改进扩展卡尔曼滤波的四旋翼姿态估计算法

为了提高标准扩展卡尔曼姿态估计算法的精确度和快速性,将运动加速度抑制的动态步长梯度下降算法融入扩展卡尔曼中,提出一种改进扩展卡尔曼的四旋翼姿态估计算法。该算法在卡尔曼测量更新中采用梯度下降法进行非线性观测,消除标准扩展卡尔曼算法在线性化时带来的线性化误差,提高算法的准确性和快速性;对梯度下降法的梯度步长进行动态处理,使算法步长与四旋翼飞行器的运动合角速度成正比,增强微型四旋翼飞行器姿态解算的动态性能;对强机动运动过程中机体产生的运动加速度进行抑制处理,消除运动加速度对姿态解算的不利影响,提高了微型四旋翼飞行器姿态解算的跟踪精度。为了验证所设计算法的可行性和有效性,基于STM32单片机搭建四旋翼实验平台系统进行实时在线性能验证。结果表明,所设计算法能提高四旋翼飞行器在强机动、高速运动情况下的姿态跟踪精度、动态性能,增强姿态融合算法的抗干扰性,保证微型四旋翼飞行器的稳定飞行。     

Efficient algorithms of clustering adaptive nonlinear filters

This paper proposes a new class of efficient adaptive nonlinear filters whose estimation error performance (in a minimum mean square sense) is superior to that of competing approximate nonlinear filters, e.g., the well-known extended Kalman filter (EKF). The proposed filters include as special cases both the EKF and previously proposed partitioning filters. The new methodology performs an adaptive selection of appropriate reference points for linearization from an ensemble of generated trajectories that have been processed and clustered accordingly to span the whole state space of the desired signal. Through a series of simulation examples, the approach is shown significantly superior to the classical EKF with comparable computational burden     

Estimating Vehicle State by GPS/IMU Fusion with Vehicle Dynamics

In this paper, a low-cost navigation system with high integrity and reliability is proposed. A high-integrity estimation filter is proposed to obtain a high-accuracy state estimate. The filter utilizes a vehicle velocity constraint measurement to enhance the accuracy of the estimate. Two estimation filters, the extended Kalman filter (EKF) and the extended information filter (EIF), are designed and compared to obtain the estimate of the vehicle state. An instrumentation system that consists of a microcontroller, GPS receiver, IMU, velocity encoder, and Zigbee transceiver is used. The microcontroller provides a vehicle navigation solution at 50 Hz by fusing the measurements of the IMU and GPS receiver using the proposed filter design. Extensive experimental tests are conducted to verify the accuracy of the proposed algorithm. These results are processed with and without the velocity constraints. The estimation accuracy improvement with the addition of the velocity constraints is shown. A more than 16 % reduction in the computational time is demonstrated when using the EIF in comparison to the EKF approach.     

永磁同步电机多采样率EKF转速辨识

永磁同步电机（Permanent Magnet Synchronous Motor,PMSM）具有响应快、高精度、高转矩比等诸多优点,同时无传感器控制策略研究能有效提高PMSM系统的简易性和鲁棒性。在分析EKF和多采样率数字控制系统的基础上,建立永磁同步电机输入多采样率EKF算法,将其用于转速估计。通过仿真和实时实验验证其算法在辨识精度及收敛稳定性方面均优于单采样率EKF算法,并和高频单采样率EKF有着一致的辨识效果,而多采样率EKF算法的数据量及运算量均小于高频单采样率EKF。     

一种基于PSO的自适应神经网络预测控制

针对非线性系统,提出了一种基于微粒群优化(PSO)的自适应神经网络预测控制方法.采用对角递归网络(DRNN)对非线性系统进行建模,并利用扩展卡尔曼滤波(EKF)递推估计算法在线计算网络模型参数的Jacobian矩阵以实现模型参数的自适应.利用PSO算法在线优化求解非线性系统的预测控制律,以克服传统基于梯度法的非线性规划方法求解预测控制律时对初始条件非常敏感的缺点.生化发酵过程的仿真结果表明,所提出的控制方法具有良好的跟踪能力和抗干扰能力.     

