Gaussian Particle Filter Research Articles

Quasi-Monte Carlo Gaussian Particle Filtering Acceleration Using CUDA

A CUDA accelerated Quasi-Monte Carlo Gaussian particle filter (QMC-GPF) is proposed to deal with real-time non-linear non-Gaussian problems. GPF is especially suitable for parallel implementation as a result of the elimination of resampling step. QMC-GPF is an efficient counterpart of GPF using QMC sampling method instead of MC. Since particles generated by QMC method provides the best-possible distribution in the sampling space, QMC-GPF can make more accurate estimation with the same number of particles compared with traditional particle filter. Experimental results show that our GPU implementation of QMC-GPF can achieve the maximum speedup ratio of 95 on NVIDIA GeForce GTX 460.

A novel system for robust lane detection and tracking

This paper presents a lane detection and tracking system based on a novel lane feature extraction approach and the Gaussian Sum Particle filter (GSPF). The proposed feature extraction approach is based on the fact that by zooming into the vanishing point of the lanes, the lane markings/boundaries will only move on the same straight lines they are on. Objects other than the lanes in the frame do not share this property and can be ignored during the model parameter estimation. This algorithm is able to iteratively refine various traditional feature maps and to operate with curved roads. The tracking part of the system is initialised by a deformable template matching algorithm. Three types of tracking algorithms are compared in our study: the original Sequential Importance Resampling (SIR) particle filter, the Gaussian Particle Filter (GPF) and the Gaussian Sum Particles Filter (GSPF). The GSPF achieves the best performance by integrating a novel likelihood function and an intuitive parameter selection process. Both the GSPF and GPF provide improved tracking performance and require less computational power than the SIR. It has also been found that the detection and tracking performance is enhanced significantly by incorporating the refined feature map.

Robust Clock Synchronization in Wireless Sensor Networks Through Noise Density Estimation

Assuming that the network delays are normally distributed and the network nodes are subject to clock phase offset errors, the maximum likelihood estimator (MLE) and the Kalman filter (KF) have been recently proposed with the goal of maximizing the clock synchronization accuracy in wireless sensor networks (WSNs). However, because the network delays may assume any distribution and the performance of MLE and KF is quite sensitive to the distribution of network delays, designing clock synchronization algorithms that are robust to arbitrary network delay distributions appears as an important problem. Adopting a Bayesian framework, this paper proposes a novel clock synchronization algorithm, called the Iterative Gaussian mixture Kalman particle filter (IGMKPF), which combines the Gaussian mixture Kalman particle filter (GMKPF) with an iterative noise density estimation procedure to achieve robust performance in the presence of unknown network delay distributions. The Kullback-Leibler divergence is used as a measure to assess the departure of estimated observation noise density from its true expression. The posterior Cramér-Rao bound (PCRB) and the mean-square error (MSE) of IGMKPF are evaluated via computer simulations. It is shown that IGMKPF exhibits improved performance and robustness relative to MLE. The prior information plays an important role in IGMKPF. A MLE-based method for obtaining reliable prior information for clock phase offsets is presented and shown to ensure the convergence of IGMKPF.

Hybrid Estimation Using Perceptional Information: Robotic Tracking of Deep Ocean Animals

An approach to estimation for hybrid systems is presented that utilizes uncertain perceptional information about the system's mode to improve tracking of its mode and continuous states. This results in significant improvements in situations where previously reported methods of estimation for hybrid systems perform poorly due to poor distinguishability of the modes. Even in applications where the modes are more easily distinguished, the approach presented can improve performance by decreasing the mode estimation delay of the estimator. Here, state tracking is achieved using a new form of Rao-Blackwellized particle filter called the mode-observed Gaussian Particle Filter. This new filter extends existing hybrid estimation algorithms to admit uncertain but discrete mode-related observations in addition to the information available from more traditional sensors. The framework for estimation using both traditional and perceptional information is applicable to any stochastic hybrid system with mode-related perceptional observations available. Furthermore, the computational efficiency of the Rao-Blackwellized particle filter is maintained, making this filter suitable for real-time implementation. An application that motivates this research is an automatic underwater robotic observation system that follows and films individual deep ocean animals. In that context, to improve tracking of agile animals, a mode-observed Gaussian Particle Filter is applied to supplement measurements of relative position and water-relative velocities of the specimen with perception of what the animal is doing (via visual cues). In addition to improving position and velocity tracking, this filter improves estimation of animal behavior modes to facilitate potentially the automated collection of behavioral data. Performance of the new filter is demonstrated using data from simulation as well as field data collected when tracking actual specimens in the ocean.

