William J. Fitzgerald

A Bayesian approach to tracking multiple targets using sensor arrays and particle filters

We present a Bayesian approach to tracking the direction-of-arrival (DOA) of multiple moving targets using a passive sensor array. The prior is a description of the dynamic behavior we expect for the targets which is modeled as constant velocity motion with a Gaussian disturbance acting on the targets heading direction. The likelihood function is arrived at by defining an uninformative prior for both the signals and noise variance and removing these parameters from the problem by marginalization. Advances in sequential Monte Carlo (SMC) techniques, specifically the particle filter algorithm, allow us to model and track the posterior distribution defined by the Bayesian model using a collection of target states that can be viewed as samples from the posterior of interest. We describe two versions of this algorithm and finally present results obtained using synthetic data.

Bayesian curve fitting using MCMC with applications to signal segmentation

We propose some Bayesian methods to address the problem of fitting a signal modeled by a sequence of piecewise constant linear (in the parameters) regression models, for example, autoregressive or Volterra models. A joint prior distribution is set up over the number of the changepoints/knots, their positions, and over the orders of the linear regression models within each segment if these are unknown. Hierarchical priors are developed and, as the resulting posterior probability distributions and Bayesian estimators do not admit closed-form analytical expressions, reversible jump Markov chain Monte Carlo (MCMC) methods are derived to estimate these quantities. Results are obtained for standard denoising and segmentation of speech data problems that have already been examined in the literature. These results demonstrate the performance of our methods.

Near optimal detection of signals in impulsive noise modeled with a symmetric /spl alpha/-stable distribution

There has been great interest in symmetric /spl alpha/-stable distributions which have proved to be very good models for impulsive noise. However, most of the classical non-Gaussian receiver design techniques cannot be extended to the symmetric /spl alpha/-stable noise case since these techniques require an explicit compact analytical form for the probability density function (PDF) of the noise distribution which /spl alpha/-stable distributions do not possess. A new analytical representation has been suggested for the symmetric /spl alpha/-stable PDF which is based on scale mixtures of Gaussians. Based on this new analytical representation, this paper introduces a novel near-optimal receiver for the detection of signals in symmetric /spl alpha/-stable noise. The performance of the new receiver is very close to the locally optimum receiver and is significantly better than the performance of previously suggested sub-optimum receivers. The new technique has important potential in radar, sonar, and other applications.

Single-molecule level analysis of the subunit composition of the T cell receptor on live T cells

The T cell receptor (TCR) expressed on most T cells is a protein complex consisting of TCRαβ heterodimers that bind antigen and cluster of differentiation (CD) 3εδ, εγ, and ζζ dimers that initiate signaling. A long-standing controversy concerns whether there is one, or more than one, αβ heterodimer per complex. We used a form of single-molecule spectroscopy to investigate this question on live T cell hybridomas. The method relies on detecting coincident fluorescence from single molecules labeled with two different fluorophores, as the molecules diffuse through a confocal volume. The fraction of events that are coincident above the statistical background is defined as the “association quotient,” Q. In control experiments, Q was significantly higher for cells incubated with wheat germ agglutinin dual-labeled with Alexa488 and Alexa647 than for cells incubated with singly labeled wheat germ agglutinin. Similarly, cells expressing the homodimer, CD28, gave larger values of Q than cells expressing the monomer, CD86, when incubated with mixtures of Alexa488- and Alexa647-labeled antibody Fab fragments. T cell hybridomas incubated with mixtures of anti-TCRβ Fab fragments labeled with each fluorophore gave a Q value indistinguishable from the Q value for CD86, indicating that the dominant form of the TCR comprises single αβ heterodimers. The values of Q obtained for CD86 and the TCR were low but nonzero, suggesting that there is transient or nonrandom confinement, or diffuse clustering of molecules at the T cell surface. This general method for analyzing the subunit composition of protein complexes could be extended to other cell surface or intracellular complexes, and other living cells.

