Mobile robot localization with gyroscope and constrained Kalman filter

The odometry information used in mobile robot localization can contain a significant number of errors when robot experiences slippage. To offset the presence of these errors, the use of a low-cost gyroscope in conjunction with Kalman filtering methods has been considered by many researchers. However, results from conventional Kalman filtering methods that use a gyroscope with odometry can unfeasible because the parameters are estimated regardless of the physical constraints of the robot. In this paper, a novel constrained Kalman filtering method is proposed that estimates the parameters under the physical constraints using a general constrained optimization technique. The state observability is improved by additional state variables and the accuracy is also improved through the use of a nonapproximated Kalman filter design. Experimental results show that the proposed method effectively offsets the localization error while yielding feasible parameter estimation.     

Robust two-stage Kalman filters for systems with unknown inputs

A method is developed for the state estimation of linear time-varying discrete systems with unknown inputs. By making use of the two-stage Kalman filtering technique and a proposed unknown inputs filtering technique, a robust two-stage Kalman filter which is unaffected by the unknown inputs can be readily derived and serves as an alternative to the Kitanidis' (1987) unbiased minimum-variance filter. The application of this new filter is illustrated by optimal filtering for systems with unknown inputs     

Unknown input modeling and robust fault diagnosis using black box observers

A key issue that needs to be addressed while performing fault diagnosis using black box models is that of robustness against abrupt changes in unknown inputs. A fundamental difficulty with the robust FDI design approaches available in the literature is that they require some a priori knowledge of the model for unmeasured disturbances or modeling uncertainty. In this work, we propose a novel approach for modeling abrupt changes in unmeasured disturbances when innovation form of state space model (i.e. black box observer) is used for fault diagnosis. A disturbance coupling matrix is developed using singular value decomposition of the extended observability matrix and further used to formulate a robust fault diagnosis scheme based on generalized likelihood ratio test. The proposed modeling approach does not require any a priori knowledge of how these faults affect the system dynamics. To isolate sensor and actuator biases from step jumps in unmeasured disturbances, a statistically rigorous method is developed for distinguishing between faults modeled using different number of parameters. Simulation studies on a heavy oil fractionator example show that the proposed FDI methodology based on identified models can be used to effectively distinguish between sensor biases, actuator biases and other soft faults caused by changes in unmeasured disturbance variables. The fault tolerant control scheme, which makes use of the proposed robust FDI methodology, gives significantly better control performance than conventional controllers when soft faults occur. The experimental evaluation of the proposed FDI methodology on a laboratory scale stirred tank temperature control set-up corroborates these conclusions.     

基于卡尔曼滤波的路径行程时间预测方法

为提高常规卡尔曼滤波预测模型的自适应性，本文研究一种基于卡尔曼滤波的实时路径行程时间预测方法。首先通过主成分分析法考察行程时间与其影响因素时间序列之间的相关性，从而选择影响路径行程时间的主要因素，并建立相应的多元回归方程;其次，构造行程时间的卡尔曼滤波状态方程;最后，由一组卡尔曼滤波递推式计算得到行程时间的预测值。将本文算法应用于广州市某交通干道上的行程时间预测，并将本文算法和常规卡尔曼滤波方法进行比较。结论表明本文算法有效，用于路径行程时间预测具有较好的综合性能。     

强跟踪平方根容积卡尔曼滤波和 自回归模型融合的故障预测

为了解决非线性系统中不可测量参数的预测问题,提出一种带有次优渐消因子的强跟踪平方根容积卡尔曼滤波(STSCKF)和自回归(AR)模型相结合的故障预测方法.利用AR模型时间序列预测法预测未来时刻的测量值,将预测的测量值作为STSCKF的测量变量,从而将预测问题转化为滤波估计问题.STSCKF通过在预测误差方差阵的均方根中引入渐消因子调节滤波过程中的增益矩阵,克服了故障参数变化函数未知情况下普通SCKF跟踪故障参数缓慢甚至失效的局限性,使得STSCKF能较好地预测故障参数的发展趋势.连续搅拌反应釜(CSTR)仿真结果表明,STSCKF的预测精度高于普通SCKF和强跟踪无迹卡尔曼滤波(STUKF),验证了方法的有效性.     

