A generalized autocovariance least-squares method for Kalman filter tuning

This paper discusses a method for estimating noise covariances from process data. In linear stochastic state-space representations the true noise covariances are generally unknown in practical applications. Using estimated covariances a Kalman filter can be tuned in order to increase the accuracy of the state estimates. There is a linear relationship between covariances and autocovariance. Therefore, the covariance estimation problem can be stated as a least-squares problem, which can be solved as a symmetric semidefinite least-squares problem. This problem is convex and can be solved efficiently by interior-point methods. A numerical algorithm for solving the symmetric is able to handle systems with mutually correlated process noise and measurement noise.     

Continuous-time norm-constrained Kalman filtering

This paper considers continuous-time state estimation when part of the state estimate or the entire state estimate is norm-constrained. In the former case continuous-time state estimation is considered by posing a constrained optimization problem. The optimization problem can be broken up into two separate optimization problems, one which solves for the optimal observer gain associated with the unconstrained state estimates, while the other solves for the optimal observer gain associated with the constrained state estimates. The optimal constrained state estimate is found by projecting the time derivative of an unconstrained estimate onto the tangent space associated with the norm constraint. The special case where the entire state estimate is norm-constrained is briefly discussed. The utility of the filtering results developed are highlighted through a spacecraft attitude estimation example. Numerical simulation results are included.     

中心差分卡尔曼平滑器

针对一类非线性离散系统的状态平滑问题, 本文设计了一种中心差分卡尔曼平滑器(CDKS). 文中基于最小方差估计准则, 详细推导了非线性系统的状态最优平滑递推公式, 并采用中心差分变换来近似计算状态的后验均值和协方差. 相比于传统中心差分卡尔曼滤波器(CDKF), 所设计的CDKS算法有效提高了非线性状态的估计精度, 拓展了中心差分变换的应用范围. 仿真实例验证了所提出平滑器的可行性和有效性.     

基于分解四元数的自适应姿态四元数卡尔曼滤波

基于Clifford代数的四元数卡尔曼滤波在融合陀螺/加表/磁强计以估计姿态时,由于四元数各参数与欧拉角不是一一对应关系,无法独立估计各个欧拉角.这样即使重力观测量是可信的,受到干扰的磁场观测量也会影响整个估计结果.为了消除磁场观测量对四元数中横滚角和俯仰角分量的影响,对四元数进行分解,以重新组合重力/磁场观测量.同时,为了减少载体附近磁场和线性加速度干扰对姿态估计的影响,构造了观测噪声自适应算法和观测量自适应干扰补偿.消费级微机电系统(micro-electro-mechanical system,MEMS)传感器的实验结果表明,对比四元数卡尔曼滤波的原型,改进后的抗干扰能力明显提升.但由于自适应过程引入了两个经验参数,这使得其工作范围和抗干扰能力有待考验.     

FDI by extended Kalman filter parameter estimation for an industrial actuator benchmark

The extended Kalman filter (EKF) is formulated as a parameter estimator and used to estimate position sensor bias and actuator current bias signals for the industrial actuator benchmark system. These bias estimates are compared instantaneously to a threshold for fault detection and identification (FDI). The paper reports results for applying this method to given benchmark data. The FDI performance is good for detecting position sensor and actuator current faults in the presence of unmodeled nonlinear dynamics and an unmodeled load change for small-amplitude signal conditions when the EKF implementation assumes parameter pseudonoise and a slow decay in the parameter dynamics. For large-amplitude signals, the results are reasonably good, but they suggest that a more accurate model for a saturation nonlinearity could improve the method's FDI performance.     

Cubature 卡尔曼滤波与Unscented 卡尔曼滤波估计精度比较

对于不同维数下非线性系统的估计问题,为从常用的Unscented卡尔曼滤波(UKF)和Cubature卡尔曼滤波(CKF)中选取合适的滤波方法,从函数泰勒展开式和数值稳定性上对其进行了分析和比较.由于不同维数下它们捕获函数泰勒展开式高阶项的程度和数值稳定性不同,两者滤波精度出现差异,从而得到了不同维数下滤波方法的选择途径.仿真结果验证了理论分析的正确性.     

