Joint state and parameter estimation in particle filtering and stochastic optimization

In this paper, an adaptive estimation algorithm is proposed for non-linear dynamic systems with unknown static parameters based on combination of particle filtering and Simultaneous Perturbation Stochastic Approxi- mation （SPSA） technique. The estimations of parameters are obtained by maximum-likelihood estimation and sampling within particle filtering framework, and the SPSA is used for stochastic optimization and to approximate the gradient of the cost function. The proposed algorithm achieves combined estimation of dynamic state and static parameters of nonlinear systems. Simulation result demonstrates the feasibilitv and efficiency of the proposed algorithm     

A Fusion Kalman Filter and UFIR Estimator Using the Influence Function Method

In this paper,the Kalman filter(KF)and the unbiased finite impulse response(UFIR)filter are fused in the discrete-time state-space to improve robustness against uncertainties.To avoid the problem where fusion filters may give up some advantages of UFIR filters by fusing based on noise statistics,we attempt to find a way to fuse without using noise statistics.The fusion filtering algorithm is derived using the influence function that provides a quantified measure for disturbances on the resulting filtering outputs and is termed as an influence finite impulse response(IFIR)filter.The main advantage of the proposed method is that the noise statistics of process noise and measurement noise are no longer required in the fusion process,showing that a critical feature of the UFIR filter is inherited.One numerical example and a practice-oriented case are given to illustrate the effectiveness of the proposed method.It is shown that the IFIR filter has adaptive performance and can automatically switch from the Kalman estimate to the UFIR estimates according to operating conditions.Moreover,the proposed method can reduce the effects of optimal horizon length on the UFIR estimate and can give the state estimates of best accuracy among all the compared methods.     

Robust state estimation for uncertain linear systems with deterministic input signals

In this paper, we investigate state estimations of a dynamical system in which not only process and measurement noise, but also parameter uncertainties and deterministic input signals are involved. The sensitivity penalization based robust state estimation is extended to uncertain linear systems with deterministic input signals and parametric uncertainties which may nonlinearly affect a state-space plant model. The form of the derived robust estimator is similar to that of the well-known Kalman filter with a comparable computational complexity. Under a few weak assumptions, it is proved that though the derived state estimator is biased, the bound of estimation errors is finite and the covariance matrix of estimation errors is bounded. Numerical simulations show that the obtained robust filter has relatively nice estimation performances.     

Kalman filtering with partial Markovian packet losses

We consider the Kalman filtering problem in a networked environment where there are partial or entire packet losses described by a two state Markovian process. Based on random packet arrivals of the sensor measurements and the Kalman filter updates with partial packet, the statistical properties of estimator error covariance matrix iteration and stability of the estimator are studied. It is shown that to guarantee the stability of the Kalman filter, the communication network is required to provide for each of the sensor measurements an associated throughput, which captures all the rates of the successive sensor measurements losses. We first investigate a general discrete-time linear system with the observation partitioned into two parts and give sufficient conditions of the stable estimator. Furthermore, we extend the results to a more general case where the observation is partitioned into n parts. The results are illustrated with some simple numerical examples.     

Adaptive RBF neural network control of robot with actuator nonlinearities

In this paper, an adaptive neural network control scheme for robot manipulators with actuator nonlinearities is presented. The control scheme consists of an adaptive neural network controller and an actuator nonlinearities compensator. Since the actuator nonlinearities are usually included in the robot driving motor, a compensator using radial basis function (RBF) network is proposed to estimate the actuator nonlinearities and eliminate their effects. Subsequently, an adaptive neural network controller that neither requires the evaluation of inverse dynamical model nor the time-consuming training process is given. In addition, GL matrix and its product operator are introduced to help prove the stability of the closed control system. Considering the adaptive neural network controller and the RBF network compensator as the whole control scheme, the closed-loop system is proved to be uniformly ultimately bounded (UUB). The whole scheme provides a general procedure to control the robot manipulators with actuator nonlinearities. Simulation results verify the effectiveness of the designed scheme and the theoretical discussion.     

An improved self-calibration approach based on adaptive genetic algorithm for position-based visual servo

An improved self-calibrating algorithm for visual servo based on adaptive genetic algorithm is proposed in this paper. Our approach introduces an extension of Mendonca-Cipolla and G. Chesi＇s self-calibration for the positionbased visual servo technique which exploits the singular value property of the essential matrix. Specifically, a suitable dynamic online cost function is generated according to the property of the three singular values. The visual servo process is carried out simultaneous to the dynamic self-calibration, and then the cost function is minimized using the adaptive genetic algorithm instead of the gradient descent method in G. Chesi＇s approach. Moreover, this method overcomes the limitation that the initial parameters must be selected close to the true value, which is not constant in many cases. It is not necessary to know exactly the camera intrinsic parameters when using our approach, instead, coarse coding bounds of the five parameters are enough for the algorithm, which can be done once and for all off-line. Besides, this algorithm does not require knowledge of the 3D model of the object. Simulation experiments are carried out and the results demonstrate that the proposed approach provides a fast convergence speed and robustness against unpredictable perturbations of camera parameters, and it is an effective and efficient visual servo algorithm.     

