Target torque estimation for gearshift in dual clutch transmission with uncertain parameters

The target torque of engaging clutches during gearshift is a key factor that affects the dynamic response of powertrains equipped with the dual clutch transmissions (DCT). This paper investigates a method to estimate the target torque of engaging clutches under conditions where engine torque and measurement signals contain white noise and some vehicle parameters (the radius of wheel and rolling friction coefficient) are uncertain. To compute the target torque accurately, the state of system should be estimated when the uncertain parameters exist. The vehicle powertrain is modeled as the 3DOF system when one clutch is closed and the 4DOF system when two clutches are open, while the measured signals include speeds of the engine, transmission, and vehicle (rotational speed of wheels). In addition to traditional extended Kalman filter (EKF), both the joint extended Kalman filter (JEKF) and dual extended Kalman filter (DEKF) are used to estimate the target torque. The simulation results show that DEKF and JEKF provide much higher accuracy in the estimation of target torque than EKF when some parameters of the model are uncertain, so as to produce a better ride performance of the transmission during gearshift, i.e. reduction of power interruption and compressed shifting time. Furthermore, the DEKF provides higher accuracy than the JEKF in estimating uncertain parameters.     

Online state of charge estimation of Li-ion battery based on an improved unscented Kalman filter approach

An improved unscented Kalman filter approach is proposed to enhance online state of charge estimation in terms of both accuracy and robustness. The goal is to address the drawback associated with the unscented Kalman filter in terms of its requirement for an accurate model and a priori noise statistics. Firstly, Li-ion battery modelling and offline parameter identification is performed. Secondly, a sensitivity analysis experiment is designed to verify which model parameter has the greatest influence on state of charge estimation accuracy, in order to provide an appropriate parameter for the model adaptive algorithm. Thirdly, an improved unscented Kalman filter approach, composed of a model adaptive algorithm and a noise adaptive algorithm, is introduced. Finally, the results are discussed, which reveal that the proposed approach’s estimation error is less than 1.79% with acceptable robustness and time complexity.     

应用DEKF算法训练模糊化神经网络

模糊MLP网络的待定参数规模比确定性MLP网络的多几倍，急需找到高效的训练算法。本文尝试用DEKF训练模糊神经网络，这是DEKF算法新的应用。仿真表明，DEKF算法比经典BP算法的收敛速度更快，训练所得网络的精度更高。     

Research on estimation model of the battery state of charge in a hybrid electric vehicle based on the classification and regression tree

ABSTRACT

In order to achieve the accurate estimation of state of charge (SOC) of the battery in a hybrid electric vehicle (HEV), this paper proposed a new estimation model based on the classification and regression tree (CART) which belongs to a kind of decision tree. The basic principle and modelling process of the CART decision tree were introduced in detail in this paper, and we used the voltage, current, and temperature of the battery in an HEV to estimate the value of SOC under the driving cycle. Meanwhile, we took the energy feedback of the HEV under the regenerative braking into consideration. The simulation data and experimental data were used to test the effectiveness of the estimation model of CART, and the results indicate that the proposed estimation model has high accuracy, the relative error of simulation is within 0.035, while the relative error of experiment is less than 0.05.     

基于单目视觉的SLAM算法研究

利用一种新型的人工路标系统-MR二维码,提出了基于单目视觉和里程计的SLAM方法.首先介绍了MR二维码系统,然后在对机器人运动模型和视觉传感器观测模型进行分析和验证的基础上,给出了一种实用的里程计位置估计误差模型.机器人移动过程中,利用扩展卡尔曼滤波器对视觉信息与里程计信息进行融合.在室内环境下进行了实际实验,实验结果表明该算法可提高机器人定位和构建地图的精度,验证了算法的有效性.     

Strapdown INS/GPS Integrated Navigation Using Geometric Algebra

A strapdown inertial navigation system (INS)/global positioning system (GPS) integrated navigation Kalman filter in terms of geometric algebra (GA) is proposed. Two error models, i.e., the additive GA error (AGAE) model and the multiplicative GA error (MGAE) model, are developed on the ground of the GA-based strapdown INS model. The AGAE model describes the navigation error by means of perturbation. In contrast, the MGAE model which is indirectly derived from the AGAE one, can physically represent the difference between the computed frame and the true frame. Subsequently, one Kalman filter is constructed on the basis of the MGAE model of the strapdown INS and the error model of GPS. A variety of simulations are carried out to test the proposed Kalman filter. The results show that the Kalman filter can reduce the navigation error remarkably.     

Periodic measurement strategies for distributed parameter systems filtering

This paper deals with the optimization of the output matrix for a discrete time linear stochastic system. The output matrix varies as a periodic function of time, and its values are constrained to belong to a finite prescribed set. The aim is to minimize the average variance of the Kalman filter estimation error in the periodic steady state. The application regards the optimization both of the measurement points and of the scanning sequence for a distributed parameter system (DPS) of parabolic type. A modal approximation is used to reduce the DPS to finite dimension. The proposed solution algorithm makes use of heuristic rules that enable to overcome the difficulties arising from the cardinality of the admissible set, the possible slow convergence of the relevant Riccati equation and the high dimensionality of the lumped approximate model of the DPS. The numerical applications show that the periodic scanning policies, found by the optimization algorithm, cause a great improvement of the filter performance, with respect to the case where a single fixed sensor is used.     

