Adapting the Sample Size in Particle Filters Through KLD-Sampling

Over the past few years, particle filters have been applied with great success to a variety of state estimation problems. In this paper we present a statistical approach to increasing the efficiency of particle filters by adapting the size of sample sets during the estimation process. The key idea of the KLD-sampling method is to bound the approximation error introduced by the sample-based representation of the particle filter. The name KLD-sampling is due to the fact that we measure the approximation error using the Kullback-Leibler distance. Our adaptation approach chooses a small number of samples if the density is focused on a small part of the state space, and it chooses a large number of samples if the state uncertainty is high. Both the implementation and computation overhead of this approach are small. Extensive experiments using mobile robot localization as a test application show that our approach yields drastic improvements over particle filters with fixed sample set sizes and over a previously introduced adaptation technique.

Spectral estimation of nonstationary EEG using particle filtering with application to event-related desynchronization (ERD)

This paper proposes non-Gaussian models for parametric spectral estimation with application to event-related desynchronization (ERD) estimation of nonstationary EEG. Existing approaches for time-varying spectral estimation use time-varying autoregressive (TVAR) state-space models with Gaussian state noise. The parameter estimation is solved by a conventional Kalman filtering. This study uses non-Gaussian state noise to model autoregressive (AR) parameter variation with estimation by a Monte Carlo particle filter (PF). Use of non-Gaussian noise such as heavy-tailed distribution is motivated by its ability to track abrupt and smooth AR parameter changes, which are inadequately modeled by Gaussian models. Thus, more accurate spectral estimates and better ERD tracking can be obtained. This study further proposes a non-Gaussian state space formulation of time-varying autoregressive moving average (TVARMA) models to improve the spectral estimation. Simulation on TVAR process with abrupt parameter variation shows superior tracking performance of non-Gaussian models. Evaluation on motor-imagery EEG data shows that the non-Gaussian models provide more accurate detection of abrupt changes in alpha rhythm ERD. Among the proposed non-Gaussian models, TVARMA shows better spectral representations while maintaining reasonable good ERD tracking performance.

Online empirical evaluation of tracking algorithms

Evaluation of tracking algorithms in the absence of ground truth is a challenging problem. There exist a variety of approaches for this problem, ranging from formal model validation techniques to heuristics that look for mismatches between track properties and the observed data. However, few of these methods scale up to the task of visual tracking, where the models are usually nonlinear and complex and typically lie in a high-dimensional space. Further, scenarios that cause track failures and/or poor tracking performance are also quite diverse for the visual tracking problem. In this paper, we propose an online performance evaluation strategy for tracking systems based on particle filters using a time-reversed Markov chain. The key intuition of our proposed methodology relies on the time-reversible nature of physical motion exhibited by most objects, which in turn should be possessed by a good tracker. In the presence of tracking failures due to occlusion, low SNR, or modeling errors, this reversible nature of the tracker is violated. We use this property for detection of track failures. To evaluate the performance of the tracker at time instant t, we use the posterior of the tracking algorithm to initialize a time-reversed Markov chain. We compute the posterior density of track parameters at the starting time t=0 by filtering back in time to the initial time instant. The distance between the posterior density of the time-reversed chain (at t=0) and the prior density used to initialize the tracking algorithm forms the decision statistic for evaluation. It is observed that when the data are generated by the underlying models, the decision statistic takes a low value. We provide a thorough experimental analysis of the evaluation methodology. Specifically, we demonstrate the effectiveness of our approach for tackling common challenges such as occlusion, pose, and illumination changes and provide the Receiver Operating Characteristic (ROC) curves. Finally, we also show the applicability of the core ideas of the paper to other tracking algorithms such as the Kanade-Lucas-Tomasi (KLT) feature tracker and the mean-shift tracker.

Speech enhancement based on nonlinear models using particle filters

Motivated by the reportedly strong performance of particle filters (PFs) for noise reduction on essentially linear speech production models, and the mounting evidence that the introduction of nonlinearities can lead to a refined speech model, this paper presents a study of PF solutions to the problem of speech enhancement in the context of nonlinear, neural-type speech models. Several variations of a global model are presented (single/multiple neurons; bias/no bias), and corresponding PF solutions are derived. Different importance functions are given when beneficial, Rao-Blackwellization is proposed when possible, and dual/nondual versions of each algorithms are presented. The method shown can handle both white and colored noise. Using a variety of speech and noise signals and different objective quality measures, the performance of these algorithms are evaluated against other PF solutions running on linear models, as well as some traditional enhancement algorithms. A certain hierarchy in performance is established between each algorithm in the paper. Depending on the experimental conditions, the best-performing algorithms are a classical Rao-Blackwellized particle filter (RBPF) running on a linear model, and a proposed PF employing a nondual, nonlinear model with multiple neurons and no biases. With consistence, the neural-network-based PF outperforms RBPF at low signal-to-noise ratio (SNR).

A Bayesian approach for the estimation of AR coefficients from noisy biomedical data

In this paper we study the identification of AR parameters in a biomedical signal corrupted by additive white gaussian noise. The identification of AR parameter is treated as a signal estimation problem, whose aim is to obtain an estimate of the clean signal, given the noisy observations, and after that to obtain the noise free AR parameters. The novelty of our approach is the simultaneous estimation of AR parameter and the model order of the AR process. This is done adopting a Bayesian framework and using a special form for the prior of AR parameters. To obtain the solution we use the Variational Bayesian (VB) Framework. Simulation results have shown that the proposed approach correctly identifies the model order of AR process while at the same time produces an estimate for the AR parameters.

Consistency checks for particle filters

An "inconsistent" particle filter produces--in a statistical sense--larger estimation errors than predicted by the model on which the filter is based. Two test variables are introduced that allow the detection of inconsistent behavior. The statistical properties of the variables are analyzed. Experiments confirm their suitability for inconsistency detection.