The divided difference 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.

With the wide application of lithium-ion battery in various fields, the State of Health (SOH) estimation has become a research hotspot for advanced battery management system (BMS). Accurate SOH estimation is helpful to ensure the safe operation of equipment or system in practical applications. Among various lithium-ion battery health diagnosis methods, particle filter and its variants are the mainstream with the significant advantages in non-linear and non-Gaussian system modeling. But in practical applications, the BMS always suffers from the limited power supplication and finite computing resources. Therefore, this paper implemented a comparative study on particle filter (PF) and typical variants, including extended Kalman particle filter (EPF), unscented particle filter (UPF), regularized particle filter (RPF). Through the NASA’s battery degradation model, the performance of the above particle filter algorithms is compared and analyzed. The experimental results show that UPF has the highest estimation accuracy, and it is more suitable for the situation with higher prediction accuracy requirements. PF has the least time consumption and is more suitable for on-line health assessment.

A particle filter guided by iterated extended Kalman filter (IEGPF) is proposed to solve the problem of particle impoverishment. Firstly, particles are divided into two groups adaptively according to the maximum likelihood ratio, which is defined to measure how well the particles, drawn from transition prior density, match the likelihood model. Particles in one group are drawn from transition prior density, while those in the other group are drawn from the Gaussian approximate posterior density, obtained by running an iterated extended Kalman filter (IEKF). The results of numerical simulations, conducted at different observation noise level, show that IEGPF can produce more accurate estimate than extended Kalman particle filter (EPF) and unscented Kalman particle filter (UPF), whereas the computational cost is comparable to that of SIR.

In this paper, we investigate the problem of autonomous integrated navigation of strapdown inertial navigation system (SINS)/ celestial navigation system (CNS) for a ballistic missile. To handle the nonlinear missile dynamic model, three filtering methods including extended Kalman filter (EKF), extended Kalman particle filter (EKPF) and unscented particle filter (UPF) are utilized to fusion the integrated navigation system and improve the navigation accuracy. The performance of the navigation system based on the three methods is analyzed and compared. Simulation results indicate that the UPF can provide the highest navigation accuracy with the price of highest computation burden.

Data assimilation is the process of estimating the state of dynamic systems (linear or nonlinear, Gaussian or non-Gaussian) as accurately as possible from noisy observational data. Although the Three Dimensional Variational (3D-VAR) methods, Four Dimensional Variational (4D-VAR) methods and Ensemble Kalman filter (EnKF) methods are widely used and effective for linear and Gaussian dynamics, new methods of data assimilation are required for the general situation, that is, nonlinear non-Gaussian dynamics. General Bayesian recursive estimation theory is reviewed in this thesis. The Bayesian estimation approach provides a rather general and powerful framework for handling nonlinear, non-Gaussian, as well as linear, Gaussian estimation problems. Despite a general solution to the nonlinear estimation problem, there is no closed-form solution in the general case. Therefore, approximate techniques have to be employed. In this thesis, the sequential Monte Carlo (SMC) methods, commonly referred to as the particle filter, is presented to tackle non-linear, non-Gaussian estimation problems. In this thesis, we use the SMC methods only for the nonlinear state estimation problem, however, it can also be used for the nonlinear parameter estimation problem. In order to demonstrate the new methods in the general nonlinear non-Gaussian case, we compare Sequential Monte Carlo (SMC) methods with the Ensemble Kalman Filter (EnKF) by performing data assimilation in nonlinear and non-Gaussian dynamic systems. The models used in this study are referred to as state-space models. The Lorenz 1963 and 1966 models serve as test beds for examining the properties of these assimilation methods when used in highly nonlinear dynamics. The application of Sequential Monte Carlo methods to different fixed parameters in dynamic models is considered. Four different scenarios in the Lorenz 1063 [sic] model and three different scenarios in the Lorenz 1996 model are designed in this study for both the SMC methods and EnKF method with different filter siz

Combining the interacting multiple model (IMM) and the unscented particle filter (UPF), a new multiple model filtering algorithm is presented. Multiple models can adapt to targets’ high maneuvering. Particle filter can deal with the nonlinear or non-Gaussian problems and the unscented Kalman filter (UKF) may improve the approximate accuracy. Compared with other interacting multiple model algorithms in the target tracking simulations, the results demonstrate the validity of the new filtering method, that is, particle filter with the UKF proposal.

Particle filter tracking, a type of sequential Monte Carlo method, has long been considered to be a very promising but time-consuming tracking technique. Methods have been developed to include a particle filter as part of a Variable Structure, Interactive Multiple Model (VS-IMM) structure and to integrate it into the Multiple Hypothesis Tracker (MHT) scoring structure. By integrating a particle filter as just one of many filters in Raytheon's MHT, the particle filter is applied sparingly on difficult off-road targets. This dramatically reduces the computation time as well as improves tracking performance in circumstances in which the other filters do not excel. Moreover, terrain information may be taken into account in the particle propagation process. In particular, an Unscented Particle Filter (UPF) was implemented in order to address the potential dominance of a small set of degenerate particles and/or poor prior distribution sampling from hampering the ability of the particle filter to accurately handle a maneuver. The Unscented Particle Filter treats every particle as its own Kalman filter. After the distribution of particles is adjusted in order to take into account the terrain, each particle is divided into sigma point states. These sigma points are propagated forward in time and then recombined to form a new composite particle state and covariance. These reformed particles are used in scoring and can be updated with a new observation. Since the Unscented Particle Filter includes the covariances in these calculations, this particle filter approach is more accurate and potentially requires fewer particles than an ordinary particle filter. By adding an Unscented Particle Filter to the other filters in an MHT tracker, the advantages of the UPF can be utilized in an efficient manner in order to enhance tracking performance.

