The curse of dimensionality in particle filtering can be mitigated by approximating the posterior distribution by a product of marginals on disjoint low dimensional subspaces of the state space. One such approach is known as the block particle filter in which the correction and resampling steps in particle filtering are run separately for estimating each marginal.In the linear and Gaussian case, the particle filter converges to the optimal Bayesian solution, i.e. the Kalman filter, as the number of particle increases. In this paper, we introduce the block based approach in the Kalman filter and show that the block particle filter asymptotically acts as the resulting block Kalman filter. It provides a relevant framework to disambiguate the bias incurred by the blocking step from the Monte Carlo estimation error.

Among sequential Monte Carlo methods, sampling importance resampling (SIR) algorithms are based on importance sampling and on some (resampling-based) rejuvenation algorithm that aims at fighting against weight degeneracy. However, this mechanism tends to be insufficient when applied to informative or high-dimensional models. In this letter, we revisit the rejuvenation mechanism and propose a class of parameterized SIR-based solutions that enable us to adjust the tradeoff between computational cost and statistical performances.

In many signal processing applications we aim to track a state of interest given available observations. Among existing techniques, sequential Monte Carlo filters are importance sampling-based algorithms meant to propagate in time a set of weighted particles which represent the a posteriori density of interest. As is well known weights tend to degenerate over time, and resampling is a commonly used rescue for discarding particles with low weight. Unfortunately conditionally independent resampling produces a set of dependent samples and the technique suffers from sample impoverishment. In this paper we modify the resampling step of particle filtering techniques in order to produce independent samples per iteration. We validate our technique via simulations.

We develop a new algorithm for spatial field reconstruction in heterogeneous (mixed analog & digital sensors) wireless sensor networks (WSNs). We consider spatial physical phenomena which are observed by a heterogeneous WSN, meaning that it is partially consists of sparsely deployed high-quality sensors and partially of low-quality sensors. The high-quality sensors transmit their (continuous) noisy observations to the Fusion Centre (FC), while the low-quality sensors first perform a simple thresholding operation and then transmit their binary values over imperfect wireless channels to the FC. We develop a novel algorithm that is based on a multivariate series expansion approach resulting in a Saddle-point type approximation. We then present comprehensive study of the performance gain that can be obtained by augmenting the high-quality sensors with low-quality sensors using real data of insurance storm surge database known as the Extreme Wind Storms Catalogue.

Impulsive interference is a strong limitation in ultra wide band systems or ad hoc networks. However, many work rely on the assumption of independent interference samples which is in many situations an unrealistic assumption. We propose to model the dependence structure using natural extensions to existing interference models based on parameter copula models. We focus on a particular flexible class of models based on the skewed-t copula family. They allow one to capture interesting dependence features based on extremal concordance such as multivariate generalizations of joint extreme correlation known as tail dependence. In the skew-t copula family this can arise in both homogeneous and heterogeneous forms in the extreme quadrants of the multivariate distribution. Importantly, by considering the skew-t copula it is also amenable to efficient scalability to high dimensions. In a second step, we study the impact of these dependence in the receivers' performance when they are designed assuming i.i.d. signals.

In this paper, we focus on the challenging task of the online estimation of the state and the unknown measurement noise density in nonlinear dynamic state-space models. We are especially interested in making inference in the presence of impulsive and time-varying noise. A flexible Bayesian nonparametric noise model based on an extension of Dirichlet Process Mixtures, namely the Time Varying Dirichlet process Mixtures, is introduced. A novel method based on sequential Monte Carlo methods is proposed to perform the optimal online estimation. Simulation results demonstrate the efficiency and the robustness of this method.

Microscopic analyses of paper printing show some regularly spaced dots whose the shape depends on the technology and the tuning of the printer as well as on the paper properties. The modeling and the identification of paper and ink interactions are required for qualifying the printing quality, for controlling the printing process and also for authentication issues. In this paper, we propose to model the micrometric scan of document printing by a binary response model whose the parameters depend on the location and the shape of dots. A maximum likelihood identification algorithm is provided, its performance is assessed through simulations and true data. Furthermore, we illustrate the benefice of a such model and estimation algorithm in the case of authentication of printer from micro-tag made of four dots.