Critical evaluation of non-linear filter configurations for the state estimation of Continuous Stirred Tank Reactor

A systematic approach has been attempted to design a non-linear observer to estimate the states of a non-linear system. The neural network based state filtering algorithm proposed by A.G. Parlos et al. has been used to estimate the state variables, concentration and temperature in the Continuous Stirred Tank Reactor (CSTR) process. (CSTR) is a typical chemical reactor system with complex nonlinear dynamics characteristics. The variables which characterize the quality of the final product in CSTR are often difficult to measure in real-time and cannot be directly measured using the feedback configuration. In this work, the comparison of the performances of an extended Kalman filter (EKF), unscented Kalman filter (UKF) and neural network (NN) based state filter for CSTR that rely solely on concentration estimation of CSTR via measured reactor temperature has been done. The performances of these three filters are analyzed in simulation with Gaussian noise source under various operating conditions and model uncertainties.     

A switching models gain rotation algorithm for tracking a maneuvering target

Tracking of a target maneuvering in a 3D space is studied. Based on switching models describing the maneuver and/or nonmaneuver scenarios, the so-called switching models gain rotation algorithm (SMGRA) is presented. The proposed scheme incorporates a simple Kalman filter and a detector. Further it switches between the above two scenarios according to the detector's decision of target maneuverability. In both situations, the required gains of the algorithm are computed for uncoupled filters. A comparison study of the proposed scheme and several well-known filters is carried out for typical target trajectories in a naval gun fire control system. The tracking errors for the present algorithm are nearly identical to the extended Kalman filter (EKF), while the computation requirements are reduced by a factor of nine.     

Experimental Study of Iterated Kalman Filters for Simultaneous Localization and Mapping of Autonomous Mobile Robots

In this paper, we investigate the role of iteration in Kalman filters family for improvement of the estimation accuracy of states in simultaneous localization and mapping (SLAM). The linearized error propagation existing in Kalman filters family can result in large errors and inconsistency in the SLAM problem. One approach to alleviate this situation is the use of iteration in extended Kalman filter (EKF) and sigma point Kalman filter (SPKF) based SLAM. The main contribution is to present that the iterated versions of Kalman filters can increase consistency and robustness of these filters against linear error propagation. Experimental results are presented to validate this improvement of state estimate convergence through repetitive linearization of the nonlinear observation model in EKF-SLAM and SPKF-SLAM algorithms.     

Mobile-robot pose estimation and environment mapping using an extended Kalman filter

In this paper an extended Kalman filter (EKF) is used in the simultaneous localisation and mapping (SLAM) of a four-wheeled mobile robot in an indoor environment. The robot’s pose and environment map are estimated from incremental encoders and from laser-range-finder (LRF) sensor readings. The map of the environment consists of line segments, which are estimated from the LRF’s scans. A good state convergence of the EKF is obtained using the proposed methods for the input- and output-noise covariance matrices’ estimation. The output-noise covariance matrix, consisting of the observed-line-features’ covariances, is estimated from the LRF’s measurements using the least-squares method. The experimental results from the localisation and SLAM experiments in the indoor environment show the applicability of the proposed approach. The main paper contribution is the improvement of the SLAM algorithm convergence due to the noise covariance matrices’ estimation.     

CDKF在车载捷联惯导自对准中的应用

研究了车载捷联惯导在大方位失准角下的静基座自对准。采用Sigma点卡尔曼滤波,根据均值与协方差信息按非线性映射传播的特点,直接利用非线性模型,可以消除EKF存在的需要解析Jacobi矩阵以及将非线性系统线性化后的系统模型误差问题不易调整的弊端,其中的中心差分卡尔曼滤波(CDKF)精度高,且对状态协方差阵不敏感。仿真结果表明,在大方位失准角下采用CDKF进行初始对准,比用传统的EKF更精确且收敛速度更快。     

改进的扩展卡尔曼滤波算法研究

扩展卡尔曼滤波已被广泛地应用到工程实际等各领域,但是此算法因假设过程噪声固定而带来误差,精度不高。研究了一种改进的EKF算法,主要通过假设过程噪声由滤波结果和观测结果得到,再用差分进化算法对所得到的过程噪声方差进行最优化选择来提高滤波精度,通过Matlab对算法进行验证,并与EKF滤波效果、无迹卡尔曼滤波效果进行比较,结果表明,改进的扩展卡尔曼滤波算法减小了状态估计偏差,获得了比较理想的滤波效果,提高了滤波精度。     

