Gaussian Particle Filter Research Articles

Gaussian Particle Filtering for Nonlinear Systems With Heavy-Tailed Noises: A Progressive Transform-Based Approach.

The Gaussian particle filter (GPF) is a type of particle filter that employs the Gaussian filter approximation as the proposal distribution. However, the linearization errors are introduced during the calculation of the proposal distribution. In this article, a progressive transform-based GPF (PT-GPF) is proposed to solve this problem. First, a progressive transformation is applied to the measurement model to circumvent the necessity of linearization in the calculation of the proposal distribution, thereby ensuring the generation of optimal Gaussian proposal distributions in sense of linear minimum mean-square error (LMMSE). Second, to mitigate the potential impact of outliers, a supplementary screening process is employed to enhance the Monte Carlo approximation of the posterior probability density function. Finally, simulations of a target tracking example demonstrate the effectiveness and superiority of the proposed method.

Gaussian Mixture Filtering with Nonlinear Measurements Minimizing Forward Kullback-Leibler Divergence

A Gaussian mixture filter is proposed for the state estimation of dynamical systems with nonlinear measurements. The filter is derived by solving an assumed density filtering problem where Kullback-Leibler (KL) divergence from the assumed posterior, which is a Gaussian mixture, to the true posterior (which we call forward KL divergence) is minimized. The approximate solution to this problem gives an iterative measurement update by which the weights, means and covariances of the assumed posterior are optimized. The resulting Gaussian mixture filter is shown to be a generalization of the (damped) posterior linearization filter to Gaussian mixture posteriors. The performance of the proposed filter is illustrated and compared to alternatives on a challenging example of target tracking in a sensor network and on an example of tracking with a radar. The results show that the proposed filter can outperform Gaussian filters as well as the Gaussian sum filter and the Gaussian sum particle filter yielding results very close to a bootstrap particle filter when the number of components in the assumed posterior is sufficiently large.

Adaptive Kernel Kalman Filter

Sequential Bayesian filters in non-linear dynamic systems require the recursive estimation of the predictive and posterior distributions. This paper introduces a Bayesian filter called the adaptive kernel Kalman filter (AKKF). With this filter, the arbitrary predictive and posterior distributions of hidden states are approximated using the empirical kernel mean embeddings (KMEs) in reproducing kernel Hilbert spaces (RKHSs). In parallel with the KMEs, some particles, in the data space, are used to capture the properties of the dynamical system model. Specifically, particles are generated and updated in the data space, while the corresponding kernel weight mean vector and covariance matrix associated with the feature mappings of the particles are predicted and updated in the RKHSs based on the kernel Kalman rule (KKR). Simulation results are presented to confirm the improved performance of our approach with significantly reduced particle numbers, by comparing with the unscented Kalman filter (UKF), particle filter (PF) and Gaussian particle filter (GPF). For example, compared with the GPF, the proposed approach provides around 5% logarithmic mean square error (LMSE) tracking performance improvement in the bearing-only tracking (BOT) system when using 50 particles.

Prediction of fatigue crack propagation based on dynamic Bayesian network

To address the problem of low prediction accuracy in the current research on fatigue crack propagation prediction, a prediction method of fatigue crack propagation based on a dynamic Bayesian network is proposed in this paper. The Paris Law of crack propagation and the extended finite element method (XFEM) are combined to establish the state equation of crack propagation. The uncertain factors of crack propagation are analyzed, and the prediction model of fatigue crack propagation based on the dynamic Bayesian network is constructed. A Bayesian inference algorithm based on the combination of Gaussian particle filter and firefly algorithm is proposed. The fatigue experiment of the specimen with the pre-cracks is carried out to test the correlation between the fatigue load cycles and the crack propagation depth. The experimental results show that the crack propagation prediction method proposed in this paper can effectively improve the prediction accuracy of crack propagation depth.

H∞ filter-based dynamic joint carrier frequency offset and linear phase noise tracking for CO-OFDM systems.

In this paper, a robust, dynamic and joint carrier frequency offset (CFO) and linear phase noise (LPN) tracking algorithm is proposed by utilizing the H∞ filter for CO-OFDM systems. The dynamic tracking is implemented by Bayesian filtering which time-recursively updates the posterior state estimates based on the prior state information and calculated gain. To improve the robustness of the dynamic tracking process against the uncertainty of the noise terms, we adopt the H∞ filter, which designs a min-max optimization problem with a performance bound-defined constraint. The H∞ filter obtains the state estimates by limiting the worst-case estimation error, which guarantees its robustness to the system uncertain noise terms and external disturbances. After the joint estimation of CFO and LPN, we then propose a decision-feedback algorithm to achieve accurate signal detection. The accuracy and robustness of the proposed algorithm are verified in an 88.9 Gb/s 16-QAM CO-OFDM system, by comparing with the conventional extended Kalman filter (EKF) and Gaussian particle filter (GPF). Simulation results show that the MSEs of CFO and LPN by H∞ filter can reach the Cramér-Rao Lower Bounds (CRLBs) as well as the Bayesian CRLB (BCRLB), and possesses excellent noise and chromatic dispersion (CD) tolerance.