An Efficient Constrained Gaussian Particle Filter

AbstractThe paper deals with a state estimation of nonlinear stochastic dynamic systems subject to a nonlinear inequality constraint. A special focus is paid to particle filters, which provide an estimate of the whole probability density as opposed to the local filters, such as the extended Kalman filter or the unscented Kalman filter, which provide a point estimate only. Within the particle filtering framework, there are several approaches to the constrained state estimation, mostly based on discarding samples violating the constraint with a possible increase of their number to improve the estimate quality. The paper aims at proposing a modification to an importance function of the particle filter in order to increase efficiency of sampling while keeping the computational complexity low. The proposed modification is utilized within the Gaussian particle filter which is advantageous for its low computational complexity. Complexity and estimation quality of the proposed constrained Gaussian particle filter is compared to other constrained particle filters in a numerical example.

Contour tracking using Gaussian particle filter

Gaussian particle filter algorithm provides a framework to estimate the state of a moving object. However, it is a known fact that parameters like noise variance and particle number affect the effectiveness of the filter greatly. To improve the performance of Gaussian particle filter in contour tracking, the authors propose a parameter adapting mechanism. To simplify the filter's implementation, a variant sampling method is also proposed. This sampling method combines sampling step with prediction step by taking advantage of the Gaussian assumption and by exploring the linear structure of the system dynamic model. Finally, comparative experiments are provided, which demonstrate the merits of the proposed algorithm.

Multitarget bearings-only tracking using fuzzy clustering technique and Gaussian particle filter

In this paper, a novel multitarget bearings-only tracking algorithm that combines the fuzzy clustering data association technique together with a Gaussian particle filter (GPF) is presented. Firstly, to deal with the data association problem that arises due to the uncertainty of the measurements, the fuzzy clustering method with the maximum entropy principle is utilized, which eliminates those invalid measurements. Secondly, this paper employs GPF to update each target state independently, since it has a much-improved performance and versatility over other Gaussian filters, especially when nontrivial nonlinearities are present. Moreover, in the multisensor scenario, a statistic test method based on the cotangent values of bearings is proposed, for associating the target bearing data observed at each sensor. Simulation results demonstrate the effectiveness of the algorithm.

Adaptive hybrid likelihood model for visual tracking based on Gaussian particle filter

We present a new scheme based on multiple-cue integration for visual tracking within a Gaussian particle filter framework. The proposed method integrates the color, shape, and texture cues of an object to construct a hybrid likelihood model. During the measurement step, the likelihood model can be switched adaptively according to environmental changes, which improves the object representation to deal with the complex disturbances, such as appearance changes, partial occlusions, and significant clutter. Moreover, the confidence weights of the cues are adjusted online through the estimation using a particle filter, which ensures the tracking accuracy and reliability. Experiments are conducted on several real video sequences, and the results demonstrate that the proposed method can effectively track objects in complex scenarios. Compared with previous similar approaches through some quantitative and qualitative evaluations, the proposed method performs better in terms of tracking robustness and precision.

Energy-Efficient Estimation of Clock Offset for Inactive Nodes in Wireless Sensor Networks

For a meaningful processing of the information sensed by a wireless sensor network (WSN), the clocks of the individual nodes need to be matched through some well-defined procedures. Extending the idea of having silent nodes in a WSN overhear the two-way timing message communication between two active (master and slave) nodes, this paper derives the maximum-likelihood estimator (MLE) for the clock offsets of the listening nodes located within the communication range of the active nodes by assuming an exponential link delay modeling, hence synchronizing with the reference node at a very low cost. A vital advantage for adopting such an approach is that the performance of sender-receiver protocols can be compared with receiver-receiver protocols on equal footings, because their main critical aspect was associated with the high-communication overhead induced by the point-to-point nature of communication links relative to broadcast communications. The MLE is also shown to be the minimum variance unbiased estimator (MVUE) of the clock offset when the mean of exponential link delays is known. Since it is attractive to know in advance the extent to which an estimator can perform through its lower bound, the Chapman-Robbins bound and the Barankin bound for the clock offset estimator are also derived. It is shown that for an exponential link delay model, the mean square error of the clock offset estimator is inversely proportional to the square of the number of observations, and hence its performance is on a similar scale, albeit slightly lesser, as compared to the usual sender-receiver clock offset estimator. In addition, a novel method referred to as the Gaussian mixture Kalman particle filter (GMKPF) is proposed herein to estimate the clock offsets of the listening nodes in a WSN. GMKPF represents a better and flexible alternative to the MLE for the clock offset estimation problem due to its improved performance and applicability in arbitrary and generalized non-Gaussian random delay models.

