Conventional Particle Filter Research Articles

A Novel Coupled State/Load/Parameter Identification Method Based on the Improved Particle Filter Algorithm

There have been increasing research studies focusing on the identification of structural load with uncertain model in recent years. This paper presents a novel approach based on the improved Particle Filter (PF) algorithm for the nonlinear structural system. The main strategy of the approach is the fusion of the weighted least-square algorithm and the conventional PF algorithm. The weighted least-square algorithm is derived for the estimation of the unknown loads, and the PF algorithm is used for the identification of the augmented states which includes the structural displacement, velocity and unknown parameters. Additionally, the parallel algorithm is adopted for the improvement of computing speed, and a resampling step is also used for alleviating the degeneracy of the particles to improve the accuracy. A numerical example modelling as a four-story hysteretic shear-beam building is studied to validate the capability of the presented approach.

Enhancing state and parameter estimations of a dynamic crop model by a recombination particle filter

Crop simulation models are essential tools in supporting sustainable agricultural management. However, due to uncertainty in model parameters, the model predictions may not be sufficiently accurate. Data assimilation (DA) is a common approach to improve dynamic crop modeling by combining it with observation data. Among DA approaches, particle filter (PF) is a popular choice. Since conventional PF (CPF) may suffer from sample impoverishment problems, various filter modifications have been proposed in the literature, including the application of genetic operators (arithmetic cross-over and mutations). In this study, a novel PF approach inspired by the gene’s recombination process has been developed. In this new filter, named “recombination” PF (RPF), particle diversity is increased via information exchange between surviving particles and intermediate particles which are located close to existing particles. In turn, increased particle diversity reduces the chances of sample impoverishment and thus improves filter performance. The proposed method was tested on two synthetic study cases using the open-source AquaCrop model (v5.0a) and assuming weekly observations of canopy cover and soil water content. When CPF was implemented, the overall average normalized root mean square error (NRMSE), combining state and parameter estimations, and yield forecasts, all performed throughout the season, ranged from 4.0 to 5.1 % for ensemble sizes ranging from 150 to 500 particles. When RPF was implemented with a similar number of particles, the overall average NRMSE decreased to 3.6–3.7 %, corresponding to a 7–26 % improvement. Furthermore, higher stability of the results was observed, and the final parameter estimations improved in all the ensemble sizes investigated by approximately 40 %, which would be very beneficial for predicting crop growth in the next season.

Marginalized particle filtering for online parameter estimation of PEMFC applied to hydrogen UAVs

Proton exchange membrane fuel cells (PEMFCs) are an emerging candidate for clean power generation, with applications in smart grids, vehicles, and unmanned aerial vehicles. Accurate modeling of the power characteristics of PEMFC is required for system management purposes, where an electro-chemical model with unknown parameters is often adopted. Estimation of the unknown parameters is challenging as operating condition shifts and system degradation will lead to variation in PEMFC characteristics, particularly in the presence of system nonlinearities and noise. In this paper, a novel online parameter estimation approach for PEMFC is proposed based on the marginalized particle filtering approach. By introducing a filter derivation based on Bayesian inference and estimating the linear and nonlinear parameters separately, the marginalized approach has reduced computation cost compared with conventional particle filters. Estimation accuracy of the proposed approach is validated by experimental and simulation results, where superior accuracy compared with extended Kalman filter is obtained. Furthermore, a self-designed hydrogen quadrotor was flight-tested and energy management studies were conducted to assess the performance of the proposed estimator in hydrogen unmanned aerial vehicle applications using real flight data.

Convergence of Regularized Particle Filters for Stochastic Reaction Networks

Filtering for stochastic reaction networks (SRNs) is an important problem in systems/synthetic biology aiming to estimate the state of unobserved chemical species. A good solution to it can provide scientists valuable information about the hidden dynamic state and enable optimal feedback control. Usually, the model parameters need to be inferred simultaneously with state variables, and a conventional particle filter can fail to solve this problem accurately due to sample degeneracy. In this case, the regularized particle filter (RPF) is preferred to the conventional ones, as the RPF can mitigate sample degeneracy by perturbing particles with artificial noise. However, the artificial noise introduces an additional bias to the estimate, and, thus, it is questionable whether the RPF can provide reliable results for SRNs. In this paper, we aim to identify conditions under which the RPF converges to the exact filter in the filtering problem determined by a bimolecular network. First, we establish computationally efficient RPFs for SRNs on different scales using different dynamical models, including the continuous-time Markov process, tau-leaping model, and piecewise deterministic process. Then, by parameter sensitivity analyses, we show that the established RPFs converge to the exact filters if all reactions leading to an increase of the molecular population have linearly growing propensities and some other mild conditions are satisfied simultaneously. This ensures the performance of the RPF for a large class of SRNs, and several numerical examples are presented to illustrate our results.

