Sampling density design for particle filters

This paper proposes a novel particle filter, namely, the auxiliary iterated extended Kalman particle filter (AIEKPF). To generate the importance density, based on the auxiliary particle filtering (APF) technique the proposed filter uses the iterated extended Kalman filter (IEKF) to integrate the latest measurements into state transition density. This new filter can match the posterior density well, because of the robustness of the APF and the importance density generated by the IEKF. The performance of the presented particle filter is evaluated by two different estimation problems with the noise of Gaussian distribution and Gamma distribution, respectively. The experimental results illustrate that the AIEKPF is superior to the extended Kalman filter and some existing particle filters, such as the standard particle filter (PF), the extended Kalman particle filter, the unscented Kalman particle filter (UKPF) and the auxiliary extended Kalman particle filter, where the number of particles is relatively small, such as 200 and 1,000. However, with an increase of particles, the superiority of the proposed method may decline compared with the PF and APF as showed in the experiments. Also, the AIEKPF has less running time than the UKPF under the same conditions, and from the viewpoint of the average effective sample sizes, it is clear that the AIEKPF has the slightest degeneracy in all filters presented in the experiments.

Robust particle filter for state estimation in presence of bounded but uncertain parameters based on ellipsoidal set membership approach

We estimate the state of a noisy robot arm and underactuated hand using an implicit Manifold Particle Filter (MPF) informed by contact sensors. As the robot touches the world, its state space collapses to a contact manifold that we represent implicitly using a signed distance field. This allows us to extend the MPF to higher (six or more) dimensional state spaces. Earlier work, which explicitly represents the contact manifold, was only capable of scaling to three dimensions. Through a series of experiments, we show that the implicit MPF converges faster and is more accurate than a conventional particle filter during periods of persistent contact. We present three methods of drawing samples from an implicit contact manifold, and compare them in experiments.

Data assimilation is the process of estimating the state of dynamic systems (linear or nonlinear, Gaussian or non-Gaussian) as accurately as possible from noisy observational data. Although the Three Dimensional Variational (3D-VAR) methods, Four Dimensional Variational (4D-VAR) methods and Ensemble Kalman filter (EnKF) methods are widely used and effective for linear and Gaussian dynamics, new methods of data assimilation are required for the general situation, that is, nonlinear non-Gaussian dynamics. General Bayesian recursive estimation theory is reviewed in this thesis. The Bayesian estimation approach provides a rather general and powerful framework for handling nonlinear, non-Gaussian, as well as linear, Gaussian estimation problems. Despite a general solution to the nonlinear estimation problem, there is no closed-form solution in the general case. Therefore, approximate techniques have to be employed. In this thesis, the sequential Monte Carlo (SMC) methods, commonly referred to as the particle filter, is presented to tackle non-linear, non-Gaussian estimation problems. In this thesis, we use the SMC methods only for the nonlinear state estimation problem, however, it can also be used for the nonlinear parameter estimation problem. In order to demonstrate the new methods in the general nonlinear non-Gaussian case, we compare Sequential Monte Carlo (SMC) methods with the Ensemble Kalman Filter (EnKF) by performing data assimilation in nonlinear and non-Gaussian dynamic systems. The models used in this study are referred to as state-space models. The Lorenz 1963 and 1966 models serve as test beds for examining the properties of these assimilation methods when used in highly nonlinear dynamics. The application of Sequential Monte Carlo methods to different fixed parameters in dynamic models is considered. Four different scenarios in the Lorenz 1063 [sic] model and three different scenarios in the Lorenz 1996 model are designed in this study for both the SMC methods and EnKF method with different filter siz

In the application of particle filter algorithm for target tracking in wireless sensor networks, an Auxiliary particle filter (APF) and Gaussian particle filter (GPF) are discussed to solve the particle degradation problem of Particle Filter (PF). By introducing an auxiliary variable and two rounds weighted processes, APF makes the particle weights stable and relaxes particle degradation. GPF uses a Gaussian density function to approximately estimate posterior probability distribution. It doesn’t require re-sampling, and there is no particle degradation. Therefore, three algorithm are applied to single-target tracking in wireless sensor networks. Finally, the comparison of three algorithm’s performance in target tracking is presented and the simulation results are also given. From these results we can see that APF has better accuracy than PF algorithm and GPF has better accuracy and real-time performance than PF algorithm.

The application of the auxiliary particle filter to the robot localization problem is considered. The auxiliary particle filter (APF) is an enhancement of the generic particle filter. However, APF suffers from the impoverishment problem and needs a large number of particles to represent the system posterior probability density function. An evolutionary computing method, the genetic algorithm is introduced into APF to remove early convergence yet improves the quality of potential solutions. Experiment results show that the evolutionary APF algorithm needs fewer particles and is more precise and robust for mobile robot localization in dynamic environment.KeywordsMobile RobotParticle FilterGenetic AlgoRobot LocalizationAverage Localization ErrorThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

In this research, a non-infrastructure-based and low-cost indoor navigation method is proposed through the integration of smartphone built-in microelectromechanical systems (MEMS) sensors and indoor map information using an auxiliary particle filter (APF). A cascade structure Kalman particle filter algorithm is designed to reduce the computational burden and improve the estimation speed of the APF by decreasing its update frequency and the number of particles used in this research. In the lower filter (Kalman filter), zero velocity update and non-holonomic constraints are used to correct the error of the inertial navigation-derived solutions. The innovation of the design lies in the combination of upper filter (particle filter) map-matching and map-aiding methods to further constrain the navigation solutions. This proposed navigation method simplifies indoor positioning and makes it accessible to individual and group users, while guaranteeing the system’s accuracy. The availability and accuracy of the proposed algorithm are tested and validated through experiments in various practical scenarios.

