Standard Particle Filter Research Articles

Application of Gray Wolf Particle Filter Algorithm Based on Golden Section in Wireless Sensor Network Mobile Target Tracking

In order to address the issue of low tracking accuracy caused by particle depletion in the particle filter, a mobile target tracking algorithm tailored for wireless sensor networks (WSNs) is presented. This algorithm, based on the golden-section gray wolf particle filter (PF), represents a novel approach to target tracking. The algorithm’s originality lies in its ability to guide the particle swarm toward regions of higher weights, thereby striking a balance between global and local exploration capabilities. This not only alleviates issues related to sample depletion and local extrema but also enhances the diversity of the particle swarm, significantly improving tracking performance. To assess the effectiveness of the proposed algorithm, a series of simulation experiments were conducted, comparing it with the extended Kalman filter (EKF) and the standard PF algorithm. The experiments employed a constant velocity circular motion model (CM) for filtering and tracking. The root mean square error metric demonstrated a significant reduction in error of 57% and 37% in comparison to the extended Kalman filter (EKF) and the particle filter (PF), respectively. This serves to illustrate the superiority of our method in enhancing tracking accuracy.

A Secondary Particle Filter Photometric Data Inversion Method of Space Object Characteristics

A secondary particle filter (SPF) inversion method for geostationary space object characteristics based on ground photometric data is presented. The method combines the estimation results of the standard particle filter (PF) algorithm and the resampling algorithm of the particle generation process. SPF first generates N particles according to the standard PF process, and performs the standard PF without resampling. Particle weight is an important indicator to determine the closeness of particles to the real state. With the progress of PF, the weight of particles closer to the real state will gradually increase. SPF takes the particle weight value as an important basis to judge the closeness of particles to the real state. By setting a threshold, the particles closest to the real state are screened out and roughened. The SPF method in this paper uses a particle filter twice and it is a new particle filter method. The first particle filter identifies particles near the real state. Before the second particle filter, it is equivalent to the actual state distribution of the system is known, so that the distribution of initial particles can be set more efficiently and effectively, and the number of particles close to the real state of the system can be increased. Experiment results show that the estimation error and the RMSE of the inversion error of SPF are less than PF, which not only shows that the inversion result based on SPF is better than the inversion result based on PF, but also proves the effectiveness of the inversion method based on SPF.

SOC estimation of retired lithium-ion batteries for electric vehicle with improved particle filter by H-infinity filter

The echelon utilization of retired lithium-ion battery with remaining capacity of 80%, is considered as one of the most promising ways to reduce battery cost by extending their service life. The accurate state of charge (SOC) estimation for retired lithium-ion batteries is of great significance for less-stressful demanding applications. The H-infinity filter (HIF) is widely used to identify the battery model parameters and correspondingly to estimate the SOC online assisted with the Thevenin model. But the estimation accuracy cannot be ensured due to the overly simple algorithm structure. In this paper, H-infinity particle filter (HIPF) is proposed to further improve the SOC estimation accuracy. It is a particle filter (PF) improved by HIF and can suppress the particle depletion during the execution of the standard particle filter. HIPF estimated the SOC after the weights of particles were compromised. The joint estimation of model parameters by HIF and the SOC by HIPF was simulated to verify the model accuracy. In the experiment, the retired lithium–iron phosphate battery in BAIC EV150 vehicle was tested under FUDS cycle and DST cycle. The verification result shows that the mean error of the estimated SOC by HIPF is 0.63% in FUDS cycle and 0.59% in DST cycle. And in FUDS cycle and DST cycle, respectively, the proposed method’s SOC estimation accuracy was increased by 65% and 63% compared with when particle weights were not compromised.

Adaptive Particle Filter With Randomized Quasi-Monte Carlo Sampling for Unbalanced Distribution System State Estimation

Particle filter (PF) is an effective state estimation method for nonlinear unbalanced distribution systems with non-Gaussian noises. However, the computational inefficiency limits its real-time application in large-scale distribution systems. This paper proposes an adaptive PF (APF) method by using randomized quasi-Monte Carlo (RQMC) sampling to enhance computational efficiency. Firstly, an RQMC sampling method is introduced to enable uniform sampling based on the low discrepancy Sobol’ sequence. This even sampling accelerates the convergence rate of numerical integrations. Secondly, the standard PF is extended to be an RQMC-PF estimator by using the RQMC sampling instead of the MC sampling. Benefiting from the higher convergence rate, fewer particles are required to obtain precise state estimates, thus notably improving computation efficiency. Thirdly, to further make a trade-off between estimation accuracy and computational efficiency, the number of particles used in the RQMC-PF is adaptively determined with the root mean square of the estimated state covariance, yielding an APF. Test results on unbalanced distribution systems with different scales demonstrate that the proposed method can efficiently provide accurate estimates as well as achieve good scalability.

