Unscented Kalman Particle Filter Research Articles

An Iterative Augmented Unscented Kalman Particle Filter for Simultaneous State-Parameter-Input Estimation for Structural Systems Subjected to Gamma-Distribution Noise

Simultaneous estimations of the states, parameters and unknown inputs of nonlinear structural systems subjected to non-Gaussian noise are essential, because the inputs are not always available and the system noise is not always Gaussian. However, filters developed for this task require the inter-story drift measurements to be “fused” with the acceleration measurements to avoid the “drift phenomenon”. Because inter-story drifts may be inconvenient to obtain in practice, it is more desirable to use acceleration measurements only. To this end, this study develops a novel iterative augmented unscented Kalman particle filter (IAUKPF) for the simultaneous state-parameter-input estimation for systems subjected to non-Gaussian noise. The iterative strategy proposed in this study effectively corrects the “drift phenomenon” when only acceleration measurements are incorporated, so that the accuracies of the estimated unknown inputs are promoted. The importance density of the particle filter at each time step is provided by the augmented unscented Kalman filter so that the filter takes the best known information into consideration. Numerical examples of nonlinear structural systems affected by non-Gaussian noise are adopted to examine the effectiveness of the proposed IAUKPF.

Construction and Method Study of the State of Charge Model for Lithium-Ion Packs in Electric Vehicles Using Ternary Lithium Packs as an Example

Accurate and real-time estimation of pack system-level chips is essential for the performance and reliability of future electric vehicles. Firstly, this study constructed a model of a nickel manganese cobalt cell on the ground of the electrochemical process of the packs. Then, it used methods on the grounds of the unscented Kalman filter and unscented Kalman particle filter for system-level chip estimation and algorithm construction. Both algorithms are on the ground of Kalman filters and can handle nonlinear and uncertain system states. In comparative testing, it can be seen that the unscented Kalman filter algorithm can accurately evaluate the system-level chip of the nickel manganese cobalt cell under intermittent discharge conditions. The system-level chip was 0.53 at 1000 s and was reduced to 0.45 at 1500 s. These results demonstrate that the evaluation of the ternary lithium battery pack’s performance is time-dependent and indicate the accuracy of the algorithm used during this time period. These data should be considered in the broader context of the study for a comprehensive understanding of their meaning. In the later stage, the estimation error of the recursive least-squares unscented Kalman particle filter method for system-level chips began to significantly increase, gradually exceeding 1%, with a corresponding root-mean-square error of 0.002171. This indicates that the recursive least-squares optimization algorithm, the unscented Kalman particle filter algorithm, diminished its root mean square error by 27.59%. The unscented Kalman filter and unscented Kalman particle filter are effective in estimating the system-level chip of nickel manganese cobalt cells. However, UPF performs more robustly in handling complex situations, such as pack aging and temperature changes. This study provides a new perspective and method that has a high reference value for pack management systems. This helps to achieve more effective energy management and improve pack life, thereby enhancing the reliability and practicality of electric vehicles.

A New Linear Regression Kalman Filter with Symmetric Samples

Nonlinear filtering is of great significance in industries. In this work, we develop a new linear regression Kalman filter for discrete nonlinear filtering problems. Under the framework of linear regression Kalman filter, the key step is minimizing the Kullback–Leibler divergence between standard normal distribution and its Dirac mixture approximation formed by symmetric samples so that we can obtain a set of samples which can capture the information of reference density. The samples representing the conditional densities evolve in a deterministic way, and therefore we need less samples compared with particle filter, as there is less variance in our method. The numerical results show that the new algorithm is more efficient compared with the widely used extended Kalman filter, unscented Kalman filter and particle filter.

Research on guidance method of cooperative tracking ground multi-target using UAV group

Multi-UAV (unmanned aerial vehicle) cooperative tracking target is one of the standard exercises for unmanned aircraft systems, it is important to track multiple targets in actual missions due to the clustering of military missions. It is of great research interest and more difficult to use fewer multi-UAV to track more targets effectively, the aim of which is to be more efficient in tracking, and high precision positioning. This paper explores the key issues in the complex environment of UAV community cooperative multi-target monitoring. The architecture of the UAV group cooperative the multi-target tracking system is built in a complex environment firstly. Then a proposal was made for a dynamic grouping algorithm for multi-target UAV group tracking in an occlusion region, an adaptive multi-model unscented Kalman particle filter fusion algorithm, and a fast guidance method for cooperative target tracking in a restricted environment. The feasibility of the proposed method is validated by simulation and flight test evaluations. Finally, there is a prospect for the next course of research in this field.