Study of Algorithmic and Architectural Characteristics of Gaussian Particle Filters

In this paper, we analyze algorithmic and architectural characteristics of a class of particle filters known as Gaussian Particle Filters (GPFs). GPFs approximate the posterior density of the unknowns with a Gaussian distribution which limits the scope of their applications in comparison with the universally applied sample-importance resampling filters (SIRFs) but allows for their implementation without the classical resampling procedure. Since there is no need for resampling, we propose a modified GPF algorithm that is suitable for parallel hardware realization. Based on the new algorithm, we propose an efficient parallel and pipelined architecture for GPF that is superior to similar architectures for SIRF in the sense that it requires no memories for storing particles and it has very low amount of data exchange through the communication network. We analyze the GPF on the bearings-only tracking problem and the results are compared with results obtained by SIRF in terms of computational complexity, potential throughput, and hardware energy. We consider implementation on FPGAs and we perform detailed comparison of the GPF and SIRF algorithms implemented in different ways on this platform. GPFs that are implemented in parallel pipelined fashion on FPGAs can support higher sampling rates than SIRFs and as such they might be a more suitable candidate for real-time applications.

Ambulatory Hip Angle Estimation using Gaussian Particle Filter

Hip angle is a major parameter in gait analysis while gait analysis plays an important role in healthcare, animation and other applications. Accurate estimation of hip angle using wearable inertial sensors in ambulatory environment remains a challenge because 1) the non-linear nature of thigh movement has not been well addressed, and 2) the variation of micro-inertial sensor measurement noise has not been studied yet. We propose to use Hybrid Dynamic Bayesian Network (HDBN) to model the non-linear hip angle dynamics and variation of measurement noise levels, and Gaussian Particle Filter (GPF) to estimate the hip angle during gait cycles from the measurements of the wearable accelerometers that are attached to the thighs. The experiments have been conducted and the results have shown that the proposed method can achieve significant accuracy improvement over the previous work on the ambulatory hip angle estimation.

A robust estimation scheme for clock phase offsets in wireless sensor networks in the presence of non-Gaussian random delays

To cope with the Gaussian or non-Gaussian nature of the random network delays, a novel method, referred to as the Gaussian mixture Kalman particle filter (GMKPF), is proposed herein to estimate the clock offset in wireless sensor networks. GMKPF represents a better and more flexible alternative to the symmetric Gaussian maximum likelihood (SGML), and symmetric exponential maximum likelihood (SEML) estimators for clock offset estimation in non-Gaussian or non-exponential random delay models. The computer simulations illustrate that GMKPF yields much more accurate results relative to SGML and SEML when the network delays are modeled in terms of a single non-Gaussian/non-exponential distribution or as a mixture of several distributions.

Gaussian Convolution Filter and its Application to Tracking

A new recursive algorithm, called the Gaussian convolution filter (GCF), is proposed for nonlinear dynamic state space models. Based on the convolution filter (CF) and similar to the Gaussian filters, the GCF ap-proximates the posterior density of the states by Gaussian distribution. The analytical results show the ability to deal with complex observation model and small observation noise of the GCF over the Gaussian particle filter (GPF) and the lower complexity, more amenable for parallel implementation than the CF. The Simula-tion in the Tracking domain demonstrates the good performance of the GCF.

GEKF, GUKF and GGPF based prediction of chaotic time-series with additive and multiplicative noises

On the assumption that random interruptions in the observation process are modelled by a sequence of independent Bernoulli random variables, this paper generalize the extended Kalman filtering (EKF), the unscented Kalman filtering (UKF) and the Gaussian particle filtering (GPF) to the case in which there is a positive probability that the observation in each time consists of noise alone and does not contain the chaotic signal (These generalized novel algorithms are referred to as GEKF, GUKF and GGPF correspondingly in this paper). Using weights and network output of neural networks to constitute state equation and observation equation for chaotic time-series prediction to obtain the linear system state transition equation with continuous update scheme in an online fashion, and the prediction results of chaotic time series represented by the predicted observation value, these proposed novel algorithms are applied to the prediction of Mackey–Glass time-series with additive and multiplicative noises. Simulation results prove that the GGPF provides a relatively better prediction performance in comparison with GEKF and GUKF.

Collaborative tracking via particle filter in wireless sensor networks

Target tracking is one of the main applications of wireless sensor networks. Optimized computation and energy dissipation are critical requirements to save the limited resource of the sensor nodes. A framework and analysis for collaborative tracking via particle filter are presented in this paper. Collaborative tracking is implemented through sensor selection, and results of tracking are propagated among sensor nodes. In order to save communication resources, a new Gaussian sum particle filter, called Gaussian sum quasi particle filter, to perform the target tracking is presented, in which only mean and covariance of mixands need to be communicated. Based on the Gaussian sum quasi particle filter, a sensor selection criterion is proposed, which is computationally much simpler than other sensor selection criterions. Simulation results show that the proposed method works well for target tracking.

