Data fusion based EKF-UI for real-time simultaneous identification of structural systems and unknown external inputs

The extended Kalman filter (EKF) is an efficient tool for structural health monitoring and vibration control due to its superiority. However, the conventional EKF approach is only applicable when the information of external inputs to structures is available. Some improved methodologies with different complexities have been proposed in the last decade, but previous approaches based solely on acceleration measurements are inherently unstable which leads to drifts in the estimated unknown inputs and structural displacements. Although regularization schemes or post signal processing can be used to treat the drifts, they are not suitable for the real-time identification of structural systems and unknown inputs. In this paper, it is aimed to directly extend the conventional EKF for real-time simultaneous identification of structural systems and unknown external excitations. Based on the procedures of the conventional EKF, an extended Kalman filter with unknown excitations (EKF-UI) is directly derived. Moreover, data fusion of partially measured displacement and acceleration responses is applied to prevent in real time the previous drifts in the estimated structural displacements and unknown external inputs. Several numerical examples are used to demonstrate the effectiveness of the proposed EKF-UI for real-time identification of linear or nonlinear structural systems and unknown external excitations.     

Railway track geometry determination using adaptive Kalman filtering model

The Kalman filter has been widely used to solve different filtering problems especially in tracking and estimation applications. Besides its simplicity, robustness and optimality, the application of Kalman filter to nonlinear systems can be complicated. The most common method is to use extended Kalman filter which linearizes the nonlinear model so that the standard Kalman filter can be applied. In this paper, a new adaptive Kalman filtering algorithm is designed and applied to a railway track geometry surveying system which has been designed in the scope of a research project at Yildiz Technical University/Turkey. Track gauge, super-elevation, gradient and track axis coordinates which are the railway geometrical parameters can be instantly determined while making measurements by using adaptive Kalman filtering algorithm integrated surveying system.     

Nonlinear unbiased minimum-variance filter for Mars entry autonomous navigation under large uncertainties and unknown measurement bias

High-precision navigation algorithm is essential for the future Mars pinpoint landing mission. The unknown inputs caused by large uncertainties of atmospheric density and aerodynamic coefficients as well as unknown measurement biases may cause large estimation errors of conventional Kalman filters. This paper proposes a derivative-free version of nonlinear unbiased minimum variance filter for Mars entry navigation. This filter has been designed to solve this problem by estimating the state and unknown measurement biases simultaneously with derivative-free character, leading to a high-precision algorithm for the Mars entry navigation. IMU/radio beacons integrated navigation is introduced in the simulation, and the result shows that with or without radio blackout, our proposed filter could achieve an accurate state estimation, much better than the conventional unscented Kalman filter, showing the ability of high-precision Mars entry navigation algorithm.     

Robust extended Kalman filter of discrete-time Markovian jump nonlinear system under uncertain noise

This paper examines the problem of robust extended Kalman filter design for discrete-time Markovian jump nonlinear systems with noise uncertainty. Because of the existence of stochastic Markovian switching, the state and measurement equations of underlying system are subject to uncertain noise whose covariance matrices are time-varying or un-measurable instead of stationary. First, based on the expression of filtering performance deviation, admissible uncertainty of noise covariance matrix is given. Secondly, two forms of noise uncertainty are taken into account: Non-Structural and Structural. It is proved by applying game theory that this filter design is a robust mini-max filter. A numerical example shows the validity of the method.     

基于NACKF的分布式驱动电动汽车轮胎侧向力与质心侧偏角估计

针对传统容积卡尔曼滤波算法在进行车辆关键状态估计时要求噪声统计特性已知的问题,提出一种噪声自适应容积卡尔曼滤波（Noise adaptive cubature Kalman filter, NACKF）算法来进行车辆关键状态的估计。基于次优无偏极大后验估计器对量测噪声协方差进行实时更新并将其嵌入到标准容积卡尔曼算法中实现自适应容积卡尔曼滤波。针对车辆不同子系统间耦合特性对滤波精度的影响,构建双重自适应容积卡尔曼滤波器分别进行侧向力与质心侧偏角的估计,两者在估计过程中互为输入构成闭环反馈,利用分布式模块化结构弱化系统耦合特性对估计精度的影响,实现轮胎侧向力与质心侧偏角的实时准确估计。利用Simulink-Carsim联合仿真平台进行仿真验证和实车试验验证。结果表明,基于双重自适应容积卡尔曼滤波的估计算法相对标准容积卡尔曼滤波估计精度更高,较好地改善了传统容积卡尔曼滤波器在噪声先验统计特性未知条件下非线性滤波精度下降的问题。     