Distributed Acoustic Source Tracking in Noisy and Reverberant Environments With Distributed Microphone Networks

In this paper, an improved distributed unscented Kalman particle filter (DUKPF) is proposed for the problem of tracking a single moving acoustic source in noisy and reverberant environments with distributed microphone networks. The conventional DUKPF employs the unscented Kalman filter (UKF) for its proposal of particle sampling, whereas the UKF incorporates one single observation from a certain localization function, which is vulnerable to noise or reverberation. To alleviate this problem, multiple observations are extracted from the localization function at each node and incorporated into the state update of the UKF via the probability data association (PDA) technique, yielding the PDA-UKF. Next, employing the PDA-UKF for the proposal of particle sampling, the improved DUKPF is further developed. Finally, the improved DUKPF is adapted for the acoustic source tracking problem, and a distributed acoustic source tracking method is presented. Simulation results reveal that the improved DUKPF achieved better tracking performance than the conventional DUKPF in different noisy and reverberant conditions.

A Dynamic State-of-Charge Estimation Method for Electric Vehicle Lithium-Ion Batteries

With the increasing environmental concerns, plug-in electric vehicles will eventually become the main transportation tools in future smart cities. As a key component and the main power source, lithium-ion batteries have been an important object of research studies. In order to efficiently control electric vehicle powertrains, the state of charge (SOC) of lithium-ion batteries must be accurately estimated by the battery management system. This paper aims to provide a more accurate dynamic SOC estimation method for lithium-ion batteries. A dynamic Thevenin model with variable parameters affected by the temperature and SOC is established to model the battery. An unscented Kalman particle filter (UPF) algorithm is proposed based on the unscented Kalman filter (UKF) algorithm and the particle filter (PF) algorithm to generate nonlinear particle filter according to the advantages and disadvantages of various commonly used filtering algorithms. The simulation results show that the unscented Kalman particle filter algorithm based on the dynamic Thevenin model can predict the SOC in real time and it also has strong robustness against noises.

Comparative Study of Four Filter-based Algorithms for State-of-charge Estimation of Lithium-ion Batteries

Accurate estimation of state of charge (SOC) is greatly crucial for safely and reliably charging and discharging the lithium-ion batteries, especially for those used in electric vehicles (EVs). Currently, a lot of algorithms have been proposed to estimate the battery SOC. In this paper, we compared four filter-based algorithms, including the standard particle filter (PF), the unscented Kalman filter, the unscented Kalman-particle filter (UPF), and the extended Kalman-particle filter (EPF), in terms of the estimate accuracy and convergence rate. The federal urban driving schedule (FUDS) and the urban dynamometer driving schedule (UDDS) were applied to evaluate the performance of these estimation algorithms. Comparison results showed that compared with the UKF, the PF can improve the estimate accuracy, however, it takes much more time to correct the initial SOC error. By introducing the EKF and UKF into the particle filter, the convergence rate can be greatly improved without the decrease in estimate accuracy, and convergence rate is very close to that of the UKF.

Estimation of state‐of‐charge based on unscented Kalman particle filter for storage lithium‐ion battery

Estimation of state‐of‐charge based on unscented Kalman particle filter for storage lithium‐ion battery

Time-Series Filtering for Replicated Observations via a Kernel Approximate Bayesian Computation

In time-series analysis, state-space models (SSMs) have been widely used to estimate the conditional probability distributions of hidden variables and parameter values, as well as to understand structures that can generate the data. For example, the Kalman filter is used to analytically calculate the conditional probability distribution on linear SSMs in terms of minimizing the variance, and several extensions, such as the unscented Kalman filter and particle filter, have been applied to calculate the approximate distribution on nonlinear SSMs. Recently, the approximate Bayesian computation (ABC) has been applied to such time-series filtering to handle intractable likelihoods; however, it remains problematic with respect to consistently achieving a reduction of the estimation bias, evaluating the validity of the models, and dealing with replicated observations. To address these problems, in this paper, we propose a novel method combined with the kernel ABC to perform filtering, parameter estimation, and the model evaluation in SSMs. Simulation studies show that the proposed method produces inference that is comparable to other ABC methods, with the advantage of not requiring a careful calibration of the ABC threshold. In addition, we evaluate the performance of the model-selection capability using true and competitive models on synthetic data from nonlinear SSMs. Finally, we apply the proposed method to real data in rat circadian oscillations, and demonstrated the usefulness in practical situations.

Analysis of Single Channel Blind Source Separation Algorithm for Chaotic Signals

In a wireless sensor network, the signal received by the terminal processor is usually a complex single channel hybrid chaotic signal. The engineering needs to separate the useful signal from the mixed signal to perform the next transmission analysis. Since chaotic signals are nonlinear and unpredictable, traditional blind separation algorithms cannot effectively separate chaotic signals. Aiming to correct these problems—based on the particle filter estimation algorithm—an extended Kalman particle filter algorithm (EPF) and an unscented Kalman particle filter algorithm (UPF) are proposed to solve the single channel blind separation problem of chaotic signals. Mixing chaotic signals of different intensities performs blind source separation. Using different evaluation indexes carries out the experiment and performance can be analyzed. The results show that the proposed algorithm effectively separates the mixed chaotic signals.

