Clock state estimation with the Kalman-like UFIR algorithm via TIE measurement

We show that recently designed the p-shift unbiased finite impulse response (UFIR) iterative algorithm is highly efficient in applications to clock state estimation via measurement of the time interval error (TIE). The algorithm is Kalman-like, but does not involve noise statistics and initial errors. Its crucial property is that the estimate becomes optimal in the minimum mean square error sense when the estimator memory is large that is typical for clocks. Examples are given for state estimation in an ovenized crystal clock and error prediction in a master clock. Based upon the experimental studies, we show that this algorithm outperforms the Kalman filter requiring the clock noise covariance matrix that is hard to specify correctly even in white Gaussian approximation.     

Combined extended FIR/Kalman filtering for indoor robot localization via triangulation

A combined unbiased finite impulse response (UFIR) and Kalman filtering algorithm is proposed for mobile robot localization via triangulation utilizing noisy measurements. We consider a mobile robot travelling on an indoor floorspace with three nodes in a view. Under the not well-known initial robot state and noise statistics, the extended Kalman filter (EKF) may produce unacceptable estimates. The iterative extended UFIR (EFIR) filter ignores the noise statistics, but requires N initial points of linear measurements which are unavailable. The combined EFIR/Kalman algorithm utilizes N first EKF estimates with approximately set initial conditions and noise statistics as linear measurements for EFIR filter. It is shown that the combined algorithm is more accurate than EKF in robot localization under the real operation conditions. Simulations are provided for piecewise and circular robot trajectories.     

基于Sage窗的自适应Kalman滤波用于钟差预报研究

钟差预报是时间保持工作中的一项关键技术。Kalman算法作为一种最优预报算法,具有实时性的特点,在时间保持工作中得到了广泛的应用。但是由于经典Kalman算法需要准确确定模型随机误差和测量误差,否则状态估计会引入一定的误差,在原子时算法中表现为原子钟噪声和钟差测量噪声。原子钟的噪声参数值通常是通过Allan方差估计,若估计不够准确,Kalman预报将会出现误差。通过研究基于Sage窗的自适应Kalman预报算法,实时修正状态模型误差。利用自适应因子调整状态预测协方差阵有效降低了模型误差,提高了预报精度,最后通过两台氢原子钟和两台铯原子钟的实测数据验证了算法的有效性。     

基于FIR优化滤波的旋转高频信号注入法及其应用

针对传统旋转高频信号注入法中信号处理精度低、延时时间长及过程复杂等缺陷,提出一种基于有限冲激响应(finite impulse response,FIR)优化滤波的改进旋转高频信号注入法.该方法采用等纹波最佳逼近FIR滤波器提取高频电流信号,实现高频电流信号提取误差最小.通过对高频电流作外差处理,提取转子位置误差信号,省去旋转高频信号注入法中的同步轴系滤波单元,降低系统的复杂性.通过线性相位补偿,实现转子速度与位置估计最小延迟.构建无轴承永磁同步电机无速度传感器矢量控制平台,验证算法的有效性.仿真实验结果表明:通过离线优化设计FIR滤波器及线性相位补偿,该方法在全速范围内能够准确估计转子的位置与速度,与卡尔曼滤波相比,其估计精度更高,鲁棒性更强.     

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。     

基于多基站IMMKF-DOA辅助车辆协同定位算法研究

针对传统卡尔曼滤波算法在进行车辆实时运动过程中难以精准定位问题,提出一种基于运动状态自适应的交互多模型卡尔曼滤波(Interacting multiple model Kalman filter,IMMKF)与多基站到达方向(Direction-of-arrival,DOA)相融合进行车辆位置实时估计算法。基于无偏估计器对测量噪声协方差进行实时更新并将其嵌入标准卡尔曼滤波算法中实现自适应交互多模型卡尔曼滤波。针对车辆不同运动状态及动态行驶环境对车辆定位估计精度的影响,构建自适应交互多模型卡尔曼滤波器与多基站信息融合算法进行车辆位置实时估计,考虑不同车速与不同基站数等行驶工况下车辆定位精度的变化趋势,实现车辆实时位置的准确估计。利用PreScan-Simulink联合仿真平台进行虚拟仿真验证和实车试验验证。结果表明,基于交互多模型卡尔曼滤波与到达方向角的融合算法相对标准的卡尔曼滤波估计精度高,较好地改善了传统单一模型的卡尔曼滤波算法在进行车辆实时运动状态估计过程中精准定位问题,实车试验验证了提出算法对车辆定位精度较传统卡尔曼滤波算法的精度提高了一个数量级,实现了更精确的车辆位置估计。     

Bayesian recursive estimation of linear dynamic system states from measurement information

The evaluation of uncertainty in dynamic measurements has recently become a demanding issue. A Bayesian approach is employed here to derive the equations required to recursively generate the solution to the problem of estimating (and predicting) the states of linear dynamic systems. It is shown that this approach allows a derivation of Kalman’s filtering algorithm which is more easily accessible to those involved with dynamic measurements. The complete time-varying Kalman filter is particularly useful when the linear dynamic system and/or signal statistics are time varying and also when optimum estimates are required from the very beginning.     