An exact minimum variance filter for a class of discrete time systems with random parameter perturbations

An exact, closed-form minimum variance filter is designed for a class of discrete time uncertain systems which allows for both multiplicative and additive noise sources. The multiplicative noise model includes a popular class of models (Cox-Ingersoll-Ross type models) in econometrics. The parameters of the system under consideration which describe the state transition are assumed to be subject to stochastic uncertainties. The problem addressed is the design of a filter that minimizes the trace of the estimation error variance. Sensitivity of the new filter to the size of parameter uncertainty, in terms of the variance of parameter perturbations, is also considered. We refer to the new filter as the ‘perturbed Kalman filter’ (PKF) since it reduces to the traditional (or unperturbed) Kalman filter as the size of stochastic perturbation approaches zero. We also consider a related approximate filtering heuristic for univariate time series and we refer to filter based on this heuristic as approximate perturbed Kalman filter (APKF). We test the performance of our new filters on three simulated numerical examples and compare the results with unperturbed Kalman filter that ignores the uncertainty in the transition equation. Through numerical examples, PKF and APKF are shown to outperform the traditional (or unperturbed) Kalman filter in terms of the size of the estimation error when stochastic uncertainties are present, even when the size of stochastic uncertainty is inaccurately identified.     

基于增秩Kalman滤波的动态荷载识别和结构响应重构

针对传统的荷载识别方法受不适定性问题影响导致识别误差较大,且受传感器数上的限制也无法监测所有结构易损伤位置处振动响应的问题,提出了一种基于增秩Kalman滤波（augmented Kalman filter, AKF）算法的动态荷载识别和结构响应重构方法.基于结构状态空间方程,形成由荷载向量和状态向量组成的增秩状态向量（augmented-rank state vector,ASV）,利用Kalman滤波算法获得增秩状态向量的最小方差无偏（minimum variance unbiased, MVU）估计,实现了状态和荷载向量的同时识别.结合最优状态估计和观测矩阵,实现了未布置传感器处的结构动力响应重构.通过三个有限元案例,初步验证了该方法的可行性和有效性.结果表明,当荷载位置固定或移动时,所提方法均能有效地识别荷载和重构响应,精度较高且对测量噪声不敏感.传感器的种类、数量和布置位置对荷载识别和响应重构精度会有一定影响.     

基于方根分解形式的带衰减因子UKF算法应用

UKF作为一种新的非线性滤波方法已在目标跟踪问题中得到应用,在状态的时间更新阶段直接使用非线性模型,不引入线性化误差,而且不必计算Jacobians矩阵.提出了一种基于方根分解形式的带有衰减因子的UKF算法(SRDMA-UKF),算法的方根形式增加了数字稳定性和状态协方差的半正定性.通过衰减因子的引入加强对当前测量数据的利用,减小历史数据对滤波的影响.仿真实验结果表明,该算法与UKF算法相比具有更好的滤波性能.     

Partitioned state and parameter estimation for real-time flood forecasting

A new algorithm is developed for simultaneous state-parameter estimation in real-time flood-forecasting applications. Dubbed the partitioned state-parameter (PSP) algorithm, is it unusual in the way that the parameter filter is formulated explicitly in terms of the identifiable parameters in the transition and input coefficient matrices. By virtue of its parallel filter structure the algorithm is very fast, yet it has been designed so that essential error interactions between the forecasting and parameter filters are preserved. Furthermore, PSP is structured so that input coefficients are only updated when the corresponding inputs are actually applied. This feature is useful for systems subject to sporadic inputs. The algorithm is tested with real and synthesized daily rainfall-runoff data from the Hillsborough River in Florida. PSP is found to produce good forecasts and parameter estimates and is much faster than the extended Kalman filter.     

On use of the Kalman filter for spatial smoothing

A state-space model to perform discrete thin plate smoothing for data on a two-dimensional rectangular lattice is proposed with the use of the Kalman filter. The use of the Kalman filter reduces computational difficulties in the maximum likelihood estimation of a smoothing parameter. A procedure to reduce computational difficulties in the estimation of trend is given also. Numerical illustration is provided using two sets of artificial data.     

Pattern recognition based Kalman filter for indoor localization using TDOA algorithm

In this paper, we will present a motion pattern recognition based Kalman filter (PRKF), and apply it to the time difference of arrival (TDOA) algorithm of indoor localization. The state matrix in Kalman filter (KF) is determined by the motion pattern which the target node is supposed to act, and this will bring new system error if the assumption is not correct. Considering this, we first create three fuzzy sets using three KFs whose state matrix stand for different motion patterns, then linearly combined the memberships of a target node of the fuzzy sets. Finally, simulation results show that the PRKF can enhance the localization accuracy about more than 20%.     