Accelerated Particle Filter With GPU for Real-Time Ballistic Target Tracking

This study addresses the problem of real-time tracking of high-speed ballistic targets. Particle filters can be used to overcome the nonlinearity of motion and measurement models in ballistic targets. However, applying particle filters (PFs) to real-time systems is challenging since they generally require a significant computation time. So, most of the existing methods of accelerating PF using a graphics processing unit (GPU) for target tracking applications have accelerated computation weight function and resampling part. However, the computational time per part varies from application to application, and in this work, we confirm that it takes a lot of computational time in the model propagation part and propose accelerated PF by parallelizing the corresponding logic. The real-time performance of the proposed method was tested and analyzed using an embedded system. And compared to conventional PF on the central processing unit (CPU), the proposed method shows that the proposed method significantly reduces computational time by at least 10 times, improving real-time performance.

A Tightly Coupled Integration Approach for Cooperative Positioning Enhancement in DSRC Vehicular Networks

Intelligent transportation system significantly relies on accurate positioning information of land vehicles for both safety and non-safety related applications, such as hard-braking ahead warning and red-light violation warning. However, existing Global Navigation Satellite System (GNSS) based solutions suffer from positioning performance degradation in challenging environments, such as urban canyons and tunnels. In this paper, we focus on the positioning performance enhancement of land vehicles via cooperative positioning under a partial GNSS environment in a Vehicular Ad-hoc NETwork (VANET). The availability of Time-of-Flight (ToF) based inter-vehicle or vehicle-to-infrastructure ranges is verified via 5.9 GHz Dedicated Short-Range Communication (DSRC) vehicle-to-everything communication with RTS/CTS unicast mechanism. An inertial navigation sensor aided, tightly coupled integration approach for land vehicle cooperative positioning using DSRC ToF ranges and carrier frequency offset range-rates is proposed, where a digital map is used to constrain the position estimates. If available, the GNSS pseudorange and Doppler shift under partial GNSS environment can also be incorporated. A Rao–Blackwellized particle filter is utilized to estimate the unknown variables allowing for reduced computational complexity in comparison with the conventional particle filter. The posterior Cramer–Rao lower bound is also derived to give a theoretical performance guideline. Both simulation and experimental results show the validity of our proposed approach.

Vehicle Behavior-Cognition-Based Particle-Filter-Enabled mmWave Beam Tracking for Connected Automated Vehicles

Considering the low-latency and high data rate requirements for automated vehicles (AVs), the millimeter-wave (mmWave) technology can support tens of Gb/s raw sensor information sharing for connected AVs (CAVs). However, the challenging problem is how to achieve fast and robust mmWave beam tracking for CAVs. To solve this problem, we propose a novel vehicle behavior cognition-based particle-filter (VBC-PF)-enabled beam tracking algorithm. The beam-space subset is predicted based on the beam change rate and the position-yaw information from the vehicle behavior cognition in CAVs, which effectively reduces the beam search overhead. In the proposed VBC-PF algorithm, the particle weight updating schemes are designed based on the optimal vehicle behavior cognition to avoid the particle divergence and the error accumulation. Simulation and hardware testbed results verify that the accuracy and efficiency of the proposed VBC-PF algorithm outperform the conventional particle filter (PF) and the extended Kalman filter (EKF) algorithms.

Improved weighting in particle filters applied to precise state estimation in GNSS.