A Novel UHF-RFID Dual Antenna Signals Combined With Gaussian Process and Particle Filter for In-Pipe Robot Localization

Condition assessment of underground infrastructures such as pipe networks is crucial for aging cities around the globe. Recent development of robotic technologies facilitated application of them in condition assessment of pipe networks. However, there is still a gap for accurate localization technology in pipes due to complexity of the environment. In this letter, we propose a novel ultra-high frequency radio frequency identification (UHF-RFID) technology dual antenna system combined with Gaussian process and Particle filter algorithms to achieve millimeter level localization accuracy. The system is capable of achieving millimeter level accuracy over 50 m of length without an apparent estimation drift. The results were validated through experiments conducted using an extracted water pipe section.

Dynamic Joint Frequency Offset and Phase Noise Tracking by Number-Theoretic Net-Based Gaussian Particle Filter in Coherent Optical Systems

A number-theoretic net (NT-net)-based Gaussian particle filter (NT-GPF) is proposed for the joint estimation of frequency offset (FO) and linear phase noise (LPN) in a dynamic and real-time manner. Based on the concept of uniform design, the NT-net can uniformly generate particles on an ellipse for a given bivariate normal distribution. As a result, the NT-GPF can achieve accurate FO and LPN tracking with only a small number of particles, which greatly improves the estimation efficiency and noise tolerance compared with the conventional GPF. We also propose a recursive signal detection algorithm to further enhance the final system bit error rate (BER) performance. Simulations verify the accuracy, robustness and efficiency of the NT-GPF.

Clustering Methods for Particle Filters With Gaussian Mixture Models

New clustering methods are proposed to develop novel particle filters with Gaussian mixture models (PFGMM). In the PFGMM, the propagated samples are clustered to recover a Gaussian mixture model (GMM) using a clustering algorithm, which plays a fundamental role in the filter's performance. Two clustering methods are introduced that simultaneously minimize the covariance of each of the GMM components and maximize the likelihood function. Under the scenarios considered in this paper, it is shown through numerical simulation that the PFGMMs with the proposed clustering algorithms lead to better performance than the PFGMM employing the K-means or the expectation-maximization (EM) algorithms as well as the regularized particle filter (RPF) and the Gaussian sum particle filter (GSPF).

Computationally efficient application of Sequential Monte Carlo expectation maximization to confined single particle tracking.

Single Particle Tracking (SPT) plays a crucial role in biophysics through its ability to reveal dynamic mechanisms and physical properties of biological macromolecules moving inside living cells. Such molecules are often subject to confinement and important information can be revealed by understanding the mobility of the molecules and the size of the domain they are restricted to. In previous work, we introduced a method known as Sequential Monte Carlo-Expectation Maximization (SMC-EM) to simultaneously estimate particle trajectories and model parameters. In this paper, we describe three modifications to SMC-EM aimed at improving its computationally efficiency and demonstrate it through analysis of simulated SPT data of a particle in a three dimensional confined environment. The first two modifications use approximation methods to reduce the complexity of the original motion and measurement models without significant loss of accuracy. The third modification replaces the previous SMC methods with a Gaussian particle filter combined with a backward simulation particle smoother, trading off some level of generality for improved computational performance. In addition, we take advantage of the improved efficiency to investigate the effect of data length on performance in localization and parameter estimation.

A kind of fast Gaussian particle filter based on Artificial Fish School Algorithm

This paper proposes an improved Gaussian particle filter integratingthe Artificial Fish School Algorithm to optimise the measured values to improve the overall estimation accuracy of the system. Meanwhile, it also solves the problems of susceptibility to interference and insufficient estimation accuracy in nonlinear systems. Furthermore, since the calculation time of the fusion algorithm increases, in order to ensure the speed of state estimation, the linear transformation of standard particle swarm is used to replace the particle sampling link of Gaussian particle filter. Simulation results show that the calculation speed of a fast Gaussian Particle Filter based on the Artificial Fish School Algorithm is 21.7% faster than the Particle Filter based on the Artificial Fish School Algorithm. Compared with Particle Filter, Gaussian particle filter, and the Artificial Fish School Algorithm, the proposed algorithm has a higher accuracy.