We develop a novel distributional upper bound on the interference created in an ultra-wideband wireless communication systems under two general assumptions: the first is that there is an unknown number of interferers who are distributed according to a homogeneous Poisson point process randomly in space; and the second is that the frequency bands occupied by the unknown number of interferers is also a random variable in an ultra-wideband setting. Then given these two general assumptions, we derive a distributional upper bound representation of the total interference.

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In this paper, we address the problem of online state and measurement noise density estimation in nonlinear dynamic state-space-models. We are especially interested in making inference in the presence of impulsive and multimodal noise. The proposed method relies on the introduction of a flexible Bayesian nonparametric noise model based on Dirichlet Process mixtures. A novel approach based on sequential Monte Carlo methods is proposed to perform the optimal online estimation. Simulation results demonstrate the efficiency and the robustness of this approach.

We develop a sequential estimation methodology for a class of nonlinear, non-Gaussian state space models in which the observation process is intractable to express in closed form, but trivial to simulate. In addition we consider models in which the latent state vector and the observation vector are very high dimensional. To overcome these two difficulties we propose the class of Sequential Markov chain Monte Carlo (SMCMC) algorithms in which we incorporate a component of Approximate Bayesian Computation (ABC). In doing so we tackle both the curse of dimensionality via the SMCMC and the intractability of the likelihood via the ABC component. We demonstrate how the proposed algorithm outperforms alternative approaches in two challenging state space model examples.

We present in this paper a new visual tracking framework based on the MCMC-based particle algorithm. Firstly, in order to obtain a more informative likelihood, we propose to combine the color-based observation model with a detection confidence density obtained from the Histograms of Oriented Gradients (HOG) descriptor. The MCMC-based particle algorithm is then employed to estimate the posterior distribution of the target state to solve the tracking problem. The global system has been tested on different real datasets. Experimental results demonstrate the robustness of the proposed system in several difficult scenarios.

In this paper, we tackle the problem of interference mitigation in ad hoc networks. In such context, the multiple access interference (MAI) is known to be of an impulsive nature. Therefore, the conventional Gaussian assumption can not be considered to model this type of interference. Contrariwise, it can be accurately modeled by stable distributions. Here, this issue is addressed within an Orthogonal Frequency Division Multiplexing (OFDM) transmission link assuming a symmetric α-stable model for the signal distortion due to MAI. For this purpose, we propose a method for the joint estimation of the transmitted multicarrier signal and the noise parameters. Based on sequential Monte Carlo (SMC) methods, the proposed scheme allows the online estimation using a Rao-blackwellized particle filter.

In this paper, we present a joint blind channel estimation and symbol detection for decoding a blurred and noisy 1D barcode captured image. From an information transmission point of view, we show that the channel impulse response, the noise power and the symbols can be efficiently estimated by taking into account the signal structure such as the cyclostationary property of the hidden Markov process to estimate. Based on the Expectation-Maximisation method, we show that the new algorithm offers significative performance gain compared to classical ones pushing back the frontiers of the barcode technology.

In this paper we investigate ad hoc networks based on impulse radio ultra wideband. Due to multiple access, the interference distribution is not Gaussian. One important reason for errors is the presence of close interferers generating pulse collision. However such events are rare and we propose an α-stable model compatible with this fact due to its heavy tailed distribution. We derive the analytical expression of the two significant parameters. They depend on the attenuation coefficient, the users' density, the pulse collision probability and the pulse shape. We finally propose receiver strategies (Cauchy receiver and p-norm) that outperforms the classical Gaussian receiver.

In this paper, we address the problem of OFDM channel estimation in the presence of phase noise (PHN) and carrier frequency offset (CFO). For OFDM systems, PHN and CFO cause two effects: the common phase error (CPE) and the intercarrier interference (ICI) which severely degrade the accuracy of the channel estimate. In literature, several algorithms have been proposed to solve this problem. Here, we propose the joint estimation of channel impulse response (CIR), CFO and PHN with no prior statistical knowledge of PHN and SNR. The proposed approach uses a training OFDM symbol to track and estimate these many unknowns in the time domain by particle filtering. The particle filter is efficiently implemented by combining the principles of the Rao-Blackwellization technique and the hybrid importance function which encompasses the advantages of both the optimal and the prior importance functions. Simulation results are provided to illustrate the effectiveness of the proposed algorithm.