Enhanced particle filter for states and parameters estimation in structural health monitoring applications

In this paper, an iterated square-root central difference Kalman particle filter method (ISRCDKF-PF) is used for the estimation of the state variables and model parameters of nonlinear structural systems. In the current work, we propose to extend our previous work (Mansouri et al. in J Civil Struct Health Monit 5(4):493–508, 2015) to deal with non-parametric Monte Carlo sampling-based method and propose to use an enhanced PF technique which incorporates the latest observations into a prior updating scheme using the ISRCDKF algorithm. Various conventional and state-of-the-art state estimation methods are compared for the estimation performance, namely the unscented Kalman filter (UKF), the square-root central difference Kalman filter (SRCDKF), the iterated unscented Kalman filter (IUKF), the iterated square-root central difference Kalman filter (SRCDKF), the conventional particle filter (PF), the unscented Kalman particle filter (UKF-PF), the SRCDKF-PF, the iterated unscented Kalman particle filter (IUKF-PF) and the developed ISRCDKF-PF, in two comparative studies through two examples, one using synthetic data and the other using simulated three DOF damped system data. In the first comparative study, the state variables are estimated from noisy measurements of these variables, and the comparison of the different estimation techniques is performed by computing the root mean square error (RMSE) of the state with respect to the noise-free data. In the second comparative study, both the state variables and the model parameters are simultaneously estimated, and the impact of the used measurement noise, and number of estimated states/parameters on the performances of the estimation techniques are investigated. The ISRCDKF-PF algorithm consists of a PF based on ISRCDKF to obtain a better importance proposal distribution. This proposal is able to integrate the latest observation into the state density, then it can improve the posteriori density. The results of both comparative study show that PF, UKF-PF, SRCDKF-PF, IUKF-PF and ISRCDKF-PF provide improved estimation performance over the UKF, SRCDKF, IUKF, ISRCDKF. The results also show that ISRCDKF-PF provides improved estimation performance over IUKF-PF, even with abrupt changes in estimated states, and both of them provide better accuracy than the conventional PF, UKF-PF and SRCDKF-PF. These advantages of the ISRCDKF-PF are due to the fact that it uses an optimal proposal distribution which make efficient use of the latest observation by using the ISRCDKF algorithm.

Modified sequential importance resampling filter

In order to deal with the particle degeneracy and impoverishment problems existed in particle filters, a modified sequential importance resampling (MSIR) filter is proposed. In this filter, the resampling is translated into an evolutional process just like the biological evolution. A particle generator is constructed, which introduces the current measurement information (CMI) into the resampled particles. In the evolution, new particles are first produced through the particle generator, each of which is essentially an unbiased estimation of the current true state. Then, new and old particles are recombined for the sake of raising the diversity among the particles. Finally, those particles who have low quality are eliminated. Through the evolution, all the particles retained are regarded as the optimal ones, and these particles are utilized to update the current state. By using the proposed resampling approach, not only the CMI is incorporated into each resampled particle, but also the particle degeneracy and the loss of diversity among the particles are mitigated, resulting in the improved estimation accuracy. Simulation results show the superiorities of the proposed filter over the standard sequential importance resampling (SIR) filter, auxiliary particle filter and unscented Kalman particle filter.

UPF Tracking Method Based on Color and SIFT Features Adaptive Fusion

Based on the problems that target appears rotation and noise interference in complex environment, an improved multi-feature adaptive fusion tracking method is proposed. The algorithm adopts unscented Kalman particle filter (UPF) to update the measurement information in the sample particles, better overcome the problem of the particle weight degradation. In addition, in order to overcome the defects of additive and multiplicative fusion algorithm in the feature selection, the multiple adaptive fusion characteristics method that target color distribution and scale invariance feature (SIFT) are used as complementary information. Experimental results show that the proposed method is superior to the traditional methods which are based on fixed weight or standard particle filter.

