Marginalized Particle Filters for Mixed Linear/Nonlinear State-Space Models (original) (raw)

The marginalized particle filter for automotive tracking applications

IEEE Proceedings. Intelligent Vehicles Symposium, 2005., 2005

This paper deals with the problem of estimating the vehicle surroundings (lane geometry and the position of other vehicles), which is needed for intelligent automotive systems, such as adaptive cruise control, collision avoidance and lane guidance. This results in a nonlinear estimation problem. For automotive tracking systems, these problems are traditionally handled using the extended Kalman filter. In this paper we describe the application of the marginalized particle filter to this problem. Studies using both synthetic and authentic data shows that the marginalized particle filter can in fact give better performance than the extended Kalman filter. However, the computational load is higher.

Approximate Conditional Mean Particle Filtering for Linear/Nonlinear Dynamic State Space Models

IEEE Transactions on Signal Processing, 2000

We consider linear systems whose state parameters are separable into linear and nonlinear sets, and evolve according to some known transition distribution, and whose measurement noise is distributed according to a mixture of Gaussians. In doing so, we propose a novel particle filter that addresses the optimal state estimation problem for the aforementioned class of systems. The proposed filter, referred to as the ACM-PF, is a combination of the approximate conditional mean filter and the sequential importance sampling particle filter. The algorithm development depends on approximating a mixture of Gaussians distribution with a moment-matched Gaussian in the weight update recursion. A condition indicating when this approximation is valid is given.

Unscented Kalman Filters and Particle Filter Methods for Nonlinear State Estimation

Procedia Technology, 2014

For nonlinear state space models to resolve the state estimation problem is difficult or these problems usually do not admit analytic solution. The Extended Kalman Filter (EKF) algorithm is the widely used method for solving nonlinear state estimation applications. This method applies the standard linear Kalman filter algorithm with linearization of the nonlinear system. This algorithm requires that the process and observation noises are Gaussian distributed. The Unscented Kalman Filter (UKF) is a derivative-free alternative method, and it is using one statistical linearization technique. The Particle Filter (PF) methods are recursive implementations of Monte-Carlo based statistical signal processing. The PF algorithm does not require either of the noises to be Gaussian and the posterior probabilities are represented by a set of randomly chosen weighted samples.

Particle Kalman Filtering: A Nonlinear Bayesian Framework for Ensemble Kalman Filters

2011

Abstract: This paper investigates an approximation scheme of the optimal nonlinear Bayesian filter based on the Gaussian mixture representation of the state probability distribution function. The resulting filter is similar to the particle filter, but is different from it in that, the standard weight-type correction in the particle filter is complemented by the Kalman-type correction with the associated covariance matrices in the Gaussian mixture.

State Estimation for General Class of Dynamical Systems: An Extension to Particle Filters

Proceedings of the 3rd International Conference of Control, Dynamic Systems, and Robotics (CDSR'16), 2016

Many physical systems are nonlinear and non-Gaussian in their state-space models. Particle Filter (PF) is a sequential Monte Carlo method that uses sets of sample scenarios, i.e. "particles" to represent probability densities, and it can be applied for state estimation in nonlinear/non-Gaussian state-spaces models. Conventional variants of PF do not assume any noise for the system input, while the corresponding measurement models disregard the system input as an argument. In reality, physical systems receive inputs contaminated with the measurement noise. In this work, a generalized particle filter algorithm is developed that handles the noisy input of the state-space model in a probabilistic framework. Three advanced variants of PF are then developed to improve the filtering accuracy. Performance of the developed filters are then verified with simulation of univariate and bivariate non-stationary growth models as benchmarks.

The Coordinate Particle Filter - A novel Particle Filter for High Dimensional Systems

Parametric filters, such as the Extended Kalman Filter and the Unscented Kalman Filter, typically scale well with the dimensionality of the problem, but they are known to fail if the posterior state distribution cannot be closely approximated by a density of the assumed parametric form. For nonparametric filters, such as the Particle Filter, the converse holds. Such methods are able to approximate any posterior, but the computational requirements scale exponentially with the number of dimensions of the state space. In this paper, we present the Coordinate Particle Filter which alleviates this problem. We propose to compute the particle weights recursively, dimension by dimension. This allows us to explore one dimension at a time, and resample after each dimension if necessary. Experimental results on simulated as well as real data confirm that the proposed method has a substantial performance advantage over the Particle Filter in high-dimensional systems where not all dimensions are...

Interacting particle filters for simultaneous state and parameter estimation

arXiv: Numerical Analysis, 2017

Simultaneous state and parameter estimation arises from various applicational areas but presents a major computational challenge. Most available Markov chain or sequential Monte Carlo techniques are applicable to relatively low dimensional problems only. Alternative methods, such as the ensemble Kalman filter or other ensemble transform filters have, on the other hand, been successfully applied to high dimensional state estimation problems. In this paper, we propose an extension of these techniques to high dimensional state space models which depend on a few unknown parameters. More specifically, we combine the ensemble Kalman-Bucy filter for the continuous-time filtering problem with a generalized ensemble transform particle filter for intermittent parameter updates. We demonstrate the performance of this two stage update filter for a wave equation with unknown wave velocity parameter.

Particle filters for positioning, navigation, and tracking

IEEE Transactions on Signal Processing, 2002

A framework for positioning, navigation and tracking problems using particle filters (sequential Monte Carlo methods) is developed. It consists of a class of motion models and a general non-linear measurement equation in position. A general algorithm is presented, which is parsimonious with the particle dimension. It is based on marginalization, enabling a Kalman filter to estimate all position derivatives, and the particle filter becomes low-dimensional. This is of utmost importance for highperformance real-time applications.