内燃机瞬时转速测试系统开发

瞬时转速测量的主要误差为晶振脉冲计数误差和转角计量误差。转角计量误差包括角标器分离误差，曲轴扭振产生的误差。论文对瞬时转速的滤波方法进行了分析，认为FIR低通滤波器对高频干扰有抑制作用，对低频干扰信号抑制作用较差，不适于瞬时转速信号滤波。切比雪夫与巴特沃思滤波器对低频干扰信号的抑制效果更好，推荐采用6阶巴特沃思低通滤波器对瞬时转速信号滤波。     

Identifying Bearing Rotor-Dynamic Coefficients Using an Extended Kalman Filter

An extended Kalman filter is developed to estimate the linearized direct and indirect stiffness and damping force coefficients for bearings in rotor-dynamic applications from noisy measurements of the shaft displacement in response to imbalance and impact excitation. The bearing properties are modeled as stochastic random variables using a Gauss-Markov model. Noise terms are introduced into the system model to account for all of the estimation error, including modeling errors and uncertainties and the propagation of measurement errors into the parameter estimates. The system model contains two user-defined parameters that can be tuned to improve the filter's performance; these parameters correspond to the covariance of the system and measurement noise variables. The filter is also strongly influenced by the initial values of the states and the error covariance matrix. The filter is demonstrated using numerically simulated data for a rotor-bearing system with two identical bearings, which reduces the number of unknown linear dynamic coefficients to eight. The filter estimates the direct damping coefficients and all four stiffness coefficients correlated well with actual values, whereas the estimates the cross-coupled damping coefficients were the least accurate.     

S-修正的自适应卡尔曼滤波与模糊卡尔曼滤波相结合的汽车状态估计算法

精确的汽车状态信息的获取是汽车动态控制系统正常工作的前提。建立了二自由度汽车动力学模型,提出了将S-修正的自适应卡尔曼滤波与模糊卡尔曼滤波相结合进行汽车关键状态估计的方法。模糊卡尔曼滤波利用所设计的模糊控制器通过实时监测信息实际方差与理论方差的比值,实现对时变量测噪声的协方差矩阵的实时在线估计,提高了算法在时变量测噪声情况下的鲁棒性;S-修正的自适应卡尔曼滤波算法基于滤波不发散理论推导得出实时修正因子S,进而对估计误差协方差矩阵直接加权。两种方法的结合在总体上提高了在汽车动力学系统过程噪声与量测噪声协方差矩阵不准确情况下算法的鲁棒性与估计精度,最后通过基于ADAMS的虚拟试验验证了该方法的有效性。     

Multi-frequency periodic vibration suppressing in active magnetic bearing-rotor systems via response matching in frequency domain

A method for multi-frequency periodic vibration suppressing in active magnetic bearing (AMB)-rotor systems is proposed, which is based on an adaptive finite-duration impulse response (FIR) filter in time domain. Firstly, the theoretic feasibility of the method is proved. However, two problems would be unavoidable, if the conventional adaptive FIR filter is adopted in practical application. One is that the convergence rate of the different frequency components may be highly disparate in multi-frequency vibration control. The other is that the computational complexity is significantly increased because the long memory FIR filter is required to match the transient response time of the AMB-rotor system. To overcome the problems above, the Fast Block Least Mean Square (FBLMS) algorithm is adopted to efficiently implement the computation in frequency domain at a computational cost far less than that of the conventional FIR filter. By the FBLMS algorithm, regardless of the number of the considered frequency components in vibration disturbance, the computational complexity would be invariable. Moreover, filter’s weights in the FBLMS algorithm have the intuitional relation with signal’s frequency. As a result, the convergence rate of each frequency component can be adjusted by assigning the individual step size parameter for each weight.Experiments with the reciprocating simulating disturbance test and the rotating harmonic vibration test were carried out on an AMB-rigid rotor test rig with a vertical shaft. The experiment results indicate that the proposed method with the FBLMS algorithm can achieve the good effectiveness for suppressing the multi-frequency vibration. The convergence property of each frequency component can be adjusted conveniently. Each harmonic component of the vibration can be addressed, respectively, by reconfiguring the frequency components of the reference input signal.     