In the last decades, the increasing complexity of the fusion of proprioceptive and exteroceptive sensors with Global Navigation Satellite System (GNSS) has motivated the exploration of Artificial Intelligence related strategies for the implementation of the navigation filters. In order to meet the strict requirements of accuracy and precision for Intelligent Transportation Systems (ITS) and Robotics, Bayesian inference algorithms are at the basis of current Positioning, Navigation, and Timing (PNT). Some scientific and technical contributions resort to Sequential Importance Resampling (SIR) Particle Filters (PF) to overcome the theoretical weaknesses of the more popular and efficient Kalman Filters (KFs) when the application relies on non-linear measurements models and non-Gaussian measurements errors. However, due to its higher computational burden, SIR PF is generally discarded. This paper presents a methodology named Multiple Weighting (MW) that reduces the computational burden of PF by considering the mutual information provided by the input measurements about the unknown state. An assessment of the proposed scheme is shown through an application to standalone GNSS estimation as a baseline of more complex multi-sensors, integrated solutions. By relying on the a-priori knowledge of the relationship between states and measurements, a change in the conventional PF routine allows performing a more efficient sampling of the posterior distribution. Results show that the proposed strategy can achieve any desired accuracy with a considerable reduction in the number of particles. Given a fixed and reasonable available computational effort, the proposed scheme allows for an accuracy improvement of the state estimate in the range of 20–40%.

A novel distribution system state estimator based on robust cubature particle filter used for non‐gaussian noise and bad data scenarios

State estimation is the core function of distribution management system, and its estimation accuracy directly affects the operation of other advanced application functions of distribution management system. However, the access of a large number of distributed generation brings non-Gaussian noise and bad data problems, which affect the accuracy of state estimation. Therefore, based on the conventional cubature particle filter (CPF), two new state estimation operators, robust cubature filter 1 (RCPF1) and robust cubature filter 2 (RCPF2), are proposed by introducing the Huber's M-estimation theory into the CPF algorithm and integrating a time-varying, multi-dimensional scale factor with the CPF, respectively. The simulation results based on IEEE33 bus system showed that: (1) RCPF has better estimation accuracy and robustness than conventional cubature particle filter and cubature Kalman filter; (2) RCPF2 has better estimation performance than RCPF1 in the case of non-Gaussian noise and bad data.

Design of power lithium battery management system based on digital twin

The accurate estimation of the State of Charge (SoC) of batteries has always been the focus of Battery Management System (BMS). However, the current BMS has problems such as difficult data sharing, weak data processing capability and limited data storage capacity, so the simplest ampere-time integration method is used to estimate the SoC, and the estimation results are highly biased. In this paper, an innovative digital twin-driven battery system framework is proposed and successfully developed. A joint HIF-PF online algorithm for estimating SoC under the experimental condition Beijing Bus Dynamic Stress Test (BBDST) is also proposed, which is comparable to the conventional Extended kalman filter (EKF), HIF and Particle Filter (PF). The results demonstrate the superiority of the algorithm. Then, we applied the algorithm to estimate SoC. In addition, the system implements functions such as real-time voltage and current monitoring and visualization.

Particle Filter Reinforcement via Context-Sensing for Smartphone-Based Pedestrian Dead Reckoning

Pedestrian dead reckoning based on particle filter is commonly used for enabling seamless smartphone-based indoor positioning. However, compass directions indoor are heavily distorted due to the presence of ferromagnetic materials. Conventional particle filters convert the raw compass direction to a distribution adding a constant variance noise and leveraging a particle swarm to simulate the distribution. Finally, the selection of eligible directions is performed applying external constraints mainly imposed from the indoor map. However, the choice of a constant parameter decreases the positioning performances because the variance of nearby context, including topography, ferromagnetic materials, and particle distribution, is not represented. Therefore, we propose the particle filter reinforcement able to adaptively learn and adjust the variance of the direction observing the context in real-time. Experiments in real-world scenarios show that the proposed method improves the positioning accuracy by more than 20% at the 80% probability compared with state-of-the-art methods.

Entropy Based Student's t-Process Dynamical Model.

Volatility, which represents the magnitude of fluctuating asset prices or returns, is used in the problems of finance to design optimal asset allocations and to calculate the price of derivatives. Since volatility is unobservable, it is identified and estimated by latent variable models known as volatility fluctuation models. Almost all conventional volatility fluctuation models are linear time-series models and thus are difficult to capture nonlinear and/or non-Gaussian properties of volatility dynamics. In this study, we propose an entropy based Student’s t-process Dynamical model (ETPDM) as a volatility fluctuation model combined with both nonlinear dynamics and non-Gaussian noise. The ETPDM estimates its latent variables and intrinsic parameters by a robust particle filtering based on a generalized H-theorem for a relative entropy. To test the performance of the ETPDM, we implement numerical experiments for financial time-series and confirm the robustness for a small number of particles by comparing with the conventional particle filtering.