Markov chain Monte Carlo methods with applications to signal processing

The last five years have witnessed a really significant increase in the awareness of numerical Bayesian methods, both in Statistics and in Signal Processing. It is now clear that many problems that could only be addressed using ad hoc methods, because of their complexity, can now be solved and these solutions can be applied to almost all areas of data and signal processing. Bayesian methods have been popular for decades. However, various approximations have been required in order to make progress because most of the integrations required within the framework have no analytical solutions apart from some simple models which usually involve Gaussian and linearity assumptions. This explains why sub-optimal, ad hoc approximations have been developed. The aim of this paper is to set out the foundations upon which modern numerical Bayesian methods are based, give one application to missing data in audio restoration and then give references to application areas that can be addressed.

Particle filtering for demodulation in fading channels with non-Gaussian additive noise

An efficient particle filtering algorithm is developed to solve the problem of demodulation of M-ary modulated signals under conditions of fading channels in the presence of non-Gaussian additive noise. Simulations for MDPSK signals are presented. The results show that the algorithm outperforms the current methods.

Bayesian Inference for Improved Single Molecule Fluorescence Tracking

Single molecule tracking is widely used to monitor the change in position of lipids and proteins in living cells. In many experiments in which molecules are tagged with a single or small number of fluorophores, the signal/noise ratio may be limiting, the number of molecules is not known, and fluorophore blinking and photobleaching can occur. All these factors make accurate tracking over long trajectories difficult and hence there is still a pressing need to develop better algorithms to extract the maximum information from a sequence of fluorescence images. We describe here a Bayesian-based inference approach, based on a trans-dimensional sequential Monte Carlo method that utilizes both the spatial and temporal information present in the image sequences. We show, using model data, where the real trajectory of the molecule is known, that our method allows accurate tracking of molecules over long trajectories even with low signal/noise ratio and in the presence of fluorescence blinking and photobleaching. The method is then applied to real experimental data.

Least l p -norm impulsive noise cancellation with polynomial filters

Abstract It is a common experience in signal processing that impulsive noise observed in various natural environments cannot be described with the Gaussian distribution. Recently, a heavy tailed distribution namely the α - stable distribution has become a popular model for impulsive noise since it agrees very well with empirical data and is also theoretically justified with the generalised central limit theorem. Although, it is a generalisation of the Gaussian distribution and shares important properties with it, the non-Gaussian α -stable distribution differs from the Gaussian distribution in many ways, the most notable of which is the lack of finite second-order statistics. Therefore, the classical techniques based on linear least-squares estimation perform very poorly in impulsive noise elimination. In this paper, motivated by some properties of the α -stable distribution, new techniques based on linear and nonlinear least l p -norm estimation are introduced and several simulation results are presented which show that least l p -norm estimation with a Volterra-type prediction filter performs significantly better than the conventional linear techniques such as linear least-squares estimation and than nonlinear least-squares estimation. A new measure for signal distortion in impulsive noise, namely fractional order signal-to-noise ratio (FSNR) is also introduced to quantify the performance of various impulsive noise cancellation algorithms.

Particle filtering for multiuser detection in fading CDMA channels

We address the problem of multiuser CDMA detection under fading conditions. The optimal detection problem can be reformulated as an optimal filtering problem for jump Markov linear systems, i.e., linear Gaussian state space models switching according to an unobserved finite state space Markov chain. Several approaches based on particle filtering techniques are reviewed to perform optimal filtering in this framework. A brief simulation study is carried out.

Particle filtering for joint symbol and code delay estimation in DS spread spectrum systems in multipath environment

We develop a new receiver for joint symbol, channel characteristics, and code delay estimation for DS spread spectrum systems under conditions of multipath fading. The approach is based on particle filtering techniques and combines sequential importance sampling, a selection scheme, and a variance reduction technique. Several algorithms involving both deterministic and randomized schemes are considered and an extensive simulation study is carried out in order to demonstrate the performance of the proposed methods.