Fault diagnosis and accommodation of nonlinear systems based on multiple-model adaptive unscented Kalman filter and switched MPC and H-infinity loop-shaping controller

In this paper, a new active fault tolerant control (AFTC) methodology is proposed based on a state estimation scheme for fault detection and identification (FDI) to deal with the potential problems due to possible fault scenarios. A bank of adaptive unscented Kalman filters (AUKFs) is used as a core of FDI module. The AUKF approach alleviates the inflexibility of the conventional UKF due to constant covariance set up, leading to probable divergence. A fuzzy-based decision making (FDM) algorithm is introduced to diagnose sensor and/or actuator faults. The proposed FDI approach is utilized to recursively correct the measurement vector and the model used for both state estimation and output prediction in a model predictive control (MPC) formulation. Robustness of the proposed FTC system, H_∞ optimal robust controller and MPC are combined via a fuzzy switch that is used for switching between MPC and robust controller such that FTC system is able to maintain the offset free behavior in the face of abrupt changes in model parameters and unmeasured disturbances. This methodology is applied on benchmark three-tank system; the proposed FTC approach facilitates recovery of the closed loop performance after the faults have been isolated leading to an offset free behavior in the presence of sensor/actuator faults that can be either abrupt or drift change in biases. Analysis of the simulation results reveals that the proposed approach provides an effective method for treating faults (biases/drifts in sensors/actuators, changes in model parameters and unmeasured disturbances) under the unified framework of robust fault tolerant control.     

A Filtering Approach Based on MMAE for a SINS/CNS Integrated Navigation System

This paper explores multiple model adaptive estimation (MMAE) method, and with it, proposes a novel filtering algorithm. The proposed algorithm is an improved Kalman filter-multiple model adaptive estimation unscented Kalman filter (MMAE-UKF) rather than conventional Kalman filter methods, like the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). UKF is used as a subfilter to obtain the system state estimate in the MMAE method. Single model filter has poor adaptability with uncertain or unknown system parameters, which the improved filtering method can overcome. Meanwhile, this algorithm is used for integrated navigation system of strapdown inertial navigation system (SINS) and celestial navigation system (CNS) by a ballistic missile's motion. The simulation results indicate that the proposed filtering algorithm has better navigation precision, can achieve optimal estimation of system state, and can be more flexible at the cost of increased computational burden.      

State estimation and nonlinear predictive control of autonomous hybrid system using derivative free state estimators

In this work, we develop a state estimation scheme for nonlinear autonomous hybrid systems, which are subjected to stochastic state disturbances and measurement noise, using derivative free state estimators. In particular, we propose the use of ensemble Kalman filters (EnKF), which belong to the class of particle filters, and unscented Kalman filters (UKF) to carry out estimation of state variables of autonomous hybrid system. We then proceed to develop novel nonlinear model predictive control (NMPC) schemes using these derivative free estimators for better control of autonomous hybrid systems. A salient feature of the proposed NMPC schemes is that the future trajectory predictions are based on stochastic simulations, which explicitly account for the uncertainty in predictions arising from the uncertainties in the initial state and the unmeasured disturbances. The efficacy of the proposed state estimation based control scheme is demonstrated by conducting simulation studies on a benchmark three-tank hybrid system. Analysis of the simulation results reveals that EnKF and UKF based NMPC strategies is well suited for effective control of nonlinear autonomous three-tank hybrid system.     

基于渐消卡尔曼滤波算法的航空发动机参数估计方法

针对航空发动自适应模型误差无法完全消除,可能导致参数估计结果严重偏离甚至滤波发散的问题,提出一种带渐消因子的卡尔曼参数估计方法,采用在线调整卡尔曼方程残差的权重、加强现实测量数据在状态估计中作用的策略,保证了发动机性能参数估计的准确性。仿真结果表明,该方法不仅克服了滤波发散现象,具有更优的收敛速度和估计精度,且计算量小,实现简单,便于实际应用     