A quaternion-based indirect Gaussian particle filter for nonlinear attitude estimation.

A recursively indirect quaternion estimator based on the Gaussian particle filter (GPF) is proposed for nonlinear attitude estimation. The key idea is to estimate an on-tangent-plane Gaussian distribution in the GPF scheme for interpreting the uncertainty of the unit quaternion manifold. The unit quaternion is provided with a global nonsingular attitude description in the prediction step, and the three-dimensional attitude error is estimated in the update step. Based on the framework of the GPF, the proposed filter does not need resampling and regularization compared with the PF. The performance of the proposed filter is verified theoretically and evaluated by experiments. The results show that the proposed filter has a faster convergence speed, lower complexity, and lower computational cost than the existing quaternion PF under a comparable accuracy.

Joint Estimation of Trajectory and Motion Model Parameters in Three-Dimensional Single Particle Tracking using the Double-Helix Point Spread Function

Single particle tracking (SPT) is a powerful tool for studying and analyzing dynamic mechanisms of biomolecules. Our approach to analyzing SPT data uses a generic Expectation Maximization (EM)-based framework for simultaneous localization refinement and parameter estimation. This approach has benefits in terms of estimation accuracy across a wide range of signal to noise levels. When observing a particle of interest moving in three-dimensions, the acquired data is typically a sequence of images of a 2-D slice of the point spread function (PSF) determined by the relative position of the focal plane and the particle. Unlike the standard PSF, which has only one bright spot in the image plane, the Double-Helix point spread function (DH-PSF) forms two bright spots. As the particle moves along the optical axis, these spots rotate, thereby encoding the axial position of the particle. In this work, we extend our EM-based scheme to handle the DH-PSF. Our method begins with the segmented images, using the camera data directly to jointly estimate particle locations and motion model parameters. We consider two representative methods in our framework: one uses a direct sequential importance resampling (SIR) based particle filter (PF) and particle smoother (PS), the other uses the alternative Gaussian particle filter (aGPF) and the backward-simulation particle smoother (BSPS). The aGPF/BSPS is less general but has significantly less computational load when compared to the PF/PS. Using extensive simulation studies, we demonstrate that both methods produce reliable estimates of both particle position and model parameters. In future work, we plan to consider the additional influence of readout noise determined by specific camera sensors.

Improved Particle Filter Using Clustering Similarity of the State Trajectory with Application to Nonlinear Estimation: Theory, Modeling, and Applications

A clustering similarity particle filter based on state trajectory consistency is presented for the mathematical modeling, performance estimation, and smart sensing of nonlinear systems. Starting from an information fusion model based on the consistency principle of the spatial state trajectory, the predicted observation information of the current particle filter (original trajectory) and future multistage Gaussian particle filter (modified trajectory) are selected as the state trajectories of the sampling particles. Clustering similarity methods are used to measure the state trajectories of the sampling particles and the actual system (reference trajectory). The importance weight of a first‐order Markov model is updated with the measurement results. By integrating the targeted compensation scheme of the latest measurement information into the sequential importance sampling process, the adverse effects of the particle degradation phenomenon are effectively reduced. The convergence theorems of the improved particle filter are proposed and proved. The improved filter is applied to practical cases of nonlinear process estimation, economic statistical prediction, and battery health assessment, and the simulation results show that the improved particle filter is superior to traditional filters in estimation accuracy, efficiency, and robustness.

A Digital Twin approach based on nonparametric Bayesian network for complex system health monitoring

This paper proposes a Digital Twin approach for health monitoring. In this approach, a Digital Twin model based on nonparametric Bayesian network is constructed to denote the dynamic degradation process of health state and the propagation of epistemic uncertainty. Then, a real-time model updating strategy based on improved Gaussian particle filter (GPF) and Dirichlet process mixture model (DPMM) is presented to enhance the model adaptability. On one hand, for those parameters in the nonparametric Bayesian network with prior models, the improved GPF is used to update them in real time. On the other hand, for parameters lacking a prior model, DPMM is proposed to learn hidden variables, which adaptively update the model structure and greatly reduce uncertainty. Experiments on the electro-optical system are conducted to validate the feasibility of the Digital Twin approach and verify the effectiveness of the nonparametric Bayesian network. The results of comparative experiments prove that the Digital Twin approach based on nonparametric Bayesian Network has a good model self-learning ability, which improves the accuracy of health monitoring.