Polynomial extended Kalman filter

This work presents a polynomial version of the well-known extended Kalman filter (EKF) for the state estimation of nonlinear discrete-time stochastic systems. The proposed filter, denoted polynomial EKF (PEKF), consists in the application of the optimal polynomial filter of a chosen degree /spl mu/ to the Carleman approximation of a nonlinear system. When /spl mu/=1 the PEKF algorithm coincides with the standard EKF. For the filter implementation the moments of the state and output noises up to order 2/spl mu/ are required. Numerical simulations compare the performances of the PEKF with those of some other existing filters, showing significant improvements.     

On adaptive trajectory tracking of a robot manipulator usinginversion of its neural emulator

This paper is concerned with the design of a neuro-adaptive trajectory tracking controller. The paper presents a new control scheme based on inversion of a feedforward neural model of a robot arm. The proposed control scheme requires two modules. The first module consists of an appropriate feedforward neural model of forward dynamics of the robot arm that continuously accounts for the changes in the robot dynamics. The second module implements an efficient network inversion algorithm that computes the control action by inverting the neural model. In this paper, a new extended Kalman filter (EKF) based network inversion scheme is proposed. The scheme is evaluated through comparison with two other schemes of network inversion: gradient search in input space and Lyapunov function approach. Using these three inversion schemes the proposed controller was implemented for trajectory tracking control of a two-link manipulator. Simulation results in all cases confirm the efficacy of control input prediction using network inversion. Comparison of the inversion algorithms in terms of tracking accuracy showed the superior performance of the EKF based inversion scheme over others.     

基于RLS和EKF算法的全钒液流电池SOC估计

针对全钒液流电池的荷电状态(SOC)估计精度低、估计成本较高等问题,提出一种基于递推最小二乘算法(RLS)与扩展卡尔曼滤波算法(EKF)相结合的估计方法.该方法通过RLS算法辨识所建立的钒电池数学模型参数,通过EKF算法估计钒电池的SOC,将二者结合实现电池参数发生变化时准确估计钒电池的SOC.以5kW/ 30kWh的钒电池为对象,应用所提出的算法实现钒电池的SOC估计.结果表明,该算法可以准确估计钒电池的SOC,且可节省额外增加单片检测电池测量SOC的费用.     

改进粒子群算法优化扩展卡尔曼滤波器电机转速估计

针对感应电机扩展卡尔曼滤波器转速估计中难以取得卡尔曼滤波器系统噪声矩阵和测量噪声矩阵最优值的问题, 提出了一种基于改进粒子群算法优化的扩展卡尔曼滤波器转速估计方法。算法通过融合遗传算法和粒子群算法的优点, 采用可调整的算法模型对粒子群算法进行改进, 将改进的粒子群算法对扩展卡尔曼滤波器中的系统噪声矩阵和测量噪声矩阵进行优化处理, 将优化后的卡尔曼滤波器应用于感应电机转速估计。仿真实验表明, 与试探法、标准粒子群算法及遗传算法比较, 改进粒子群算法优化的扩展卡尔曼滤波器能够有效提高转速估计的精度, 从而提高无速度传感器矢量控制系统的控制性能。     

Observer‐based controller for constrained uncertain stochastic nonlinear discrete‐time systems

In this paper, an observer‐based control approach is proposed for uncertain stochastic nonlinear discrete‐time systems with input constraints. The widely used extended Kalman filter (EKF) is well known to be inadequate for estimating the states of uncertain nonlinear dynamical systems with strong nonlinearities especially if the time horizon of the estimation process is relatively long. Instead, a modified version of the EKF with improved stability and robustness is proposed for estimating the states of such systems. A constrained observer‐based controller is then developed using the state‐dependent Riccati equation approach. Rigorous analysis of the stability of the developed stochastically controlled system is presented. The developed approach is applied to control the performance of a synchronous generator connected to an infinite bus and chaos in permanent magnet synchronous motor. Simulation results of the synchronous generator show that the estimated states resulting from the proposed estimator are stable, whereas those resulting from the EKF diverge. Moreover, satisfactory performance is achieved by applying the developed observer‐based control strategy on the two practical problems. Copyright © 2015 John Wiley & Sons, Ltd.     