A derivative UKF for tightly coupled INS/GPS integrated navigation

The tightly coupled INS/GPS integration introduces nonlinearity to the measurement equation of the Kalman filter due to the use of raw GPS pseudorange measurements. The extended Kalman filter (EKF) is a typical method to address the nonlinearity by linearizing the pseudorange measurements. However, the linearization may cause large modeling error or even degraded navigation solution. To solve this problem, this paper constructs a nonlinear measurement equation by including the second-order term in the Taylor series of the pseudorange measurements. Nevertheless, when using the unscented Kalman filter (UKF) to the INS/GPS integration for navigation estimation, it causes a great amount of redundant computation in the prediction process due to the linear feature of system state equation, especially for the case with system state vector in much higher dimension than measurement vector. To overcome this drawback in computational burden, this paper further develops a derivative UKF based on the constructed nonlinear measurement equation. The derivative UKF adopts the concise form of the original Kalman filter (KF) to the prediction process and employs the unscented transformation technique to the update process. Theoretical analysis and simulation results demonstrate that the derivative UKF can achieve higher accuracy with a much smaller computational cost in comparison with the traditional UKF.     

Comparison of Linearized Kalman Filter and Extended Kalman Filter for Satellite Motion States Estimation

The performance of the conventional Kalman filter depends on process and measurement noise statistics given by the system model and measurements.The conventional Kalman filter is usually used for a linear system,but it should not be used for estimating the state of a nonlinear system such as a satellite motion because it is difficult to obtain the desired estimation results.The linearized Kalman filtering approach and the extended Kalman filtering approach have been proposed for a general nonlinear system.The equations of satellite motion are described.The satellite motion states are estimated,and the relevant estimation errors are calculated through the estimation algorithms of the both above mentioned approaches implemented in Matlab are estimated.The performances of the extended Kalman filter and the linearized Kalman filter are compared.The simulation results show that the extended Kalman filter is much better than the linearized Kalman filter at the aspect of estimation effect.     

非线性状态空间方法辨识电液伺服控制系统

针对回归神经网络辨识和建立非线性动态系统模型的问题,研究非线性状态空间描述的回归神经网络数学模型。讨论极小均方误差网络训练收敛准则,通过研究Kalman 滤波估计公式中的随机变量,提出一种参数增广的回归神经网络非线性状态方程,无导数的Kalman滤波器用于增广参数估计,人工白噪声强迫网络学习,更新网络权值,避免了扩展Kalman滤波器计算Jacobian信息和基于递度学习算法收敛慢的问题。在电液伺服系统辨识建模的应用中表明,回归神经网络较好地跟踪了液压油缸压力变化,与扩展Kalman滤波估计学习算法相比,新的算法具有较快的收敛和精度。     

基于AEKF的车辆质量与道路坡度实时估计

针对车辆在实际行驶过程中外界噪声的统计特性无法已知的问题,以车辆纵向动力学模型为基础,提出了自适应扩展卡尔曼滤波(adaptive extended Kalman filter,简称AEKF)的车辆质量及道路坡度估计算法。以动态估计车辆系统中的质量与坡度为研究对象,引入了旋转质量换算系数,建立车辆纵向动力学系统的状态空间模型,考虑了不同时刻的档位匹配与行驶特殊工况的处理。对系统状态方程进行离散化处理,得到系统状态方程与系统测量方程,在扩展卡尔曼滤波(extended Kalman filter,简称EKF)的基础上引入带遗忘因子的噪声统计估计器,通过AEKF对状态方程与测量方程实时更新,进行在线估计和校正噪声统计值,从而解决系统的噪声时变问题。本研究算法与EKF算法估计及实测结果的对比分析表明,本研究算法能够很好地对车辆质量和坡度信号进行有效滤波和估计,在短时间内逐渐收敛并逼近实测值,从而能够合理有效地检测车辆在行驶过程中的状态信息。     