Using DragPushing to Refine Concept Index for Text Categorization

Concept index （CI） is a very fast and efficient feature extraction （FE） algorithm for text classification. The key approach in CI scheme is to express each document as a function of various concepts （centroids） present in the collection. However,the representative ability of centroids for categorizing corpus is often influenced by so-called model misfit caused by a number of factors in the FE process including feature selection to similarity measure. In order to address this issue, this work employs the ＂DragPushing＂ Strategy to refine the centroids that are used for concept index. We present an extensive experimental evaluation of refined concept index （RCI） on two English collections and one Chinese corpus using state-of-the-art Support Vector Machine （SVM） classifier. The results indicate that in each case, RCI-based SVM yields a much better performance than the normal CI-based SVM but lower computation cost during training and classification phases.     

Normalized estimation of fundamental frequency and measurement of harmonics/interharmonics

An adaptive notch filter is presented to estimate the fundamental frequency and measure both harmonics and interharmonics of an almost periodic signal with unknown time-variant fundamental frequency, which has the robustness that the convergence speed is determined by neither amplitude nor frequency of fundamental component. The algorithm forms a one-dimensional slow adaptive integral manifold whose existence and stability are proved by averaging method and Lyapunov stability theorem. The local exponential stability and the ultimate boundedness of fundamental frequency estimation are proved. The local exponential stability makes sure that the fundamental frequency, the harmonic and interharmonic components can be all fast tracked. The principle for adjusting the parameters with their influences on transient and steady-state performance is investigated and decreasing parameters can improve noise characteristic. The validity is verified by simulation results.     

Formation and obstacle avoidance control for multiagent systems

This paper considers the problems of formation and obstacle avoidance for multiagent systems.The objective is to design a term of agents that can reach a desired formation while avoiding collision with obstacles.To reduce the amount of information interaction between agents and target,we adopt the leader-follower formation strategy.By using the receding horizon control (RHC),an optimal problem is formulated in terms of cost minimization under constraints.Information on obstacles is incorporated online as sensed in a limited sensing range.The communication requirements between agents are that the followers should obtain the previous optimal control trajectory of the leader to each update time.The stability is guaranteed by adding a terminal-state penalty to the cost function and a terminal-state region to optimal problem.Finally,simulation studies are provided to verify the effectiveness of the proposed approach.     

An Evolving Autoregressive Predictor for Time Series Forecasting

AR （Autoregressive） model is a common predictor that has been extensively used for time series forecasting. Many training methods can used to update AR model parameters, for instance, least square estimate and maximum likelihood estimate; however, both techniques are sensitive to noisy samples and outliers. To deal with the problems, an evolving AR predictor---EAR, is developed in this work to enhance prediction accuracy and mitigate the effect of noisy samples and outliers. The model parameters of EAR are trained with an ALSE （adaptive least square estimate） method, which can learn samples characteristics more effectively. In each training epoch, the ALSE weights the samples by their fitting accuracy. The samples with larger fitting errors will be given a larger penalty value in the cost function; however, the penalties of difficult-to-predict samples will be adaptively reduced to enhance the prediction accuracy. The effectiveness of the developed EAR predictor is verified by simulation tests. Test results show that the proposed EAR predictor can capture the dynamics of the time series effectively and predict the future trend accurately.     

一种用于移动机器人状态和参数估计的自适应UKF算法

为了提高 UKF 的估计精度和收敛性, 提出了一种新的自适应滤波方法. 新息方差阵的测量值和其相应的估计/预测值的差被用于构造指标函数. MIT 规则被用于构造自适应机制以指标函数最小来在线更新过程不确定性的方差值. 更新后的方差反馈给常规 UKF. 这种自适应机制主要用于补偿过程噪声分布的先验信息不足以及提高 UKF 状态和参数的主动估计性能. 讨论了自适应 UKF 的渐进稳定性. 在全方位移动机器人上进行了仿真, 结果表明与常规的 UKF 相比自适应 UKF 更有效更精确.     

传感器故障条件下的自适应UKF 算法

针对目标跟踪中传感器故障导致滤波发散或者滤波精度不高的问题, 提出一种自适应无迹卡尔曼滤波(UKF) 算法. 该算法在滤波过程中, 根据自适应估计原理引入自适应矩阵因子, 实时调整系统状态向量和量测新息向量的协方差, 以满足无迹卡尔曼滤波算法的最优性条件, 并采取措施对滤波发散的情况进行判断和抑制. 与传统UKF和已有自适应UKF算法相比, 该自适应UKF算法显著提高了滤波精度和数值稳定性, 且具有应对传感器故障的自适应能力. 仿真实验结果表明了所提出算法的有效性.

