Rayleigh particle filter for nonlinear tracking system (original) (raw)
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Particle filter for tracking linear Gaussian target with nonlinear observations
2003
ABSTRACT In this paper, a solution to the TENET nonlinear ltering challenge is presented. The proposed approach is based on particle ltering techniques. Particle methods have already been used in this context but our method improves over previous work in several ways: better importance sampling distribution, variance reduction through Rao-Blackwellisation etc. We demonstrate the e ciency of our algorithm through simulation. Keywords: target tracking, particle lter, linear Gaussian target, nonlinear observations
A Tutorial on Particle Filters for Online Nonlinear/Non-Gaussian Bayesian Tracking
IEEE Transactions on …, 2002
Increasingly, for many application areas, it is becoming important to include elements of nonlinearity and non-Gaussianity in order to model accurately the underlying dynamics of a physical system. Moreover, it is typically crucial to process data on-line as it arrives, both from the point of view of storage costs as well as for rapid adaptation to changing signal characteristics. In this paper, we review both optimal and suboptimal Bayesian algorithms for nonlinear/non-Gaussian tracking problems, with a focus on particle filters. Particle filters are sequential Monte Carlo methods based on point mass (or "particle") representations of probability densities, which can be applied to any state-space model and which generalize the traditional Kalman filtering methods. Several variants of the particle filter such as SIR, ASIR, and RPF are introduced within a generic framework of the sequential importance sampling (SIS) algorithm. These are discussed and compared with the standard EKF through an illustrative example.
Signal Processing, 2010
A generalized likelihood function model of a sampling importance resampling (SIR) particle filter (PF) has been derived for state estimation of a nonlinear system in the presence of non-stationary, non-Gaussian white measurement noise. The measurement noise is modeled by Gaussian mixture probability density function and the noise parameters are estimated by maximizing the log likelihood function of the noise model. This model is then included in the likelihood function of the SIR particle filter (PF) at each time step for online state estimation of the system. The performance of the proposed algorithm has been evaluated by estimating the states of (i) a non-linear system in the presence of non-stationary Rayleigh distributed noise and (ii) a radar tracking system in the presence of glint noise. The simulation results show that the proposed modified SIR PF offers best performance among the considered algorithms for these examples.
Tracking problem for mobile robots has been a topic of interest for many researchers recently. Decades of research has been fruitful, resulting in numbers of techniques and tools to solve this problem. One particular framework that is widely used is so called bayesian filter. This framework incorporates bayesian rule in estimating posterior belief of robots state. Variants of bayesian filter are kalman filter and particle filter. In this paper, we emphasize on studying the principle of particle filter, deriving particle filter for robots localization problem and discuss the comparison between kalman filter and particle filter.
The particle filters and their applications
Chemometrics and Intelligent Laboratory Systems, 2008
Particle filtering is a Monte Carlo simulation method designed to approximate non-linear filters that estimate and track the state of a dynamic system. We present the general principle of these algorithms and show the wide domain of applications using some examples.
Visual Communications and Image Processing 2006, 2006
In the visual tracking domain, Particle Filtering (PF) can become quite inefficient when being applied into high dimensional state space. Rao-Blackwellisation [1] has been shown to be an effective method to reduce the size of the state space by marginalizing out some of the variables analytically [2]. In this paper based on our previous work [3] we propose an RBPF tracking algorithm with adaptive system noise model. Experiments using both simulation data and real data show that the proposed RBPF algorithm with adaptive noise variance improves its performance significantly over conventional Particle Filter tracking algorithm. The improvements manifest in three aspects: increased estimation accuracy, reduced variance for estimates and reduced particle numbers are needed to achieve the same level of accuracy. The last two performance improvements are evaluated in this paper using simulation data.
The hitchhiker’s guide to the particle filter
2008
Suppose one wants to model a dynamic process that is contaminated by noise, i.e. one seeks the state of the process given some noisy measurements. From a Bayesian point of view, the aim is to find the joint probabilistic density function (pdf) of the state and measurement vector; a complete solution for the problem. Conceptually this problem can be solved by the recursive Bayes filter. If the relevant pdfs are Gaussian and the processes are linear, this conceptual solution is the Kalman filter. However, for more general cases, e.g. the case when processes are non-linear and the pdfs are multi-modal, the exact solution is intractable due to insolvable integrals. Monte Carlo methods provide a numerical solution for these intractable integrals. The Monte Carlo approximation of the recursive Bayes filter is known as the particle filter. The concepts presented here have been extensively investigated in the literature. Our aim is to provide a concise summary of the theory of particle filters, together with an application in tracking and references for further reading.
2021
Both the particle and Kalman filters attempt to approximate the minimum mean-square error (MMSE) estimate of the time-varying parameter. In this scenario, a prior model of the time evolution of the parameter of interest is assumed before the MMSE estimation takes place. The Kalman filter is the (optimal) MMSE estimator for a linear dynamical system with Gaussian noise. For a nonlinear system with nonGaussian noise, the particle filter approximates the mean of posterior distribution at each discrete time step with a finite number of samples or particles. For these general nonlinear systems, the particle filter approaches the MMSE estimator as the number of particles approaches infinity.
Target / Object Tracking Using Particle Filtering
2008
Particle filtering techniques have captured the attention of many researchers in various communities, including those in signal processing, communication and image processing. Particle filtering is particularly useful in dealing with nonlinear state space models and non-Gaussian probability density functions. The underlying principle of the methodology is the approximation of relevant distributions with random measures composed of particles (samples from the space of the unknowns) and their associated weights. This dissertation makes three main contributions in the field of particle filtering. The first problem deals with target tracking in radar signal processing. The second problem deals with object tracking in video. The third problem deals with estimating error bounds for particle filtering based symbol estimation in communication systems. viii