NONLINEAR ESTIMATION METHODS FOR AUTONOMOUS TRACKED VEHICLE WITH SLIP

In order to achieve precise,robust autonomous guidance and control of a tracked vehicle,a kinematic model with longitudinal and lateral slip is established,Four different nonlinear filters are used to estimate both state vector and time-varying parameter vector of the created model jointly.The first filter is the well-known extended Kalman filter.The second filter is an unscented version of the Kalman filter.The third one is a particle filter using the unscented Kalman filter to generate the importance proposal distribution.The last one is a novel and guaranteed filter that uses a linear set-membership estimator and can give an ellipsoid set in which the true state lies.The four different approaches have different complexities,behavior and advantages that are surveyed and compared.     

基于UKF算法的汽车状态估计

准确实时获取行驶过程中的状态信息是汽车动态控制系统研究的关键问题。将unscented卡尔曼滤波(UKF)算法应用到汽车的状态估计之中,建立了包含时不变统计特性噪声和非线性轮胎的汽车动力学模型,采用具有对称采样策略和比例修正的UKF算法对汽车估计了多个关键状态量。将UKF估计器与常见的EKF估计器进行了比较分析,基于ADAMS/Car的虚拟试验和实车试验验证了UKF在汽车状态估计中的可行性。     

A modified NARMAX model-based self-tuner with fault tolerance for unknown nonlinear stochastic hybrid systems with an input–output direct feed-through term

A modified nonlinear autoregressive moving average with exogenous inputs (NARMAX) model-based state-space self-tuner with fault tolerance is proposed in this paper for the unknown nonlinear stochastic hybrid system with a direct transmission matrix from input to output. Through the off-line observer/Kalman filter identification method, one has a good initial guess of modified NARMAX model to reduce the on-line system identification process time. Then, based on the modified NARMAX-based system identification, a corresponding adaptive digital control scheme is presented for the unknown continuous-time nonlinear system, with an input–output direct transmission term, which also has measurement and system noises and inaccessible system states. Besides, an effective state space self-turner with fault tolerance scheme is presented for the unknown multivariable stochastic system. A quantitative criterion is suggested by comparing the innovation process error estimated by the Kalman filter estimation algorithm, so that a weighting matrix resetting technique by adjusting and resetting the covariance matrices of parameter estimate obtained by the Kalman filter estimation algorithm is utilized to achieve the parameter estimation for faulty system recovery. Consequently, the proposed method can effectively cope with partially abrupt and/or gradual system faults and input failures by the fault detection.     

自适应滤波算法在导弹动力系统故障诊断中的应用

基于时间序列的AR模型方法在用于液体导弹动力系统稳态工作段故障检测时遇到了两难题。其一,由于系统差异,在以试车时的动力系统状态的均值作为实际运行时动力系统状态均值时,得到的时间序列必定不再是零均值;其二,导弹动力系统工作环境不同时刻不尽相同,表现在AR模型中其观测噪声是时变的。在实践中,我们采用了基于扩展Kalm an滤波的自适应算法以及带有时变噪声统计的自适应滤波算法很好地解决了相关问题。     

基于扩展Kalman滤波器测量氮爆式液压锤的性能

考虑到在缸体内运动的活塞,难以用传感器直接测量其运动状态：速度、加速度以及摩擦力、未知阻力。根据系统理论的方法,以活塞的位置、速度、加速度作为状态矢量,在采样间隔内,将活塞运动视为匀加速度运动,建立具有未知输入的活塞运动状态方程。将未知阻力视为有色噪声,并作为系统未知输入,设计扩展状态的Kalman滤波结构。依据气体的变化规律,得到活塞在采样各时刻的位置坐标。以最小方均误差作为测量准则,研究有色噪声输入线性系统的Kalman递推状态估计算法。算法自适应跟踪未知输入的变化,估算活塞冲程、回程的速度和未知的阻力,从而测量氮爆式液压冲击锤的冲击能量。测量结果表明,该方法具有较高的测量精度,与理论设计基本一致。     

Maximum correntropy square-root cubature Kalman filter with application to SINS/GPS integrated systems