Iterative learning Kalman filter for repetitive processes

In this paper, a discrete-time iterative learning Kalman filter scheme is proposed for repetitive processes to reject repeatable disturbances as well as random noises. The proposed state estimator scheme integrates Kalman filter with iterative learning control. The estimation process contains two stages: a conventional Kalman filter is applied in the first stage; the second stage refines the estimates in an iterative learning fashion, leading to a gradual improvement on the estimation performance. According to the estimates that the first stage feeds to the second stage, the optimal design includes two types – posterior type and priori type. In order to reduce the memory and computation load of the optimal design, two suboptimal estimators are provided as well. The stability of the both suboptimal estimators is also studied. Furthermore, a lower bound is given to estimate the ultimate estimation performance before implementing any estimation. Finally, an illustrative example of injection molding is given to verify the performance of the four estimators developed.     

Pole-assignment fixed-interval Kalman smoother with an exponential stability

Using the innovation analysis method in the time domain, based on the autoregressive moving average (ARMA) innovation model and white noise estimators, a pole-assignment fixed-interval steady-state Kalman smoother is presented for discrete-time linear stochastic systems. It avoids the computation of the optimal initial smoothing estimate, and can rapidly eliminate the effect of arbitrary initial smoothing estimate by assigning the poles of the smoother, with an exponentially decaying rate. Several simulation examples show its effectiveness.     

Kalman filter for controlled hybrid systems

The linear partially observed discrete-continuous (hybrid) stochastic controllable system described by differential equations with measures is considered. The optimal filtering equations in the form of generalized Kalman filter are obtained in the case of non-anticipating control. This result could be a theoretical basis for the optimal control in stochastic hybrid systems with incomplete information.     

Relation between filter using covariance information and Kalman filter

This paper presents sequential algorithms for the optimal impulse function, Kalman gain and the error variance in linear least squares filtering problems, when the autocovariance function of the signal is given in the form of a semi-degenerate kernel, and the additive observation noise in white Gaussian. A digital simulation result indicates that the algorithms presented in this paper are feasible, and that the values of Kalman gain and the error variance calculated by these algorithms approach to those obtained by the Kalman filter theory, for time sufficiently large.     

Chebyshev polynomial Kalman filter

A novel Gaussian state estimator named Chebyshev polynomial Kalman filter is proposed that exploits the exact and closed-form calculation of posterior moments for polynomial nonlinearities. An arbitrary nonlinear system is at first approximated via a Chebyshev polynomial series. By exploiting special properties of the Chebyshev polynomials, exact expressions for mean and variance are then provided in computationally efficient vector-matrix notation for prediction and measurement update. Approximation and state estimation are performed in a black-box fashion without the need of manual operation or manual inspection. The superior performance of the Chebyshev polynomial Kalman filter compared to state-of-the-art Gaussian estimators is demonstrated by means of numerical simulations and a real-world application.     

Distributed optimal component fusion weighted by scalars for fixed-lag Kalman smoother

Based on the optimal fusion criterion in the linear minimum variance sense, a distributed optimal fusion fixed-lag Kalman smoother with a three-layer fusion structure is given for the discrete time-varying linear stochastic control systems with multiple sensors and correlated noises. Its components are estimated by scalar weighting fusion, respectively. It only requires in parallel a series of computations of the weighted scalars, and avoids the computations of the weighted matrices, so that the computational burden can obviously be reduced. Further, the steady-state fusion smoother is also given for the discrete time-invariant linear stochastic control systems. The scalar weights can be obtained by fusing once after all local estimations reach steady state. It can reduce the online computational burden. Also, the computation formulas of smoothing error cross-covariance matrices are given. Two simulation examples show the performance.     

An alternative Kalman innovation filter approach for receiver position estimation based on GPS measurements

This article presents an alternative Kalman innovation filter approach for receiver position estimation, based on pseudorange measurements of the global positioning system. First, a dynamic pseudorange model is represented as an ARMAX model and a pseudorange state-space innovation model suitable for both parameter identification and state estimation. The Kalman gain in the pseudorange coordinates is directly calculated from the identified parameters without prior knowledge of the noise properties and the receiver parameters. Then, the pseudorange state-space innovation model is transformed into the receiver state-space innovation model for optimal estimation of the receiver position. Hence, the proposed approach overcomes the drawbacks of the classical Kalman filter approach since it does not require prior knowledge of the noise properties, and the receiver's dynamic model to calculate the Kalman gain. In addition, due to its simplicity, it can be easily implemented in any receiver. To demonstrate the effectiveness of the approach, it is utilized to estimate the position of a stationary receiver and its performance is compared against two versions of the classical Kalman filter approach. The results show that the proposed approach yields consistently good estimation of the receiver position and outperforms the other methods.     