We present a new unscented particle filter for dynamic systems that outperforms the general particle filter and the unscented particle filter when the variance of the observation noise is small. Our algorithm uses a bank of unscented Kalman filters to refine the prediction in particle filter. The key difference with the traditional unscented particle filter is the introduction of an auxiliary model and a bank of unscented Kalman filter with this auxiliary model to generate the importance distribution in the particle filter. This structure makes efficient use of the latest observation information. Our new algorithm use fewer particles than the general particle filters and its performance outperforms them.

The square root cubature particle filter (SRCPF) uses the square root cubature Kalman filter (SRCKF) for generating the proposal distribution. The SRCPF algorithm is easy to be implemented and has numerical stability. Moreover, the SRCKF based proposal distribution approximates the optimal importance distribution by incorporating the current measurement. Simulation results demonstrate that the SRCPF algorithm has the better performance for state estimation than the generic particle filter (GPF), extended particle filter (EPF) and unscented particle filter (UPF), and its calculation cost decreases largely.

In this paper, an algorithm of 3-D single observer passive location for fixed emitters based on the extended kalman particle filter (EPF) using the azimuth angle and its changing rate is proposed. EPF is a method of particle filter (PF) using the extended Kalman filter (EKF) as the importance function. The method obtains target emitter's position by the principle of kinematic geometry. The raw location results are rectified and smoothed by EPF algorithm to realize fast and high precision passive target's location. Simulation results show that the performance of algorithm based on EPF is better than EKF's has faster and steady convergence speed, better filtering effect and better location precision.

In this paper, we investigate an autonomous navigation method using a red shift navigation in solar system, utilizing the solar system celestial body as the light source and information source. The flight velocity of the spacecraft in the inertial coordinate system is gained by the real time measurement of the red shift. In order to reduce the computation burden of particle filter, a method for particle filter based on scaled spherical simplex unscented transformation (SSSUT) is proposed, this method uses scaled spherical simplex unscented Kalman filter to generate importance distribution of particle filter. The scaled spherical simplex unscented particle filter introduces the parameters α, β, κ, these parameters can solve sampling non-local effects and shrink the distance of sigma points from the center. The simulation results show that compared with conventional unscented particle filter (UPF), the computation complexity of SSSUPF can be reduced by 50 percent, the computation burden can be reduced by 31 percent, and has the same accuracy with UPF.

This paper presents a new robust adaptive unscented particle filtering algorithm by adopting the concept of the adaptive robust filtering to the unscented particle filter. This algorithm adaptively determines the equivalent weight function and adaptively adjusts the adaptive factor constructed from predicted residuals to resist the disturbances of singular observations and the kinematic model noise, thus preventing particles from degeneracy. It also uses the unscented transformation to improve the accuracy of particle filtering, thus providing the reliable state estimation for improving the performance of adaptive robust filtering. Experiments and comparison analysis demonstrate that the proposed filtering algorithm can effectively resist disturbances due to system state noise and observation noise, and the filtering accuracy is much higher than the extended Kalman filter, unscented Kalman filter, standard particle filter and unscented particle filter.

A new physical parameter identification method with a name of EKPF-LS is proposed for shear frame structures under limited inputs and outputs by a combination of extended Kalman particle filter (EKPF) and least square (LS) algorithm. The basic principle of EKPF-LS is to establish the proposed distribution function of the particle filter through EKF-LS. In this method, EKPF is introduced to get rid of the restriction of Gaussian white noise model and reduce the linearization error caused by EKF. Meanwhile, LS is utilized to address the problem of unmeasured excitation estimations. The effectiveness and accuracy of the proposed EKPF-LS method is verified by a numerical example of a four-story hysteretic shear frame under an earthquake excitation and an experimental test of a four-story shear type frame using Gaussian white noise and sine sweep signal as excitations, respectively. Gaussian colored noises are then added to the solved and measured response signals in the numerical example and experimental test, respectively. The results demonstrate that the proposed method can identify the stiffness of shear frame structures effectively and is superior to the existed EKF-LS approach when the structural system is nonlinear structural system or Colored noise model.

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.

A hybrid sampling strategy is considered in multimode sampling based particle filter to alleviate the degeneracy as one of the most typical problems in the particle filter. However, to achieve high accuracy, expensive computation cost is inevitable when generating the hybrid distribution. To overcome this problem, a novel framework of particle filter is proposed in this paper with an improved hybrid sampling strategy. The main novelty is that this framework can simplify the generation of the hybrid distribution and makes the selection of particles more reasonable, in which the likelihood of particle is used to select the particles and determine the weights of multiple basic proposal distributions. Two simulation examples are implemented to test performances of the proposed filter algorithm. The obtained results show that the proposed framework has several superior performances in comparison with the standard particle filter, the unscented particle filter and the multimode sampling based particle filter.