SOC estimation based on the gas‐liquid dynamics model using particle filter algorithm

Lithium-ion battery state of charge (SOC) estimation is the basis for other state estimations in electric vehicle (EV) battery management systems. Accurate SOC estimation can prevent overcharge and discharge of the battery, improve discharge efficiency and prolong cycle life. A high-precision SOC estimation method based on the gas-liquid dynamics (GLD) model is presented. The standard particle filter (PF) and the unscented particle filter (UPF) algorithm are successively used for optimizing and improving the chattering problem of the original GLD model. The results show that the two kinds of PF algorithms can effectively solve the chattering problem of the GLD model and improve the estimation accuracy. Among them, UPF has higher accuracy and the maximum estimation error is less than 2%. The PF method for estimating SOC introduced in this paper has the characteristics of high precision and large amount of calculation. Due to the above characteristics, this method can be used as a cloud SOC calculation method to periodically correct the local SOC of the vehicle.

Prediction of fatigue crack propagation in metals based on IBAS-PF

Owing to particle leanness, the standard Particle Filter (PF) algorithm is prone to the problem of reduced prediction accuracy when predicting fatigue crack propagation. An improved particle filter algorithm based on the optimization algorithm of beetle antenna search (IBAS-PF) for fatigue crack propagation in metals is proposed in this paper. The discrete Paris formula was used to establish the state equation of fatigue crack propagation, in which the uncertainty of material and crack propagation process were considered. Meanwhile, the characteristics of Lamb wave signals under different crack lengths were extracted to establish the observation equation. The sampling process of the PF algorithm was optimized based on the beetle antennae search algorithm to improve the particle diversity and the prediction accuracy. Compared with the standard PF algorithm, the improved BASO-PF algorithm has higher accuracy for metal fatigue crack propagation, as well as better state estimation ability.

A Hybrid Data-Driven Method for State-of-Charge Estimation of Lithium-Ion Batteries

As a portable energy storage system, lithium-ion batteries (LIBs) are widely used in wireless sensor networks, electric vehicles and other fields. To ensure the continuity of power supply, it is necessary to monitor the state of charge (SOC) of LIBs. However, due to the nonlinearity of battery operation, accurate SOC estimation has become a challenging task. In this paper, a SOC estimation method based on long-term short-term memory (LSTM) network and improved particle filter (IPF) is proposed, which maps the easily observed voltage, current and temperature to the target SOC. Firstly, through a layer of the LSTM network, the timing characteristics of the data are fully utilized to obtain the SOC variation trend of LIBs. Then, the noise variance adaptive algorithm and particle distribution optimization algorithm are introduced to improve the standard particle filter (PF). On this basis, the estimation results of the LSTM network are optimized by IPF. In addition, the performance of the proposed LSTM-IPF method is compared with other methods. The results show that the estimation performance of the proposed model is excellent, and the root mean squared error (RMSE) and maximum error (MAX) are controlled below 1% and 2% respectively, which meets the requirements of SOC estimation and verifies the effectiveness of the proposed method.

Particle filter underwater terrain-aided navigation based on gradient fitting

Inertial navigation systems (INSs) are widely used for autonomous underwater vehicle navigation, with excellent short-term precision. However, the positioning error of an INS accumulates with time. It is imperative to adopt other approaches to mitigate drift errors, especially for long-term sailing tasks. To that end, underwater terrain-based navigation (TBN) is effective in bounding the drift errors. In particular, the particle filtering (PF) method is extensively employed in TBN to tackle the highly nonlinear measurement equation. In our previous work, the statistical properties of the digital terrain model gradient were exploited and we proposed the use of three probability density functions to characterize the normalized data, i.e. Gaussian, gamma and Weibull distributions. In this paper, the likelihood was modified according to the gradient fitting results, i.e. an optimal distribution selection. Moreover, to prevent the measurement data with large gradients from generating particles with lower weights, a pre-screen procedure was proposed to stabilize particle filter sampling. As shown and demonstrated in simulations, our proposed improved PF method outperforms the comparative ones in terms of root mean square error and standard deviation, as well as accuracy, especially for long-term sailing tasks. In terms of computational cost, a smaller number of measurement data are employed and the proposed method is faster than the standard PF method.