Remaining useful life prediction of lithium-ion battery based on auto-regression and particle filter

PurposeWith the rapid development and stable operated application of lithium-ion batteries used in uninterruptible power supply (UPS), the prediction of remaining useful life (RUL) for lithium-ion battery played an important role. More and more researchers paid more attentions on the reliability and safety for lithium-ion batteries based on prediction of RUL. The purpose of this paper is to predict the life of lithium-ion battery based on auto regression and particle filter method.Design/methodology/approachIn this paper, a simple and effective RUL prediction method based on the combination method of auto-regression (AR) time-series model and particle filter (PF) was proposed for lithium-ion battery. The proposed method deformed the double-exponential empirical degradation model and reduced the number of parameters for such model to improve the efficiency of training. By using the PF algorithm to track the process of lithium-ion battery capacity decline and modified observations of the state space equations, the proposed PF + AR model fully considered the declined process of batteries to meet more accurate prediction of RUL.FindingsExperiments on CALCE dataset have fully compared the conventional PF algorithm and the AR + PF algorithm both on original exponential empirical degradation model and the deformed double-exponential one. Experimental results have shown that the proposed PF + AR method improved the prediction accuracy, decreases the error rate and reduces the uncertainty ranges of RUL, which was more suitable for the deformed double-exponential empirical degradation model.Originality/valueIn the running of UPS device based on lithium-ion battery, the proposed AR + PF combination algorithm will quickly, accurately and robustly predict the RUL of lithium-ion batteries, which had a strong application value in the stable operation of laboratory and other application scenarios.

Robust particle filtering with enhanced outlier resilience and real-time disturbance compensation

This paper is concerned with the state estimation problem for nonlinear/non-Gaussian systems suffered from both time-varying disturbances (TVD) and measurement outliers. Conventional particle filtering (PF) approach can be used to track the non-Gaussian probability density functions, but its sampling efficiency is degraded in the presence TVD. To address this problem, we propose a disturbance observer based PF (DOBPF) method where the knowledge on the dynamics of TVD are fully exploited and real-time disturbance compensation is achieved. Furthermore, to enhance the resilience of our method against outliers, we adopt the skew-t distribution to characterize both skewness and heavy-tailedness of the measurement noise. On this basis, the variational Bayes approach is incorporated into the DOBPF under the marginalization PF framework to infer the noise statistics. Compared with conventional PF approaches, the proposed outlier-resilient DOBPF method exhibits improved resilience against measurement outliers and increased sampling efficiency in the presence of TVD. Simulation and experimental results confirm the effectiveness of the proposed algorithm.

Robust Particle Filtering With State Transition Uncertainties: A Student’s t Disturbance Observer-Based Approach

This article is concerned with robust particle filtering (PF) for nonlinear systems with state transition uncertainties. The uncertainty under consideration is characterized in part by an additive uncertainty term (AUT) in the state transition equation and in part by the parametric uncertainty in the probability distribution of process noises. To maintain the sampling efficiency of the PF algorithm in the presence of AUT, the disturbance observer (DO)-based PF approach is adopted, which consists of the DO for real-time AUT reconstruction and a modified PF with AUT-compensated sampling. Instead of using the traditional Kalman filter-based DO, a novel student’s $t$ DO is proposed to handle uncertain noise parameters and achieve robust disturbance estimation. The enhanced robustness of the proposed method, named student’s $t$ DO-based robust PF , has been demonstrated via numerical example. Furthermore, experimental tests on the skylight polarization-aided attitude and heading reference system show that the standard deviation of our method decreases by over 40% as compared with the conventional PF.