FPGA implementation of extended Kalman filter for SOC estimation of lithium‐ion battery in electric vehicle

A FPGA implementation for a model‐based state of charge (SOC) estimation is described in this paper. A Thevenin equivalent circuit model is designed for SOC estimation. The extended Kalman filter (EKF) is designed to complete the SOC estimation, and the error is within 1 % . The FPGA is chosen to achieve realtime SOC estimation. A fast matrix method is proposed to improve the calculation speed of the EKF in FPGA because the EKF algorithm requires many matrix operations. In addition, the embedded system based on the FPGA with a system on a programmable chip (SOPC) technique is built using the Qsys platform in Quartus II. Based on the embedded system, an online testing platform is established to monitor the terminal voltage and load current of the experimental battery in real time; experimental results show that the online SOC estimation is successful. The measurement results show that the FPGA embedded scheme of the EKF allows for successful implementation of the SOC estimation with accuracy and speed. The fast matrix method requires 0.00007 s to implement the SOC estimation and is four times faster than the conventional matrix method.     

Nonlinear Kalman Filters and Particle Filters for integrated navigation of unmanned aerial vehicles

The paper studies and compares nonlinear Kalman Filtering methods and Particle Filtering methods for estimating the state vector of Unmanned Aerial Vehicles (UAVs) through the fusion of sensor measurements. Next, the paper proposes the use of the estimated state vector in a control loop for autonomous navigation and trajectory tracking by the UAVs. The proposed nonlinear controller is derived according to the flatness-based control theory. The estimation of the UAV’s state vector is carried out with the use of (i) Extended Kalman Filtering (EKF), (ii) Sigma-Point Kalman Filtering (SPKF), (iii) Particle Filtering (PF), and (iv) a new nonlinear estimation method which is the Derivative-free nonlinear Kalman Filtering (DKF). The performance of the nonlinear control loop which is based on these nonlinear state estimation methods is evaluated through simulation tests. Comparing the aforementioned filtering methods in terms of estimation accuracy and computation speed, it is shown that the Sigma-Point Kalman Filtering is a reliable and computationally efficient approach to state estimation-based control, while Particle Filtering is well-suited to accommodate non-Gaussian measurements. Moreover, it is shown that the Derivative-free nonlinear Kalman Filter is faster than the rest of the nonlinear filters while also succeeding accurate, in terms of variance, state estimates.     

基于UKF的闪烁噪声机动目标跟踪

闪烁噪声下的机动目标跟踪是一个非线性非高斯系统滤波问题,传统的卡尔曼理论很难保证其跟踪精度.文中提出了一种基于UKF的闪烁噪声机动目标跟踪算法,首先对目标系统的状态方程进行无味变换,然后再进行滤波估计,以减小跟踪误差.UKF不需要求导,它能比EKF更好地迫近目标运动模型的非线性特性,具有更高的估计精度,计算量却与EKF同阶.在仿真实验中采用"协同转弯模型"作为机动目标的运动模型,雷达的量测方程也是非线性的,分别应用UKF和EKF跟踪闪烁噪声下的机动目标,结果表明,UKF能够较好地解决闪烁噪声下跟踪机动目标的难题,其跟踪精度要远远高于EKF.     

A recursive algorithm based on the extended Kalman filter for the training of feedforward neural models

The extended Kalman filter (EKF) is a well-known tool for the recursive parameter estimation of static and dynamic nonlinear models. In particular, the EKF has been applied to the estimation of the weights of feedforward and recurrent neural network models, i.e. to their training, and shown to be more efficient than recursive and nonrecursive first-order training algorithms; nevertheless, these first applications to the training of neural networks did not fully exploit the potentials of the EKF. In this paper, we analyze the specific influence of the EKF parameters for modeling problems, and propose a variant of this algorithm for the training of feedforward neural models which proves to be very efficient as compared to nonrecursive second-order algorithms. We test the proposed EKF algorithm on several static and dynamic modeling problems, some of them being benchmark problems, and which bring out the properties of the proposed algorithm.