Improved Particle Filtering-Based Estimation of the Number of Competing Stations in IEEE 802.11 Networks

This letter proposes a new method to estimate the number of competing stations in IEEE 802.11 networks. Due to the nonlinear/non-Gaussian nature of measurement model, a nonlinear filtering algorithm, called the Gaussian mixture sigma point particle filter (GMSPPF), is proposed herein to estimate the number of competing stations. Since GMSPPF represents a better alternative to the conventional extended Kalman filter (EKF), unscented Kalman filter (UKF), particle filter (PF), and unscented particle filter (UPF) for nonlinear/non-Gaussian (or Gaussian) tracking problems, we apply this filter for IEEE 802.11 WLANs. GMSPPF provides a more viable means for tracking in any conditions the number of competing stations in IEEE 802.11 WLANs relative to EKF, UKF, PF, and UPF. Further, GMSPPF presents both high accuracy as well as prompt reactivity to changes in the network occupancy status. For the more accurate method (GMSPPF), the combined access mode is shown to maximize the system throughput by switching between the basic access mode and the RTS/CTS access mode.

Performance Comparison of Gaussian-Based Filters Using Information Measures

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In many situations, solutions to nonlinear discrete- time filtering problems are available through approximations. Many of these solutions are based on approximating the posterior distributions of the states with Gaussian distributions. In this letter, we compare the performance of Gaussian-based filters including the extended Kalman filter, the unscented Kalman filter, and the Gaussian particle filter. To that end, we measure the distance between the posteriors obtained by these filters and the one estimated by a sequential Monte Carlo (particle filtering) method. As a distance metric, we apply the Kullback-Leibler and X² information measures. Through computer simulations, we rank the performance of the three filters. </para>

Gaussian particle filter based pose and motion estimation

Determination of relative three-dimensional (3D) position, orientation, and relative motion between two reference frames is an important problem in robotic guidance, manipulation, and assembly as well as in other fields such as photogrammetry. A solution to pose and motion estimation problem that uses two-dimensional (2D) intensity images from a single camera is desirable for real-time applications. The difficulty in performing this measurement is that the process of projecting 3D object features to 2D images is a nonlinear transformation. In this paper, the 3D transformation is modeled as a nonlinear stochastic system with the state estimation providing six degrees-of-freedom motion and position values, using line features in image plane as measuring inputs and dual quaternion to represent both rotation and translation in a unified notation. A filtering method called the Gaussian particle filter (GPF) based on the particle filtering concept is presented for 3D pose and motion estimation of a moving target from monocular image sequences. The method has been implemented with simulated data, and simulation results are provided along with comparisons to the extended Kalman filter (EKF) and the unscented Kalman filter (UKF) to show the relative advantages of the GPF. Simulation results showed that GPF is a superior alternative to EKF and UKF.

Design Methodology for Domain Specific Parameterizable Particle Filter Realizations

This paper presents a reconfigurable particle filter design methodology for a real-time bearings-only tracking application. The methodology provides the capability of selecting a single particle filter from multiple particle filter realizations with maximum resource sharing. The autonomous buffer controller mechanism for the architecture ensures correct operation of the particle filters. Parameter adaptation and algorithm reconfiguration can be accomplished with negligible reconfiguration overhead through buffer controllers and a set of switches for transforming dataflow structures such that any desired particle filter can be implemented. Two target particle filters, sample importance resample filter (SIRF) and Gaussian particle filter (GPF), are realized using field programmable gate array (FPGA) based on the proposed methodology. However, the architecture can be extended for a wide range of particle filters with different sets of dynamics. This paper successfully demonstrates that implementation of a domain specific processor for particle filters is feasible with performance that is much higher than that of commercially available digital signal processors (DSPs).

Multiuser channel estimation using robust recursive filters for CDMA system

In this paper, we present a novel blind adaptive multiuser detector structure and three robust recursive filters to improve the performance in CDMA environments: Sigma point kalman filter (SPKF), particle filter (PF), and Gaussian mixture sigma point particle filter (GMSPPF). Our proposed robust recursive filters have superior performance over a conventional extended Kalman filter (EKF). The proposed multiuser detector algorithms initially use Kalman prediction form to estimated channel parameters, and unknown data symbol be predicted. Second, based on this predicted data symbol, the robust recursive filters (e.g., GMSPPF) is a refined estimation of joint multipaths and time delays. With these estimated multipaths and time delays, data symbol detection is carried out (Kalman correction form). Computer simulations show that the proposed algorithms outperform the conventional blind multiuser detector with the EKF. Also we can see it provides a more viable means for tracking time-varying amplitudes and time delays in CDMA communication systems, compared to that of the EKF for near-far ratio of 20 dB. For this reason, it is believed that the proposed channel estimators can replace well-known filter such as the EKF.