsupervised framework. Two different kinds of Metropolis–Hastings moves are introduced to accelerate the convergence of the Gibbs sampler. The first move is based on multiple dipole shifts within each MCMC chain, whereas the second exploits proposals associated with different MCMC chains. Experiments with focal synthetic data shows that the proposed algorithm is more robust and has a higher recovery rate than the weighted ℓ21 mixed norm regularization. Using real data, the proposed algorithm finds sources that are spatially coherent with state of the art methods, namely a multiple sparse prior approach and the Champagne algorithm. In addition, the method estimates waveforms showing peaks at meaningful timestamps. This information can be valuable for activity spread characterization.