Remaining useful life prediction for auxiliary power unit based on particle filter

Auxiliary power unit is one of the indispensable systems for civil aviation aircraft but the traditional planned maintenance cannot meet the actual needs of airlines. In this work, the key performance parameters of the auxiliary power unit are selected by using recursive feature elimination method. With the selected parameters, the remaining useful flight cycle of the auxiliary power unit is predicted by applying particle filter techniques. Some improved algorithms such as Gaussian particle filter and auxiliary particle filter are also compared. The experimental results demonstrate that the particle filter-based method has high prediction accuracy and engineering application value.

Pipeline Gaussian Particle Filter and Hardware Design for Attitude Estimation with UAV

This paper based on the Gaussian particle filter (GPF) deals with the attitude estimation of UAV. GPF algorithm has better estimation accuracy than the general nonlinear non-Gaussian state estimation and is usually used to improve the system’s real-time performance whose noise is specific such as Gaussian noise during the mini UAV positioning and navigation. The attitude estimation algorithm is implemented on FPGA to verify the effectiveness of the Gaussian particle filter. Simulation results have illustrated that the GPF algorithm is effective and has better real-time performance than that of the particle filter.

Parameter estimation based-FDI method enhancement with mixed particle filter

Mobile robots have a crucial role in many domains. Currently, service robots can be found in our homes, transportation robots in warehouses, logistic robots in factories and even on Mars, where rovers are exploring its surface. These intelligent machines are becoming increasingly autonomous, as they have to achieve longer and longer missions. Thus, to maintain autonomy and to guarantee material security, Fault Detection and Isolation (FDI) is a mandatory task. A fault causes a mission to fail or, worse, it may damage materials and operators if the robot goes out of control. In this paper, we propose to address the FDI process. First, we present two modified versions of two known methods based on parameter estimation. Then, a mixed version of Particle Filter (PF) which combines a standard PF and a Gaussian PF to generate a better performing FDI method is proposed. These methods are studied in the case of a wheel block fault. Simulation and real robot experimentation results prove the added value of our proposed FDI method over the other two approaches.

Structural correlation filters combined with a Gaussian particle filter for hierarchical visual tracking

Visual tracking is a key problem for many computer vision applications such as human-computer interaction, intelligent medical diagnosis, navigation and traffic control management. Most of the existing tracking methods are mainly based on correlation filters. However, boundary effect, scale estimation and template updating have not been fully resolved. Herein, this paper presents a new hierarchical tracking method combining structural correlation filters with a Gaussian Particle Filter (GPF), named KCF-GPF. Weak KCF classifiers are constructed via a Lukas-Kanade (LK) method and the preliminary target location is presented as a weighted sum of these classifiers. Specially, a facile weight strategy is implemented to estimate the reliability of each weak classifier. On the basis of the preliminary target location, the GPF using features from a Convolutional Neural Network (CNN) is employed to predict the location and scale of a target. Extensive experiments with the OTB-2013 and the OTB-2015 databases demonstrate that the proposed algorithm performs favourably against state-of-the-art trackers.

Diffusion Collaborative Feedback Particle Filter

We herein propose a distributed collaborative feedback particle filter (D-FPF) based on the diffusion strategy for nonlinear filtering problems. Each particle at each sensor is updated via a collaborative feedback structure incorporating the collaborative feedback gain and aggregate innovation. The localized intermediate state estimates are further shared among the neighbors. The importance sampling, resampling, or variance calculation, which are mandatory in the traditional distributed particle filters, are not requisite. Illustrative target tracking simulations validate that the proposed D-FPF could markedly outperform the distributed Gaussian particle filter in terms of both tracking and particle variance performance. The D-FPF could obtain favourable tracking performance even with an extremely small amount of particles.

Underwater Target Tracking Using Forward-Looking Sonar for Autonomous Underwater Vehicles.

In the scenario where autonomous underwater vehicles (AUVs) carry out tasks, it is necessary to reliably estimate underwater-moving-target positioning. While cameras often give low-precision visibility in a limited field of view, the forward-looking sonar is still an attractive method for underwater sensing, which is especially effective for long-range tracking. This paper describes an online processing framework based on forward-looking-sonar (FLS) images, and presents a novel tracking approach based on a Gaussian particle filter (GPF) to resolve persistent multiple-target tracking in cluttered environments. First, the character of acoustic-vision images is considered, and methods of median filtering and region-growing segmentation were modified to improve image-processing results. Second, a generalized regression neural network was adopted to evaluate multiple features of target regions, and a representation of feature subsets was created to improve tracking performance. Thus, an adaptive fusion strategy is introduced to integrate feature cues into the observation model, and the complete procedure of underwater target tracking based on GPF is displayed. Results obtained on a real acoustic-vision AUV platform during sea trials are shown and discussed. These showed that the proposed method is feasible and effective in tracking targets in complex underwater environments.