Index similarity assisted particle filter for early failure time prediction with applications to turbofan engines and compressors

The particle filter (PF) has been widely studied in the prognostics’ field due to its ability to deal with nonlinear and non-stationary systems. However, there is no update of the model parameters during the prediction, preventing PF to work in its traditional way to generate accurate long-term predictions. In order to solve this problem, we put forward an improved PF that is based on a novel health index (HI) similarity matching method. This method is employed to search for similar HIs in the training library and construct an optimal “similar HI” for the system under study. Finally, the obtained HI is consistently fed into the PF to deliver precise state-of-health (SoH) estimates. The effectiveness of the proposed PF was validated on the C-MAPSS datasets as well as data collected from an operational reciprocating compressor. We observed that the new similarity matching method demonstrated excellent performance in finding suitable HIs for failure time prediction. We also observed that the proposed PF framework had a superior prognostics performance over the standard PF. We obtained an averaged predictive accuracy of 96% (C-MAPSS data) and 92% (compressor data) when only the first 10% of the degradation data were used. This work highlights the promise of combining index similarity, Procrustes analysis and PF for complementing existing prognostic methods.

TIGHTLY-COUPLED INTEGRATION OF BLE AND PDR USING GRAPH OPTIMIZATION FOR INDOOR PEDESTRIAN NAVIGATION

Abstract. In this paper, we propose an indoor navigation method based on the tightly-coupled (TC) integration of Bluetooth low energy (BLE) and pedestrian dead reckoning (PDR) using a graph optimization model. We first utilize the Gaussian probability model to update the particle weights that considers the ranging model’s estimation performance at different distances to determine the particle weight. Moreover, the BLE walking-surveyed or crowdsourced landmarks, combined with accurate ranging of BLE at a short distance, is used to construct a graph optimization model, and the Levenberg-Marquardt (LM) algorithm is adopted to optimize this model to improve track tracking performance. The performance of the proposed algorithm has been verified in the hallway scene and another challenging room scene. The results show that compared with the standard particle filter (PF) method, the average positioning accuracy of the proposed algorithm is improved by 64.0% and 54.75%, and the error variance is significantly reduced by 76.23% and 68.60%, respectively, which is a significant improvement in both robustness and accuracy. Furthermore, the test shows that the proposed method can calculate reasonable trajectories even in complex room scenarios.

Localizing unknown radiation sources by unscented particle filtering based on divide-and-conquer sampling

ABSTRACT Predictive estimation of radioactive sources using Bayesian theory is of great importance in nuclear emergency response. To this aim, we put forward an unscented particle filtering algorithm based on divide-and-conquer sampling. Our method exploits the information acquired by mobile detection robots to search for radioactive sources at unknown locations. Firstly, we assume a circular and extremely thin NaI (TI) scintillator detector, then analyze the geometric relationship between the detector cross-sectional area and the square of the radiation source distance, and finally establish a radiation source search model in accordance with Bayesian method. We also introduce a divide-and-conquer strategy to solve the problems of particle dilution and particle degradation, so as to achieve higher search accuracy and speed. Through simulation experiments, compared with standard particle filter and unscented particle filter, the algorithm can effectively improve particle diversity and successfully search radioactive sources in a shorter time.

A global stochastic optimization particle filter algorithm

SummaryWe introduce a new online algorithm for expected loglikelihood maximization in situations where the objective function is multimodal or has saddle points. The key element underpinning the algorithm is a probability distribution that concentrates on the target parameter value as the sample size increases and can be efficiently estimated by means of a standard particle filter algorithm. This distribution depends on a learning rate, such that the faster the learning rate the quicker the distribution concentrates on the desired element of the search space, but the less likely the algorithm is to escape from a local optimum of the objective function. In order to achieve a fast convergence rate with a slow learning rate, our algorithm exploits the acceleration property of averaging, which is well known from the stochastic gradient literature. Considering several challenging estimation problems, our numerical experiments show that with high probability, the algorithm successfully finds the highest mode of the objective function and converges to the global maximizer at the optimal rate. While the focus of this work is expected loglikelihood maximization, the proposed methodology and its theory apply more generally to optimization of a function defined through an expectation.

