Using Kalman techniques, it is possible to perform optimal estimation in linear Gaussian statespace 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 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.
Abstract-Until now, humanitarian demining has been unable to provide a solution to the landmine removal problem. Furthermore, new low-cost methods have to be developed quickly. While much progress has been made with the introduction of new sensor types, other problems have been raised by these sensors. Ground-penetrating radars (GPRs) are key sensors for landmine detection as they are capable of detecting landmines with low metal contents. GPRs deliver so-called Bscan data, which are, roughly, vertical slice images of the ground. However, due to the high dielectric permittivity contrast at the air-ground interface, a strong response is recorded at an early time by GPRs. This response is the main component of the so-called clutter noise, and it blurs the responses of landmines buried at shallow depths. The landmine detection task is therefore quite difficult, and a preprocessing step, which aims at reducing the clutter, is often needed. In this paper, a difficult case for clutter reduction, that is, when landmines and clutter responses overlap in time, is presented. A new and simple clutter removal method based on the design of a two-dimensional digital filter, which is adapted to Bscan data, is proposed. The designed filter must reduce the clutter on Bscan data significantly while protecting the landmine responses. In order to do so, a frequency analysis of a clutter geometrical model is first led. Then, the same process is applied to a geometrical model of a signal coming from a landmine. This results in building a high-pass digital filter and determining its cutoff frequencies. Finally, simulations are presented on simulated and real data, and a comparison with the classical clutter removal algorithm is made.
International audienceIn global positioning systems (GPS), classical localization algorithms assume, when the signal is received from the satellite in line-of-sight (LOS) environment, that the pseudorange error distribution is Gaussian. Such assumption is in some way very restrictive since a random error in the pseudorange measure with an unknown distribution form is always induced in constrained environments especially in urban canyons due to multipath/masking effects. In order to ensure high accuracy positioning, a good estimation of the observation error in these cases is required. To address this, an attractive flexible Bayesian nonparametric noise model based on Dirichlet process mixtures (DPM) is introduced. Since the considered positioning problem involves elements of non-Gaussianity and nonlinearity and besides, it should be processed on-line, the suitability of the proposed modeling scheme in a joint state/parameter estimation problem is handled by an efficient Rao-Blackwellized particle filter (RBPF). Our approach is illustrated on a data analysis task dealing with joint estimation of vehicles positions and pseudorange errors in a global navigation satellite system (GNSS)-based localization context where the GPS information may be inaccurate because of hard reception conditions
The Probability Hypothesis Density (PHD) is a well-known method for single-sensor multi-target tracking problems in a Bayesian framework, but the extension to the multi-sensor case seems to remain a challenge. In this paper, an extension of Mahler's work to the multi-sensor case provides an expression of the true PHD multi-sensor data update equation. Then, based on the configuration of the sensors' fields of view (FOVs), a joint partitioning of both the sensors and the state space provides an equivalent yet more practical expression of the data update equation, allowing a more effective implementation in specific FOV configurations.
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