The auxiliary iterated extended Kalman particle filter

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

Multiple-sensor Fusion Tracking Based on Square-root Cubature Kalman Filtering

Nonlinear state estimation and fusion tracking are always hot research topics for information processing. Compared to linear fusion tracking, nonlinear fusion tracking takes many new problems and challenges. Especially, the performances of fusion tracking, based on different nonlinear filters, are obviously different. The conventional nonlinear filters include extended Kalman filter (EKF), unscented Kalman filter (UKF), particle filter (PF) and cubature Kalman filter (CKF), and the recent square-root cubature Kalman filter (SCKF) has been paid more and more attention by researchers because of its advantages of computation complexity and estimation accuracy over other nonlinear filters. However, the SCKF is mainly designed for single sensor system, and for present nonlinear multi-sensor system, it is not applicable. Based on the current results of fusion tracking algorithms, this paper provides a novel multi-sensor fusion tracking algorithm based on the SCKF. Firstly, a brief introduction of basic SCKF algorithm is given. Then, the centralized fusion tracking frame with augmented measurements and the sequential fusion tracking frame are presented respectively. Finally, two computer simulation examples are demonstrated. Simulations results show that the centralized SCKF can obtain better performances of accuracy, stability and convergence.

Signal reconstruction in wireless sensor networks based on a cubature Kalman particle filter

For solving the issues of the signal reconstruction of nonlinear non-Gaussian signals in wireless sensor networks (WSNs), a new signal reconstruction algorithm based on a cubature Kalman particle filter (CKPF) is proposed in this paper. We model the reconstruction signal first and then use the CKPF to estimate the signal. The CKPF uses a cubature Kalman filter (CKF) to generate the importance proposal distribution of the particle filter and integrates the latest observation, which can approximate the true posterior distribution better. It can improve the estimation accuracy. CKPF uses fewer cubature points than the unscented Kalman particle filter (UKPF) and has less computational overheads. Meanwhile, CKPF uses the square root of the error covariance for iterating and is more stable and accurate than the UKPF counterpart. Simulation results show that the algorithm can reconstruct the observed signals quickly and effectively, at the same time consuming less computational time and with more accuracy than the method based on UKPF.

Blind source separation of chaotic signals in wireless sensor networks

Chaotic signal is essentially a nonlinear and non-Gaussian signal, which involves signal quantization when used in wireless sensor networks (WSNs). It makes the blind source separation of chaotic signal in WSNs more difficult to address. To solve the problem, we propose a new source separation algorithm based on cubature Kalman particle filter (CPF) in this paper. First the probability density function of the observed signal is derived and the optimal quantization is used; this can achieve the optimal quantization of signal under the limited budget of quantization bits. After that, the algorithm uses cubature Kalman filter (CKF) to generate the important proposal distribution of the particle filter (PF), integrating the latest observation and improving the approximation to the system posterior distribution, which will improve the performance of the signal separation. Simulation results show that the algorithm can separate mixed chaotic signal effectively, it is superior over the unscented Kalman particle filter (UPF) counterpart in accuracy and computation overhead. The running time is 88.77% compared to the UPF counterpart.

Near Space Pseudolite Navigation System Design and High-Performance Filtering Algorithm

This paper analyzes the defects of satellite navigation systems that exist in positioning and precision-guided weapons and pointes out the advantages and military needs of pseudolite. The autonomous navigation nonlinear mathematical model of Near Space Pseudolite SINS/CNS/SAR autonomous navigation system is established. Based on the merits of fading filter, robust adaptive filtering and particle filter, we propose a fading adaptive Unscented Particle Filtering algorithm. The proposed filtering algorithm is applied to SINS/CNS/SAR autonomous navigation system and conducted simulation calculation with the Unscented Kalman filter and particle filter comparison. The results show that the new algorithm that is proposed meets the needs of pseudolite autonomous navigation, and the navigation accuracy is significantly higher than the Unscented Kalman filter and particle filter algorithm.

Adaptive iterated particle filter

The adaptive iterated particle filter (AIPF) is presented, where the importance density function is updated iteratively by the particle filter itself when necessary. By using a simulated annealing algorithm with an adaptive annealing parameter, the current measurement can be quickly incorporated into the sampling process, resulting in greatly improved sampling efficiency. Simulation results demonstrate the improved performance of the AIPF over the sampling importance resampling filter, unscented Kalman particle filter and auxiliary particle filter.

Particle filter with multimode sampling strategy

Particle filters provide a general numerical tool to deal with the nonlinear/non-Gaussian filtering problems. However, it is still a challenging problem to design a good proposal distribution to generate high-quality particles. In this paper, we present the concept of hybrid proposal distribution (HPD) defined by the weighted sum of multiple basic proposal distributions (BPDs), transform the adaptive particle filtering into the online weight optimization, and, as a result, propose the framework of particle filter with multimode sampling strategy. Compared with traditional sampling strategies, multimode sampling strategy is more flexible to accommodate the time-varying system characteristics. To demonstrate the efficiency of the proposed framework, a particle filter with HPD consisting of two BPDs is designed, where one BPD is the transition density and the other, first proposed in this paper, is defined by an updated system equation. The numerical simulation with two examples shows that the proposed filter outperforms the extended Kalman filter, the unscented Kalman filter, the standard particle filter and the unscented Kalman particle filter.