A hybrid unscented filtering and particle swarm optimization technique for harmonic analysis of nonstationary signals

This paper presents a modified unscented Kalman filter for accurate estimation of frequency and harmonic components of a time-varying signal embedded in noise with low signal-to-noise ratio. Further, the model and measurement error covariances along with the unscented Kalman filter parameters are selected using a modified particle swarm optimization algorithm. To circumvent the problem of premature convergence and local minima, a dynamically varying inertia weight based on the variance of the population fitness is used. This results in a better local and global searching ability of the particles, which improves the convergence of the velocity and better accuracy of the unscented Kalman filter parameters. Various simulation results for nonstationary sinusoidal signals with time varying amplitude, phase and harmonic content corrupted with noise, reveal significant improvement in noise rejection and speed of convergence and accuracy in comparison to the well known extended Kalman filter.     

Distributed and decentralized state estimation in gas networks as distributed parameter systems

In this paper, a framework for distributed and decentralized state estimation in high-pressure and long-distance gas transmission networks (GTNs) is proposed. The non-isothermal model of the plant including mass, momentum and energy balance equations are used to simulate the dynamic behavior. Due to several disadvantages of implementing a centralized Kalman filter for large-scale systems, the continuous/discrete form of extended Kalman filter for distributed and decentralized estimation (DDE) has been extended for these systems. Accordingly, the global model is decomposed into several subsystems, called local models. Some heuristic rules are suggested for system decomposition in gas pipeline networks. In the construction of local models, due to the existence of common states and interconnections among the subsystems, the assimilation and prediction steps of the Kalman filter are modified to take the overlapping and external states into account. However, dynamic Riccati equation for each subsystem is constructed based on the local model, which introduces a maximum error of 5% in the estimated standard deviation of the states in the benchmarks studied in this paper. The performance of the proposed methodology has been shown based on the comparison of its accuracy and computational demands against their counterparts in centralized Kalman filter for two viable benchmarks. In a real life network, it is shown that while the accuracy is not significantly decreased, the real-time factor of the state estimation is increased by a factor of 10.     

基于双层修正无迹卡尔曼的水下节点定位算法* .txt

摘要：针对水下无线传感网络中运动节点定位精度低的问题,提出了一种新的基于双层修正无迹卡尔曼的水下节点定位算法(DLMUKF)。该算法利用下层无迹卡尔曼滤波算法对节点状态进行预测,根据各信标节点的测距传播时延对预测的节点状态进行修正。运用上层无迹卡尔曼滤波算法对修正后的状态进行新的预测与修正。仿真实验中,DLMUKF算法的平均定位误差约为传统多边定位算法的15%,约为基于无迹卡尔曼滤波（UKF）定位算法的16%,受节点运动时间与速度的影响最小。通过实验证明DLMUKF算法能更充分利用实际距离值,可以有效减小运动节点的定位误差。 .txt     

Real-time FPGA-based Kalman filter for constant and non-constant velocity periodic error correction

Displacement measuring interferometry has high resolution and high dynamic range, which is widely used in displacement metrology and sensor calibration. Due to beam leakage in the interferometer, imperfect polarization components, and ghost reflections, the displacement measurement suffers from periodic error, whose pitch is multiple harmonics of the Doppler frequency. In dynamic measurements, periodic error is usually on the order of nanometers, which impacts the dynamic measurement accuracy. This paper presents an approach to estimate and correct periodic error in real time based on an extended Kalman filter, which has the capability to deal with both constant and non-constant velocity motions. This algorithm is implemented on an application-specific hardware architecture in an FPGA, which has advantages in throughput and resource usage compared with conventional implementations. The measurement validation shows that this approach can effectively eliminate the periodic error for both constant and non-constant velocity motion, and the residual error reaches to the level of the background noise of the interferometer.     

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.     

分布式驱动电动汽车双无迹卡尔曼滤波状态参数联合观测

为实时观测分布式驱动电动汽车行驶过程中的车身质心侧偏角等状态及车辆惯性参数如车辆质量、横摆转动惯量等信息,针对车辆惯性参数估计易敏感于载荷参数变化的挑战,发展面向载荷参数不确定（乘客或货物加载）的纵向、侧向、横摆运动的四轮车辆非线性动力学系统估计模型,在融合轮毂转矩等车载多传感器信息的基础上,将能适应强非线性系统的无迹卡尔曼滤波引入到车辆惯性参数估计中,设计车辆并联双无迹卡尔曼滤波状态参数联合观测系统,其中一个无迹卡尔曼滤波器观测车辆速度、车身质心侧偏角等状态,而另一个无迹卡尔曼滤波器观测车辆惯性参数。在CarSim/Matlab高保真环境中使用双移线、正弦工况对观测器在不同的载荷加载条件的可行性和有效性进行仿真验证,结果表明：该观测系统能实时观测车辆运行的状态及车辆惯性参数,即使在重载荷加载条件下仍具有较高的观测精度。     

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.     

基于BP神经网络的Kalman滤波算法的改进

针对传统的Kalman滤波算法在机动较强的目标跟踪中误差变大甚至发散的缺点,考虑到BP神经网络具有较强的非线性逼近能力,提出了用BP神经网络辅助Kalman滤波的新算法,仿真表明该算法优于传统的Kalman滤波算法.