基于多项式拟合的扩展卡尔曼滤波算法

弹道修正弹内的弹载计算机必须实时对卫星定位接收机获取的弹丸状态数据进行滤波降噪,用于预测弹丸落点,传统滤波方法滤波时间长,滤波实时性差,提出一种基于多项式拟合的方法。通过适当降低卫星定位接收机数据更新频率,并用多项式拟合插值出的数据代替数据更新时间间隔内的弹丸状态数据。仿真实验表明,该算法在不降低滤波效果的前提下,较普通扩展卡尔曼滤波时间降低7/8,提高了滤波实时性,对于弹道修正弹关键技术的研究提供了重要参考。同时该方法可推广应用到其他滤波算法当中,具有很强的可移植性。     

基于Huber M估计的鲁棒Cubature 卡尔曼滤波算法

Cubature卡尔曼滤波器(CKF)在非高斯噪声或统计特性未知时滤波精度将会下降甚至发散,为此提出了统计回归估计的鲁棒CKF算法.推导出线性化近似回归和直接非线性回归的鲁棒CKF算法,直接非线性回归克服了观测方程线性化近似带来的不足.具有混合高斯噪声的仿真实例比较了3种Cubature卡尔曼滤波器的滤波性能,结果表明这两种鲁棒CKF滤波精度及估计一致性明显优于CKF,直接非线性回归的CKF的鲁棒性更强,滤波性能更好.     

Evolutionary-Programming-Based Kalman Filter for Discrete-Time Nonlinear Uncertain Systems

Some observations and improvements on the conventional Kalman filtering scheme to function properly are presented. The improvements can be achieved using the minimal principle evolutionary programming (EP) technique. A new linearization methodology is presented to obtain the exact linear models of a class of discrete-time nonlinear time-invariant systems at operating states of interest, so that the conventional Kalman filter can work for the nonlinear stochastic systems. Furthermore, a Kalman innovation filtering algorithm and such an algorithm based on the evolutionary programming optimal-search technique are proposed in this paper for discrete-time time-invariant nonlinear stochastic systems with unknown-but-bounded plant uncertainties and noise uncertainties to find a practically implementable “best” Kalman filter. The worst-case realization of the discrete-time nonlinear stochastic uncertain systems represented by the interval form with respect to the implemented “best” nominal filter is also found in this paper for demonstrating the effectiveness of the proposed filtering scheme.     

Identification of process and measurement noise covariance for state and parameter estimation using extended Kalman filter

The performance of Bayesian state estimators, such as the extended Kalman filter (EKF), is dependent on the accurate characterisation of the uncertainties in the state dynamics and in the measurements. The parameters of the noise densities associated with these uncertainties are, however, often treated as ‘tuning parameters’ and adjusted in an ad hoc manner while carrying out state and parameter estimation. In this work, two approaches are developed for constructing the maximum likelihood estimates (MLE) of the state and measurement noise covariance matrices from operating input-output data when the states and/or parameters are estimated using the EKF. The unmeasured disturbances affecting the process are either modelled as unstructured noise affecting all the states or as structured noise entering the process predominantly through known, but unmeasured inputs. The first approach is based on direct optimisation of the ML objective function constructed by using the innovation sequence generated from the EKF. The second approach - the extended EM algorithm - is a derivative-free method, that uses the joint likelihood function of the complete data, i.e. states and measurements, to compute the next iterate of the decision variables for the optimisation problem. The efficacy of the proposed approaches is demonstrated on a benchmark continuous fermenter system. The simulation results reveal that both the proposed approaches generate fairly accurate estimates of the noise covariances. Experimental studies on a benchmark laboratory scale heater-mixer setup demonstrate a marked improvement in the predictions of the EKF that uses the covariance estimates obtained from the proposed approaches.     

一种具有在线参数调整功能的Kalman滤波及其应用

本文提出了一种具有在线调整噪声参数功能的卡尔曼自适应滤波算法及其在船舶导航目标跟踪中的应用。实际中系统噪声和量测噪声的统计特性是动态变化的,但在传统卡尔曼滤波中一般认为系统噪声模型是先验已知的,噪声均值和协方差都是定值,这必然造成滤波效果不理想、目标跟踪精度低甚至出现目标跟踪丢失的问题。针对这种情况,通过在线自适应调整噪声均值和协方差,动态跟踪噪声统计特性的变化,从而提高对目标的跟踪精度。在线实现可以有效地利用系统的部分数据进行更新迭代,减小计算量并且易于工程实现。最后通过船舶目标仿真实验的结果验证了本算法的有效性。     

