Francois Caron

GPS/IMU data fusion using multisensor Kalman filtering: introduction of contextual aspects

The aim of this article is to develop a GPS/IMU multisensor fusion algorithm, taking context into consideration. Contextual variables are introduced to define fuzzy validity domains of each sensor. The algorithm increases the reliability of the position information. A simulation of this algorithm is then made by fusing GPS and IMU data coming from real tests on a land vehicle. Bad data delivered by GPS sensor are detected and rejected using contextual information thus increasing reliability. Moreover, because of a lack of credibility of GPS signal in some cases and because of the drift of the INS, GPS/INS association is not satisfactory at the moment. In order to avoid this problem, the authors propose to feed the fusion process based on a multisensor Kalman filter directly with the acceleration provided by the IMU. Moreover, the filter developed here gives the possibility to easily add other sensors in order to achieve performances required.

Particle Filtering for Multisensor Data Fusion With Switching Observation Models: Application to Land Vehicle Positioning

This paper concerns the sequential estimation of a hidden state vector from noisy observations delivered by several sensors. Different from the standard framework, we assume here that the sensors may switch autonomously between different sensor states, that is, between different observation models. This includes sensor failure or sensor functioning conditions change. In our model, sensor states are represented by discrete latent variables, whose prior probabilities are Markovian. We propose a family of efficient particle filters, for both synchronous and asynchronous sensor observations as well as for important special cases. Moreover, we discuss connections with previous works. Lastly, we study thoroughly a wheel land vehicle positioning problem where the GPS information may be unreliable because of multipath/masking effects

The Reality of Neandertal Symbolic Behavior at the Grotte du Renne, Arcy-sur-Cure, France

Background The question of whether symbolically mediated behavior is exclusive to modern humans or shared with anatomically archaic populations such as the Neandertals is hotly debated. At the Grotte du Renne, Arcy-sur-Cure, France, the Châtelperronian levels contain Neandertal remains and large numbers of personal ornaments, decorated bone tools and colorants, but it has been suggested that this association reflects intrusion of the symbolic artifacts from the overlying Protoaurignacian and/or of the Neandertal remains from the underlying Mousterian. Methodology/Principal Findings We tested these hypotheses against the horizontal and vertical distributions of the various categories of diagnostic finds and statistically assessed the probability that the Châtelperronian levels are of mixed composition. Our results reject that the associations result from large or small scale, localized or generalized post-depositional displacement, and they imply that incomplete sample decontamination is the parsimonious explanation for the stratigraphic anomalies seen in the radiocarbon dating of the sequence. Conclusions/Significance The symbolic artifacts in the Châtelperronian of the Grotte du Renne are indeed Neandertal material culture.

Sparse Bayesian nonparametric regression

One of the most common problems in machine learning and statistics consists of estimating the mean response <i>Xβ</i> from a vector of observations <i>y</i> assuming <i>y</i> = <i>Xβ</i> + <i>ε</i> where <i>X</i> is known, β is a vector of parameters of interest and <i>ε</i> a vector of stochastic errors. We are particularly interested here in the case where the dimension <i>K</i> of β is much higher than the dimension of <i>y</i>. We propose some flexible Bayesian models which can yield sparse estimates of β. We show that as <i>K</i> → ∞ these models are closely related to a class of Lévy processes. Simulations demonstrate that our models outperform significantly a range of popular alternatives.

Bayesian Inference for Linear Dynamic Models With Dirichlet Process Mixtures

Using Kalman techniques, it is possible to perform optimal estimation in linear Gaussian state-space models. Here, we address the case where the noise probability density functions are of unknown functional form. A flexible Bayesian nonparametric noise model based on Dirichlet process mixtures is introduced. Efficient Markov chain Monte Carlo and sequential Monte Carlo methods are then developed to perform optimal batch and sequential estimation in such contexts. The algorithms are applied to blind deconvolution and change point detection. Experimental results on synthetic and real data demonstrate the efficiency of this approach in various contexts.

Bayesian Inference for Dynamic Models with Dirichlet Process Mixtures

Using Kalman techniques, it is possible to perform optimal estimation in linear Gaussian state-space models. We address here the case where the noise probability density functions are of unknown functional form. A flexible Bayesian nonparametric noise model based on mixture of Dirichlet processes is introduced. Efficient Markov chain Monte Carlo and sequential Monte Carlo methods are then developed to perform optimal estimation in such contexts

Sparse graphs using exchangeable random measures

Summary Statistical network modelling has focused on representing the graph as a discrete structure, namely the adjacency matrix. When assuming exchangeability of this array—which can aid in modelling, computations and theoretical analysis—the Aldous–Hoover theorem informs us that the graph is necessarily either dense or empty. We instead consider representing the graph as an exchangeable random measure and appeal to the Kallenberg representation theorem for this object. We explore using completely random measures (CRMs) to define the exchangeable random measure, and we show how our CRM construction enables us to achieve sparse graphs while maintaining the attractive properties of exchangeability. We relate the sparsity of the graph to the Lévy measure defining the CRM. For a specific choice of CRM, our graphs can be tuned from dense to sparse on the basis of a single parameter. We present a scalable Hamiltonian Monte Carlo algorithm for posterior inference, which we use to analyse network properties in a range of real data sets, including networks with hundreds of thousands of nodes and millions of edges.

Two-sample Bayesian nonparametric hypothesis testing

In this article we describe Bayesian nonparametric procedures for two-sample hypothesis testing. Namely, given two sets of samples y^{(1)} iid F^{(1)} and y^{(2)} iid F^{(2)}, with F^{(1)}, F^{(2)} unknown, we wish to evaluate the evidence for the null hypothesis H_{0}:F^{(1)} = F^{(2)} versus the alternative. Our method is based upon a nonparametric Polya tree prior centered either subjectively or using an empirical procedure. We show that the Polya tree prior leads to an analytic expression for the marginal likelihood under the two hypotheses and hence an explicit measure of the probability of the null Pr(H_{0}|y^{(1)},y^{(2)}).

Efficient Bayesian Inference for Generalized Bradley–Terry Models

The Bradley–Terry model is a popular approach to describe probabilities of the possible outcomes when elements of a set are repeatedly compared with one another in pairs. It has found many applications including animal behavior, chess ranking, and multiclass classification. Numerous extensions of the basic model have also been proposed in the literature including models with ties, multiple comparisons, group comparisons, and random graphs. From a computational point of view, Hunter has proposed efficient iterative minorization-maximization (MM) algorithms to perform maximum likelihood estimation for these generalized Bradley–Terry models whereas Bayesian inference is typically performed using Markov chain Monte Carlo algorithms based on tailored Metropolis–Hastings proposals. We show here that these MM algorithms can be reinterpreted as special instances of expectation-maximization algorithms associated with suitable sets of latent variables and propose some original extensions. These latent variables allow us to derive simple Gibbs samplers for Bayesian inference. We demonstrate experimentally the efficiency of these algorithms on a variety of applications.

Least committed basic belief density induced by a multivariate Gaussian: Formulation with applications

We consider here the case where our knowledge is partial and based on a betting density function which is n-dimensional Gaussian. The explicit formulation of the least committed basic belief density (bbd) of the multivariate Gaussian pdf is provided in the transferable belief model (TBM) framework. Beliefs are then assigned to hyperspheres and the bbd follows a @g^2 distribution. Two applications are also presented. The first one deals with model based classification in the joint speed-acceleration feature space. The second is devoted to joint target tracking and classification: the tracking part is performed using a Rao-Blackwellized particle filter, while the classification is carried out within the developed TBM scheme.