Adaptive tuning of a Kalman filter via fuzzy logic for an intelligent AUV navigation system

This paper describes the implementation of an intelligent navigation system, based on the integrated use of the global positioning system (GPS) and several inertial navigation system (INS) sensors, for autonomous underwater vehicle (AUV) applications. A simple Kalman filter (SKF) and an extended Kalman filter (EKF) are proposed to be used subsequently to fuse the data from the INS sensors and to integrate them with the GPS data. The paper highlights the use of fuzzy logic techniques to the adaptation of the initial statistical assumption of both the SKF and EKF caused by possible changes in sensor noise characteristics. This adaptive mechanism is considered to be necessary as the SKF and EKF can only maintain their stability and performance when the algorithms contain the true sensor noise characteristics. In addition, fault detection and signal recovery algorithms during the fusion process to enhance the reliability of the navigation systems are also discussed herein. The proposed algorithms are implemented to real experimental data obtained from a series of AUV trials conducted by running the low-cost Hammerhead AUV, developed by the University of Plymouth and Cranfield University.     

汽油机非线性卡尔曼滤波暂态进气量估计及空燃比控制

暂态工况下缸进气量的准确估计是提高发动机空燃比控制精度的有效措施之一,为此本文提出一种基于无迹卡尔曼滤波的暂态缸进气量估计算法,并利用估计的缸进气量设计了一种前馈-反馈空燃比控制器.MATLAB环境下的仿真实验给出了所提出的算法与现有进气量估计算法的比较,同时基于暂态气量估计的空燃比控制仿真实验验证了估计的有效性.论文与现有成果的区别在于:一是暂态进气量估计模型不仅包含了歧管压力动态还考虑了曲轴角速度动态,并采用了基于非线性辨识的均值模型;二是考虑了泵气波动的影响,采用了移动平均值法的数字滤波器对泵气波动进行滤波;三是采用无迹卡尔曼滤波算法对歧管压力和曲轴角速度进行估计.     

基于模糊神经网络优化扩展卡尔曼滤波的锂离子电池荷电状态估计

电池荷电状态(state of charge,SOC)的精确估计是判断电池是否过充或过放的重要依据,是电动汽车安全、可靠运行的重要保障.传统基于扩展卡尔曼滤波(extended Kalman filter,EKF)的SOC估计方法过度依赖于精确的电池模型,并且要求系统噪声必须服从高斯白噪声分布.为解决上述问题,基于模糊神经网络(fuzzy neural network,FNN)建立模型误差预测模型,并藉此修正扩展卡尔曼滤波测量噪声协方差,以实现当模型误差较小时对状态估计进行测量更新,而当模型误差较大时只进行过程更新.仿真和实验结果表明,该算法能有效消除由于模型误差和测量噪声统计特性不确定而引入的SOC估计误差,误差在1.2%以内,并且具有较好的收敛性和鲁棒性,适用于电动汽车的各种复杂工况,应用价值较高.     

平方根体积积分卡尔曼滤波

体积积分是一种新的具有较高代数精度的积分方法。为了提高非线性滤波算法的精度和数值稳定性,将体积积分规则和平方根分解引入卡尔曼滤波框架中,提出了平方根体积积分卡尔曼滤波算法（SRCQKF）。新算法采用球半径体积规则和高斯-拉盖尔积分规则计算积分点,利用矩阵的QR分解得到协方差矩阵的平方根并传播平方根。两个典型的非线性系统的实验结果表明,与体积卡尔曼滤波相比,新算法提高了非线性状态的估计精度,具有较高的数值稳定性。     

导弹跟踪中的卡尔曼与不敏卡尔曼滤波

卡尔曼滤波是在线性高斯情况下利用最小均方误差准则获得目标的动态估计,但在实际系统中,许多情况下观测数据与目标动态参数间的关系是非线性的。对于非线性滤波问题,至今尚未得到完善的解法。本文采用了两种方法来进行滤波:一种是将观测变量进行坐标系变化,使量测方程线性化,然后直接进行线性卡尔曼滤波;另一种方法是直接采用非线性滤波方法的不敏卡尔曼滤波。对仿真导弹轨迹的仿真结果显示,第一种方法在本系统中优于第二种方法。     

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.