For a nonlinear system, the cubature Kalman filter (CKF) and its square-root version are useful methods to solve the state estimation problems, and both can obtain good performance in Gaussian noises. However, their performances often degrade significantly in the face of non-Gaussian noises, particularly when the measurements are contaminated by some heavy-tailed impulsive noises. By utilizing the maximum correntropy criterion (MCC) to improve the robust performance instead of traditional minimum mean square error (MMSE) criterion, a new square-root nonlinear filter is proposed in this study, named as the maximum correntropy square-root cubature Kalman filter (MCSCKF). The new filter not only retains the advantage of square-root cubature Kalman filter (SCKF), but also exhibits robust performance against heavy-tailed non-Gaussian noises. A judgment condition that avoids numerical problem is also given. The results of two illustrative examples, especially the SINS/GPS integrated systems, demonstrate the desirable performance of the proposed filter.     

A hybrid feedback linearizing-Kalman filtering control algorithm for a distillation column

This paper studies the design of a discrete-time multivariable feedback linearizing control (FLC) structure. The control scheme included (i) a transformer [also called the input/output (I/O) linearizing state feedback law] that transformed the nonlinear u-y to a linearized v-y system, (ii) a closed-loop observer [extended Kalman filter (EKF)], which estimated the unmeasured states, and (iii) a conventional proportional integral (PI) controller that was employed around the v-y system as an external controller. To avoid the estimator design complexity, the design of EKF for a binary distillation column has been performed based on a reduced-order compartmental distillation model. Consequently, there is a significant process/predictor mismatch, and despite this discrepancy, the EKF estimated the required states of the simulated distillation column precisely. The FLC in conjunction with EKF (FLC-EKF) and that coupled with a measured composition-based reduced-order open-loop observer (FLC-MCROOLO) have been synthesized. The FLC structures showed better performance than the traditional proportional integral derivative controller. In practice, the presence of uncertainties and unknown disturbances are common, and in such situations, the proposed FLC-EKF control scheme ensured the superiority over the FLC-MCROOLO law.     

Modeling a multivariable reactor and on-line model predictive control

A nonlinear first principle model is developed for a laboratory-scaled multivariable chemical reactor rig in this paper and the on-line model predictive control (MPC) is implemented to the rig. The reactor has three variables-temperature, pH, and dissolved oxygen with nonlinear dynamics-and is therefore used as a pilot system for the biochemical industry. A nonlinear discrete-time model is derived for each of the three output variables and their model parameters are estimated from the real data using an adaptive optimization method. The developed model is used in a nonlinear MPC scheme. An accurate multistep-ahead prediction is obtained for MPC, where the extended Kalman filter is used to estimate system unknown states. The on-line control is implemented and a satisfactory tracking performance is achieved. The MPC is compared with three decentralized PID controllers and the advantage of the nonlinear MPC over the PID is clearly shown.     

Implementation of a Kalman filter in positioning for autonomous vehicles, and its sensitivity to the process parameters

Modern autonomous vehicles are using more than one method for performing the positioning task. The most common positioning methods for indoor vehicles are odometry for relative positioning and triangulation for absolute positioning. In many cases a Kalman filter is required to merge the data from the positioning systems and determines the vehicle position based on error analysis of the measurements and calculation procedures. A Kalman filter is particularly advantageous for on-the-fly positioning, which is performed while the vehicle is in motion. This paper presents the implementation of a Kalman filter in ROBI — an AGV for material handling in a manufacturing environment. The performance of the filter in estimating the position of the AGV and the effect of motion parameters (speed, path curvature, beacon layout etc.) on filter accuracy are shown.     

Improvement on state estimation for discrete-time LTI systems with measurement loss

In this paper, we present a novel state estimation procedure for the LTI systems with loss of data at the output measurement channels. The proposed methodology aims at compensating such output measurement losses through an innovative design methodology which is based on the so-called linear prediction (LP) and Kalman filter theories. A compensated observation signal is first reconstructed using an LP subsystem and then supplied to a discrete-time Kalman filter in the closed-loop framework. We show that, under suitable assumptions, it is possible to reconstruct the lost data using an straightforward algorithm with the capability of associating an optimal filter order. A mass-spring-damper case study subject to measurement loss is provided to demonstrate some of the promising results of our proposed algorithm. Simulation results illustrate that the proposed estimation methodology is too far superior than those offered in the literature.