This paper proposes two new particle filters, namely, the auxiliary extended Kalman particle filter (AEKPF) and the auxiliary unscented Kalman particle filter (AUKPF). The theory governing the newly proposed filtering techniques is developed and the algorithms are described and contrasted. Next, a series of tests is presented in which the new filters are compared against the extended Kalman filter (EKF), the unscented Kalman filter (UKF), and several existing particle filters. The test results are from simulations with synthetic mathematical models that incorporate elements that are nonlinear, non-stationary, and stochastic. Performance results are presented for various degrees of model nonlinearity including first, second, and third order systems. Furthermore, experimental results are also reported comparing the filters performances with different signal to noise ratios and noise models, including Gaussian, Cauchy, and Gamma distributions. Various metrics are used to compare the filters performances and to make conclusions about future work. It is shown to be advantageous to use certain particle filters depending on the noise distribution of the system of interest. In particular, the AUKPF and the AEKPF outperform existing particle filters in many cases.

Tracking a maneuvering target weakens the performance of predictive-model-based Bayesian state estimators (Kalman Filter). Therefore, the particle is used to track maneuverable targets instead of Kalman filter and its extensions. The particle filter proved more efficiency compared to Kalman filter and its extensions, e.g. Extended Kalman Filter (EKF) and Interacting Multiple Model (IMM). Unfortunately, due to the highly uncertainty and incompleteness of the information in a highly-maneuverable target-tracking problem, the advantage of the particle filter is weakened. Both auxiliary and smoothing particle filter were proposed to overcome this problem. In this paper, we compare the performance of both auxiliary and smoothing particle filter in tracking a highly maneuverable target. We applied both algorithms to track a maneuverable target in a multiple-sensors network. Monte Carlo simulation showed that the smoothing particle filter has a better performance when compared to auxiliary particle filter in tracking a maneuvering target.

The particle filter has attracted considerable attention in visual tracking due to its relaxation of the linear and Gaussian restrictions in the state space model. It is thus more flexible than the Kalman filter. However, the conventional particle filter uses system transition as the proposal distribution, leading to poor sampling efficiency and poor performance in visual tracking. It is not a trivial task to design satisfactory proposal distributions for the particle filter. In this paper, we introduce an improved particle filtering framework into visual tracking, which combines the unscented Kalman filter and the auxiliary particle filter. The efficient unscented auxiliary particle filter (UAPF) uses the unscented transformation to predict one-step ahead likelihood and produces more reasonable proposal distributions, thus reducing the number of particles required and substantially improving the tracking performance. Experiments on real video sequences demonstrate that the UAPF is computationally efficient and outperforms the conventional particle filter and the auxiliary particle filter.KeywordsParticle FilterImportance SamplingObservation ModelVisual TrackingUnscented Kalman FilterThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The lack of a parameterized observation model in robot localization using occupancy grids requires the application of sampling-based methods, or particle filters. This work addresses the problem of optimal Bayesian filtering for dynamic systems with observation models that cannot be approximated properly as any parameterized distribution, which includes localization and SLAM with occupancy grids. By integrating ideas from previous works on adaptive sample size, auxiliary particle filters, and rejection sampling, we derive a new particle filter algorithm that enables the usage of the optimal proposal distribution to estimate the true posterior density of a non-parametric dynamic system. Our solution avoids approximations adopted in previous approaches at the cost of a higher computational burden. We present simulations and experimental results for a real robot showing the suitability of the method for localization.

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In this work, we propose a new ground moving target indicator (GMTI) radar based ground vehicle tracking method which exploits domain knowledge. Multiple state models are considered and a Monte-Carlo sampling based algorithm is preferred due to the manoeuvring of the ground vehicle and the non-linearity of the GMTI measurement model. Unlike the commonly used algorithms such as the interacting multiple model particle filter (IMMPF) and bootstrap multiple model particle filter (BS-MMPF), we propose a new algorithm integrating the more efficient auxiliary particle filter (APF) into a Bayesian framework. Moreover, since the movement of the ground vehicle is likely to be constrained by the road, this information is taken as the domain knowledge and applied together with the tracking algorithm for improving the tracking performance. Simulations are presented to show the advantages of both the new algorithm and incorporation of the road information by evaluating the root mean square error (RMSE).

This paper provides a solution for the multiple changepoint detection problems in financial time series prediction without knowing the number and location of changepoints. The proposed approach is a Sequential Monte Carlo (SMC) method for estimating GARCH based volatility models which are subject to an unknown number of changepoints. Recent Auxiliary Particle Filtering (APF) techniques are used to calculate the posterior densities and forecasts in real-time. This approach also automatically deals with the common path dependence problem of these type volatility models. We studied on simulated volatility data using GARCH model and have shown that the proposed approach works well with the generated data. For the non-linearity multiple changepoint detection problem, APF is investigated over the simulated volatility to model the switching regimes. In this study, a full structural changepoint specification is defined in which all parameters of the conditional variance of GARCH are subject to change respectively.

The Auxiliary Particle Filter is a variant of the common particle filter which attempts to incorporate information from the next measurement to improve the proposal distribution in the update step. This paper studies how this can be done for Mixed Linear/Nonlinear Gaussian models, it builds on a previously suggested method and introduces two new variants which tries to improve the performance by using a more detailed approximation of the true probability density function when evaluating the so called first stage weights. These algorithms are compared for a couple of models to illustrate their strengths and weaknesses.