多率系统Kalman滤波算法的鲁棒性分析

多率系统Kalman滤波算法是多率采样系统中对多源观测进行融合的重要手段. 基于化工过程的多率采样特点, 给出了多率Kalman滤波算法, 分析了该算法在模型失配情况下的鲁棒性. 在给定的假设条件下, 通过对滤波误差变化规律的分析, 给出了多率Kalman滤波稳定与发散的基本判定方法. 针对一类典型系统, 推导出了滤波稳定与发散判据. 通过仿真对该判据进行了验证, 仿真结果表明所提出的滤波鲁棒性分析方法可以用于算法的实际应用.     

改进型平方根无迹卡尔曼滤波及其在无轴承永磁同步电机无速度传感器运行中的应用

平方根无迹卡尔曼滤波(SRUKF)解决了标准无迹卡尔曼滤波(UKF)中由于误差协方差阵负定而引起的滤波发散问题, 保证了算法的数值稳定性, 但仍存在对模型参数变化的鲁棒性差、收敛速度慢及对突变状态的跟踪能力低等缺陷. 因此, 本文提出一种改进SRUKF滤波, 通过引入时变渐消因子和弱化因子, 实时修正滤波增益矩阵和误差协方差平方根矩阵, 实现残差序列正交, 确保SRUKF滤波保持对目标实际状态的准确跟踪. 将该算法在无轴承永磁同步电机无速度传感器矢量控制系统中进行仿真研究. 结果表明: 改进SRUKF非线性近似精度、数值稳定性及滤波精度更高, 在系统状态突变或负载扰动时, 鲁棒性更强, 能够有效实现转速及转子角度的准确估计, 确保转子稳定悬浮运行.     

基于信息补偿的自适应联邦滤波算法

针对采用标准卡尔曼滤波器必须知道系统噪声统计特性的局限性，研究了一类系统噪声未知情况下的自适应联邦滤波方法，指出了自适应滤波方法应用于联邦结构时应当注意的问题，提出了一种基于信息补偿的自适应联邦滤波算法。SINS／BDS／GPS组合导航系统的仿真结果表明，该方法可以有效抑制系统噪声未知情况下的滤波发散现象，提高了滤波的稳定性和估计性能。     

Robust nonlinear filter for nonlinear systems with multiplicative noise uncertainties,unknown external disturbances,and packet dropouts

This study is concerned with the robust nonlinear filtering problem for nonlinear discrete‐time stochastic system with multiplicative noise uncertainties, unknown external disturbances, and packet dropouts. The focus of this paper is to design a filter with predictor–corrector structure such that the upper bound on the state estimation error variance is minimized in the presence of multiplicative noise, unknown external disturbances, and packet dropouts. Thus, a robust nonlinear filter based on the method to obtain the upper bound on variances of multiplicative noises, unknown disturbances, and packet dropouts is designed. Further stability analysis shows that the proposed filter has robustness against multiplicative noises, unknown external disturbances, and packet dropouts. Simulation results show that the proposed filter is more effective than extended Kalman filter and other robust extended Kalman filter. Copyright © 2017 John Wiley & Sons, Ltd.     

Projection based MIMO control performance monitoring: II––measured disturbances and setpoint changes

In this paper the performance monitoring method based on subspace projections from Part I [J. Proc. Cont. 13 (2003) 739] is extended to include measured disturbances and setpoint changes. It was shown in [J. Proc. Cont. 13 (2003) 739] that the minimum variance output space is an optimal subspace of the general closed-loop output space and that orthogonal projections of filtered output data onto past closed-loop output data can be used to assess the performance of feedback controllers. This paper demonstrates that the same framework is directly applicable to systems with measured disturbances by augmenting the data matrix with those measured disturbances. Furthermore, it provides a means of separating suboptimal control performance between that arising from unmeasured disturbances and that due to measured disturbances. The effect of setpoint changes on control performance can be calculated as special feedforward variables. The controller is generally time-varying to include the case of model predictive control. A simulation example and an industrial boiler process are used to demonstrate the effectiveness of the proposed method.