A multiple template approach for robust tracking of fast motion target

Target tracking is very important in computer vision and related areas. It is usually difficult to accurately track fast motion target with appearance variations. Sometimes the tracking algorithms fail for heavy appearance variations. A multiple template method to track fast motion target with appearance changes is presented under the framework of appearance model with Kalman filter. Firstly, we construct a multiple template appearance model, which includes both the original template and templates affinely transformed from original one. Generally speaking, appearance variations of fast motion target can be covered by affine transformation. Therefore, the affine transform-enhanced templates match the target of appearance variations better than conventional models. Secondly, we present an improved Kalman filter for approximate estimating the motion trail of the target and a modified similarity evaluation function for exact matching. The estimation approach can reduce time complexity of the algorithm and keep accuracy in the meantime. Thirdly, we propose an adaptive scheme for updating template set to alleviate the drift problem. The scheme considers the following differences: the weight differences in two successive frames; different types of affine transformation applied to templates. Finally, experiments demonstrate that the proposed algorithm is robust to appearance variation of fast motion target and achieves real-time performance on middle/low-range computing platform.     

An improved tracking Kalman filter using a multilayered neural network

This paper presents a method for improving the estimation accuracy of a tracking Kalman filter (TKF) by using a multilayered neural network (MNN). Estimation accuracy of the TKF is degraded due to the uncertainties which cannot be expressed by the linear state-space model given a priori. The MNN capable of learning an arbitrary nonlinear mapping is thus added to the TKF to compensate the uncertainties. The MNN is trained so that it realizes a mapping from, the measurements to the corrections of estimations of the TKF. Simulation results show that the estimation accuracy is much improved by using the MNN.     

A state space model for rub‐off triangles

In this paper we suggest a distribution‐free state space model to be used with the Kalman filter in run‐off triangles. It works with original incremental amounts and relates the triangle with a column of observed values, which can be chosen in order to describe better the risk volume in each year. On the traditional application of run‐off triangles (the paid claims run‐off), this model relates the amount paid j years after the accident year with a column of observed values, that can be the claims paid on the first year, the number of claims, premiums, number of risks, etc. Two advantages of this model are the perfect split between observed values and random variables and the capacity to incorporate the changes in the speed of the company's reality into the model and in its projections. Particular care is taken on the evaluation of the final forecast mean square error as well as on the estimation of the model parameters, specially the error variances. Also, two sets of claims data are analysed. In comparison with other methods, namely, the chain ladder, the analysis of variance, the Hoerl curves and the state space modelling with the chain ladder linear model, the proposed model gave a final reserve with a mean square error within the smallest. Copyright © 2003 John Wiley & Sons, Ltd.     

在不确定观测下离散状态时滞系统的最优滤波

研究了在不确定观测下离散状态时滞系统的最优滤波问题,观测值的不确定性则通过一个满足Bernoulli分布且统计特性已知的随机变量来描述. 一般采用状态增广方法将时滞系统转换为无时滞随机系统, 再利用Kalman滤波器的设计方法解决最优状态估计问题, 但是当系统时滞较大时,转换后的系统状态维数很高, 这样增加了计算负担. 为此,基于最小方差估计准则, 利用射影性质和递归射影公式得到了一个新的滤波器设计方法, 而且保证了滤波器的维数与原系统相同.最后, 给出一个仿真例子说明所提方法的有效性.     

基于无线通信基站的室内三维定位问题研究

对基于无线通信基站的室内三维定位问题进行了研究,建立了测量误差模型和终端定位模型.建立了TOA测量误差模型和基于测量误差估计的终端定位模型,提出了基于空间几何约束和测量噪声抑制的定位算法;分别在相对时间误差、最大时延、最小时延和随机法四种基站筛选方案下,分析了不同基站数目对定位精度的影响;利用轨迹上相近点的信道状态信息的相关性,采用Kalman滤波算法计算了终端运动轨迹;基于假设性检验,通过递减迭代搜索算法,得到了可定位终端数;建立了基站不同覆盖范围下,终端连接度数与定位精度之间关系的分析模型.     

Divergence of the stationary Kalman filter for correct and for incorrect noise variances

The convergence properties of the estimation error covariancefor the Kalman filter are analysed. Criteria are derived forconvergence or divergence of the estimation error if the time-invariantKalman filter is used, possibly designed for incorrect noisedata. The analysis uses recently developed convergence resultsfor the solution of the matrix Riccati differential equation.     

基于粒子滤波算法的航迹误差分析

当前针对飞行预测的研究主要采用的是kalman算法,在解决非线性问题时存在着只能近似线性的而不够精确的问题.采用近年来受到广泛关注的粒子滤波算法,针对RNAV航路进行分析,结论中得到了对飞行误差仿真分析并对比了卡尔曼滤波仿真效果,证实了粒子滤波在航迹预测中更好的准确性.