Numerical Fitting-based Likelihood Calculation to Speed up the Particle Filter

The likelihood calculation of a vast number of particles is the computational bottleneck for the particle filter in applications where the observation information is rich. For fast computing the likelihood of particles, a numerical fitting approach is proposed to construct the Likelihood Probability Density Function (Li-PDF) by using a comparably small number of so-called fulcrums. The likelihood of particles is thereby analytically inferred, explicitly or implicitly, based on the Li-PDF instead of directly computed by utilizing the observation, which can significantly reduce the computation and enables real time filtering. The proposed approach guarantees the estimation quality when an appropriate fitting function and properly distributed fulcrums are used. The details for construction of the fitting function and fulcrums are addressed respectively in detail. In particular, to deal with multivariate fitting, the nonparametric kernel density estimator is presented which is flexible and convenient for implicit Li-PDF implementation. Simulation comparison with a variety of existing approaches on a benchmark 1-dimensional model and multi-dimensional robot localization and visual tracking demonstrate the validity of our approach.Comment: 42 pages, 17 figures, 4 tables and 1 appendix. This paper is a draft/preprint of one paper submitted to the IEEE Transaction

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

Parallelized Particle and Gaussian Sum Particle Filters for Large Scale Freeway Traffic Systems

Large scale traffic systems require techniques able to: 1) deal with high amounts of data and heterogenous data coming from different types of sensors, 2) provide robustness in the presence of sparse sensor data, 3) incorporate different models that can deal with various traffic regimes, 4) cope with multimodal conditional probability density functions for the states. Often centralized architectures face challenges due to high communication demands. This paper develops new estimation techniques able to cope with these problems of large traffic network systems. These are Parallelized Particle Filters (PPFs) and a Parallelized Gaussian Sum Particle Filter (PGSPF) that are suitable for on-line traffic management. We show how complex probability density functions of the high dimensional trafc state can be decomposed into functions with simpler forms and the whole estimation problem solved in an efcient way. The proposed approach is general, with limited interactions which reduces the computational time and provides high estimation accuracy. The efciency of the PPFs and PGSPFs is evaluated in terms of accuracy, complexity and communication demands and compared with the case where all processing is centralized

Adapting the Number of Particles in Sequential Monte Carlo Methods through an Online Scheme for Convergence Assessment

Particle filters are broadly used to approximate posterior distributions of hidden states in state-space models by means of sets of weighted particles. While the convergence of the filter is guaranteed when the number of particles tends to infinity, the quality of the approximation is usually unknown but strongly dependent on the number of particles. In this paper, we propose a novel method for assessing the convergence of particle filters online manner, as well as a simple scheme for the online adaptation of the number of particles based on the convergence assessment. The method is based on a sequential comparison between the actual observations and their predictive probability distributions approximated by the filter. We provide a rigorous theoretical analysis of the proposed methodology and, as an example of its practical use, we present simulations of a simple algorithm for the dynamic and online adaption of the number of particles during the operation of a particle filter on a stochastic version of the Lorenz system

Robust automatic target tracking based on a Bayesian ego-motion compensation framework for airborne FLIR imagery

Automatic target tracking in airborne FLIR imagery is currently a challenge due to the camera ego-motion. This phenomenon distorts the spatio-temporal correlation of the video sequence, which dramatically reduces the tracking performance. Several works address this problem using ego-motion compensation strategies. They use a deterministic approach to compensate the camera motion assuming a specific model of geometric transformation. However, in real sequences a specific geometric transformation can not accurately describe the camera ego-motion for the whole sequence, and as consequence of this, the performance of the tracking stage can significantly decrease, even completely fail. The optimum transformation for each pair of consecutive frames depends on the relative depth of the elements that compose the scene, and their degree of texturization. In this work, a novel Particle Filter framework is proposed to efficiently manage several hypothesis of geometric transformations: Euclidean, affine, and projective. Each type of transformation is used to compute candidate locations of the object in the current frame. Then, each candidate is evaluated by the measurement model of the Particle Filter using the appearance information. This approach is able to adapt to different camera ego-motion conditions, and thus to satisfactorily perform the tracking. The proposed strategy has been tested on the AMCOM FLIR dataset, showing a high efficiency in the tracking of different types of targets in real working conditions