Enhancing Athlete Tracking Using Data Fusion in Wearable Technologies

In recent years, the use of wearable devices to track athlete performance has increased sharply. Using onboard sensors, wearable devices can provide critical information about athlete’s performance and well-being. Athlete tracking is an important functionality of wearable devices that rely on positioning data, which also influences the accuracy of numerous other attributes. However, accurate athlete tracking is a challenging task due to the nonlinear nature of the problem and the presence of non-Gaussian noise. In the literature, researchers have used the particle filter (PF) to improve athlete tracking accuracy. While the PF algorithm, in general, works well, they perform poorly when athletes take the sharp change of direction (COD), a common and important movement in the sport that is not currently captured. In this article, we introduce a sensor fusion technique to address this challenge. Our proposed solution combines the positioning data and inertial sensor data to accurately track an athlete’s movements. We then analyze the accuracy using data collected from a commercially used athlete tracking wearable device. We have found that the obtained results are very promising, and the proposed solution performs up to five times better than a conventional PF sensor fusion algorithm for positioning.

State and parameter estimation of the AquaCrop model for winter wheat using sensitivity informed particle filter

Crop models play a paramount role in providing quantitative information on crop growth and field management. However, its prediction performance degrades significantly in the presence of unknown, uncertain parameters and noisy measurements. Consequently, simultaneous state and parameter estimation (SSPE) for crop model is required to maximize its potentials. This work aims to develop an integrated dynamic SSPE framework for the AquaCrop model by leveraging constrained particle filter, crop sensitivity analysis and UAV remote sensing. Both Monte Carlo simulation and one winter wheat experimental case study are performed to validate the proposed framework. It is shown that: (i) the proposed framework with state/parameter bound and parameter sensitivity information outperforms conventional particle filter and constrained particle filter in both state and parameter estimation in Monte Carlo simulations; (ii) in real-world experiment, the proposed approach achieves the smallest root mean squared error for canopy cover estimation among the three algorithms by using day forward-chaining validation method.

A power transfer model-based method for lithium-ion battery discharge time prediction of electric rotatory-wing UAV

This paper develops a power transfer model-based method to estimate real-time state of energy (SOE) and predict end of discharge (EOD) time of rotatory-wing UAVs lithium batteries under dynamic operational conditions. A discrete-time state-space model of battery is first established to model the process of battery power consumption and establish a mapping of battery unobservable state of energy (SOE) to measurable parameters such as voltage and current. Then a power consumption model of UAV is established based on predetermined flight mission of UAV using aerodynamics and momentum theory, which estimates power consumption of UAV under different operational conditions. Its calculation results can be directly used in battery state-space model as its input, while its model parameters are simultaneously updated by online measurements of consumed power. Finally, a Particle Filter (PF) approach with Adam optimization algorithm is developed to estimate SOE and predict EOD time on-line, and better prediction results compared to conventional PF are achieved. Real experiments on UAV verify the effectiveness of the proposed method.

Visual odometry particle filter for improving accuracy of visual object trackers

This Letter proposes a novel state estimator called the visual odometry particle filter (VOPF) for improving accuracy of visual object trackers. For the VOPF, a novel visual odometry motion model that is better than the conventional constant velocity motion model is proposed. In addition, a new particle injection method to prevent sample impoverishment and the incorrect measurement detection method are proposed. Visual object tracking experiments using 30 visual object trackers demonstrate that the VOPF improves accuracy of the trackers and outperforms the conventional particle and Kalman filters using the CV motion model.

Particle filter combined with data reconciliation for nonlinear state estimation with unknown initial conditions in nonlinear dynamic process systems

State estimation is very crucial for process control and optimization in dynamic processes. The particle filter (PF) is a novel and suitable technique for state estimation of nonlinear dynamic process systems. Conventional PFs for nonlinear dynamic process systems rely on the known initial conditions for state variables, such as the known probability density function (PDF) of initial states or the known values of initial states, but the initial conditions of a nonlinear dynamical system are usually unknown in actual industrial processes. In this paper, a novel methodology, PF combined with data reconciliation, is proposed and applied to nonlinear dynamic process systems for state estimation with unknown initial conditions. The measurement test criterion and data reconciliation with sequentially increasing data information are proposed to derive reliable initial values of the state variables under sufficient information of measurements. The interactive information between PF and data reconciliation problems can improve the initial values iteratively. Finally, accurate results of state estimation can be achieved. The effectiveness of the methodology is demonstrated through two nonlinear dynamic systems.