Joint Tracking of Source and Environment Using Improved Particle Filtering in Shallow Water

Shallow water is a complex sound propagation medium, which is affected by the varying spatial–temporal ocean environment. Taking this complexity into account, the classical processing techniques of source localization and environmental inversion may be improved. In this work, a joint tracking approach for the moving source and environmental parameters of the range-dependent and time-evolving environment in shallow water is presented. The tracking scheme treats both the source parameters (e.g., source depth, range, and speed) and the environmental parameters (e.g., water column sound speed profile (SSP) and sediment parameters) at the source location as unknown variables that evolve as the source moves. To counter sample impoverishment and robustly characterize the evolution of the parameters, an improved particle filter (PF), which is an extension of the standard PF, is proposed. Two examples with simulated data in a slowly changing environment and experimental data collected during the ASIAEX experiment are utilized to demonstrate the effectiveness of the joint approach. The results show that we were able to track the source and environmental parameters simultaneously, and the uncertainties were evaluated in the form of time-evolving posterior probability densities (PPDs). The performance comparison confirms that the improved PF is superior to the standard PF, as it can reduce the parameter uncertainties. The tracking capabilities of the improved PF were verified with high accuracy in real-time source localization and well-estimated rapidly varying parameters. Moreover, the influence of different particle numbers on the improved PF tracking performance is also illustrated.

MultiPDF particle filtering in state estimation of nonlinear objects

This paper presents a new particle filter algorithm (MultiPDF) for state estimation of nonlinear systems. The proposed method is a modification of the standard particle filter approach. Due to the strong need for the acceleration of calculations and an improvement in the estimation quality of state estimation, the authors propose a method which enables one to divide the main particle filter into smaller sub-filters with an accordingly smaller number of particles for each one of them. The algorithm has been implemented for various numbers of particles and subordinate parallel filters. Estimation quality has been checked for nine nonlinear objects (both one- and multidimensional) and evaluated through the quality index, average root-mean-squared error. The computation time of the particle filter algorithm for several hardware configurations has been compared. Based on the obtained results, it can be concluded that, besides the computation acceleration, the parallelization of the particle filter’s operation also improves the estimation quality.

Peer-to-Peer Relative Localization of Aerial Robots With Ultrawideband Sensors

Robots in swarms take advantage of localization infrastructure, such as a motion capture system or global positioning system (GPS) sensors to obtain their global position, which can then be communicated to other robots for swarm coordination. However, the availability of localization infrastructure needs not to be guaranteed, e.g., in GPS-denied environments. Likewise, the communication overhead associated with broadcasting locations may be undesirable. For reliable and versatile operation in a swarm, robots must sense each other and interact locally. Motivated by this requirement, we propose an onboard relative localization framework for multirobot systems. The setup consists of an anchor robot with three onboard ultrawideband (UWB) sensors and a tag robot with a single onboard UWB sensor. The anchor robot utilizes the three UWB sensors to estimate the tag robot's location by using its onboard sensing and computational capabilities solely, without explicit interrobot communication. Because the anchor UWB sensors lack the physical separation that is typical in fixed UWB localization systems, we introduce filtering methods to improve the estimation of the tag's location. In particular, we utilize a mixture Monte Carlo localization (MCL) approach to capture maneuvers of the tag robot with acceptable precision. We validate the effectiveness of our algorithm with simulations as well as indoor and outdoor field experiments on a two-drone setup. The proposed mixture MCL algorithm yields highly accurate estimates for various speed profiles of the tag robot and demonstrates superior performance over the standard particle filter and the extended Kalman filter.

A State of Health Estimation Method for Lithium-Ion Batteries Based on Improved Particle Filter Considering Capacity Regeneration

Accurately estimating the state of health (SOH) of a lithium-ion battery is significant for electronic devices. To solve the nonlinear degradation problem of lithium-ion batteries (LIB) caused by capacity regeneration, this paper proposes a new LIB degradation model and improved particle filter algorithm for LIB SOH estimation. Firstly, the degradation process of LIB is divided into the normal degradation stage and the capacity regeneration stage. A multi-stage prediction model (MPM) based on the calendar time of the LIB is proposed. Furthermore, the genetic algorithm is embedded into the standard particle filter to increase the diversity of particles and improve prediction accuracy. Finally, the method is verified with the LIB dataset provided by the NASA Ames Prognostics Center of Excellence. The experimental results show that the method proposed in this paper can effectively improve the accuracy of capacity prediction.

Rao-Blackwellized Particle Filter for the CBERS-4 attitude and gyros bias estimation

The Rao-Blackwellized Particle Filter (RaoBPF) and the Unscented Kalman Filter (UKF) were applied in this work to attitude and gyros bias estimation using simulated orbit and attitude measurement data for CBERS-4 (China Brazil Earth Resources Satellite 4) recently in operation. CBERS-4 was launched in 2014, controlled and operated in shifts by China (Xi’an Control Center) and Brazil (Satellite Control Center). Its orbit is heliosynchronous with an inclination of 98.504 degrees, a semi-major axis of 7148.865 km, eccentricity 1.1×10−3, crossing equador line at 10h30min in a descending direction with perigee frozen at 90 degrees, which establishes a commitment relationship between a satisfactory amount of solar irradiance, contrast between targets, and the presence of clouds. This configuration provides global coverage every 26 days. The real orbit and attitude measurements were provided by the Satellite Control Center of the National Institute for Space Research (CCS - INPE) from September 1st, 2015. The dynamic attitude model is described by quaternions. The available attitude sensors are two Digital Sun Sensors (DSS), two Infrared Earth Sensor (IRES) and a triad of mechanical gyroscopes. The two IRES give direct measurements of roll and pitch angles with a certain level of error. The two DSS are nonlinear functions of roll, pitch, and yaw attitude angles. The gyros furnish the angular measurements in the body frame reference system. Gyros provide direct incremental angles or angular velocities; however, they present several sources of error, and the drift is the most troublesome. Such drifts yield along time an accumulation of errors which must be accounted in the attitude determination process. The RaoBPF estimation method used to attitude and gyros bias estimation is a technique that exploits the state space structure in order to reduce the number of particles, decreasing the processing time, avoiding the computational effort common to the standard particle filter. The logical extension of the RaoBPF provides a more general model that can be divided into purely non-linear and conditionally linear-Gaussian aspects, which explores this structure, marginalizing the conditional linear parts and estimating them using exact filters, such as the Extended Kalman Filter (EKF). The results show that it is possible to achieve precision in determining attitudes within the prescribed requirements using the RaoBPF, with lower computational cost when compared to the standard particle filter and its branches, in addition to have competitive results such as the UKF.

Robust radioactive sources research method using possibility particle filter

Of growing concern for the security of many nations are numerous incidents of lost or stolen radioactive sources or materials. The detection of and search for these abnormal radioactive sources plays an important role in monitoring nuclear safety and disposal of nuclear waste. In this paper, a method for autonomously searching for radioactive sources in a flat open rectangular-shaped field through mobile platforms was proposed. In this method, by using the possibility particle filter, the search for radioactive sources was realized according to a series of radiation information measured by the mobile platform carrying a Geiger–Müller counter. According to the inverse square law and the radiation counting governed by Poisson distribution, a radioactive source localization model was constructed. Then, a mobile platform controlled by an information entropy strategy constantly moved within the search area and detected radiation at specific points. The possibility filter algorithm, implemented via the sequential Monte Carlo method, is used to update posterior probability distributions of the source parameters. The performance of the proposed search algorithm, including a comparison with a standard particle filter algorithm, is studied by simulations. The simulation experiment proves that the possibility particle filter algorithm has good robustness. The successful application of the experimental dataset collected in the simulations verifies the measurement model and theoretical consideration.

Sequential Parameter Estimation of Modal Dispersion Curves with an Adaptive Particle Filter in Shallow Water: Experimental Results

An adaptive particle filter method is presented for performing sequential geoacoustic estimation of a shallow water acoustic environment using the explosive sound sources. This approach treats environmental parameters and source–receiver distance as unknown random variables that evolve as the source moves. As a sequential estimation method, this approach reduces the expense of computation than genetic algorithm and yields results with the same accuracy. Comparing with standard Particle filter, proposed method can adjust control parameters to adapt to a rapidly changing environment. This approach is demonstrated on the shallow water sound propagation data which was collected during the ASIAEX 2001 experiment. The results indicate that the geoacoustic parameters are well estimated and source–receiver distance are also well determined.

Novel prior position determination approaches in particle filter for ultra wideband (UWB)‐based indoor positioning

<h3>Abstract</h3> Filtering-based indoor positioning using ultra wideband (UWB) requires known velocity to predict prior position in the prediction stage. Velocity can be obtained from an inertial measurement unit (IMU) sensor or the posterior state vector at the previous time stamp. Both methods have limitations when using them in practice. This paper proposes two novel velocity determination approaches, which use measurements to approximate velocity in a self-contained way. They are integrated into particle filtering algorithms for prior position determination. The test result shows that the particle filter with the proposed approaches performs similarly to the Rao-Blackwellized particle filter and slightly better than the particle filter with IMU. Compared with the standard particle filter, the particle filters with our proposed approaches achieve similar positioning accuracies with less computation time. Moreover, it is found that the integration of Angle-of-Arrival measurements in particle-filter-based positioning improves the 3-D positioning accuracy by about 37.3% on average.