     

改进型粒子滤波算法在多站纯方位被动跟踪中的应用

针对多站纯方位被动定位与跟踪问题,给出了一种基于均匀重采样和带白适应因子的改进型粒子滤波算法．首先,基于无迹卡尔曼（UKF）粒子滤波器,将参考分布融入最新观测信息,得到符合真实状态的后验概率分布：借助重采样和使用鲁棒估计,改善了粒子滤波的退化问题．其次,引入自适应因子以调整UKF的状态模型协方差与观测模型协方差的比例,得到较高精度的概率分布．仿真结果表明,改进的粒子滤波算法能够实现多站纯方位被动跟踪,比传统非线性滤波器有更高的跟踪精度．     

基于通用FLAC的模糊自适应UKF算法及其应用

针对量测噪声方差统计值未知的非线性UKF(Unscented Kalman Filter)滤波问题,提出了一种基于通用FLAC(Fussy Logic Adaptive Controller)的模糊自适应UKF算法.在标准的非线性UKF算法基础上,以残差的实际方差与理论方差的比值作为FLAC的输入,使FLAC对滤波模型的依赖性减弱,强化了模糊自适应UKF方法的通用性;在对未知的量测噪声方差阵进行动态调节的过程中设置了指数调节参数,可不同程度地放大或缩小方差阵调节的幅度,使算法的调节速度和精度得到控制.将算法应用于GPS/DR(Dead-Reckoning)组合导航系统中,仿真结果表明了该算法的有效性.     

带噪声统计估计器的Unscented卡尔曼滤波器设计

针对传统Unscented卡尔曼滤波器(UKF)在噪声先验统计未知或不准确时滤波精度下降甚至发散的问题,基于极大后验(MAP)估计原理,设计了一种带噪声统计估计器的UKF.该UKF滤波算法在进行状态估计的同时,能实时估计和修正噪声均值和协方差.相比于传统UKF,所提出的UKF具有应对噪声统计变化的自适应能力.仿真结果表明了该UKF滤波算法的有效性.

Abstract：

For the problem that the accuray of the conventional UKF declines and further diverges when the prior noise statistic is unknown or inaccurate, an unscented Kalman filter (UKF) with noise statistic estimator is designed.This UKF filtering algorithm based on maximum a posterior (MAP) estimation can estimate and correct the mean and covariance of the noise in real time while it estimates the states.The proposed UKF has the adaptive capability of dealing with variable noise statistic.The simulation results show the effectiveness of the proposed UKF filtering algorithm.     

自适应无迹卡尔曼滤波算法在地磁导航中的应用

考虑到地磁导航过程中,无迹卡尔曼滤波(UKF)受初始值误差、系统噪声不确定性和环境磁异常扰动这些因素的影响,将自适应估计原理引入到UKF算法,提高UKF算法的收敛性和地磁导航系统的稳定性.计算结果表明,在地磁导航系统数据处理中,UKF算法略优于扩展卡尔曼滤波(EKF),自适应UKF算法优于自适应EKF算法,自适应UKF算法能够很好地抑制初始化误差、系统噪声不确定性和环境磁异常扰动对导航解的影响,进一步提高地磁导航系统的定位精度和可靠性.     

用四元数状态切换无迹卡尔曼滤波器估计的飞行器姿态

在较大初始姿态误差角下, 针对捷联惯导/CCD星敏感器(strap-intertial navigation system/CCD star sensor, SINS/CCD)姿态估计系统扩展卡尔曼滤波(extended Kalman filter, EKF)算法精度下降的问题, 提出了基于四元数的状态切换无迹卡尔曼滤波算法. 通过状态实时切换降低了全维无迹卡尔曼滤波(unscented Kalman filter, UKF)的维数, 减小了计算复杂度, 提高了系统的实时性. 文中采用基于特征向量求解的代价函数法计算四元数均值避免了UKF算法中四元数规范化的限制; 利用乘性误差四元数表示姿态更新点与估计点之间的距离, 解决了四元数协方差阵奇异性问题. 仿真实验结果表明: 与EKF相比, 该算法在精度上有较大提高; 与全维UKF算法和修正罗德里格斯参数UKF算法相比, 该算法精度相当但估计时间均有不同程度的减少.     

An adaptive unscented Kalman filter approach to secure state estimation for wireless sensor networks

Wireless sensor networks are vulnerable to false data injection attacks, which may mislead the state estimation. To solve this problem, this paper presents a chi-square test-based adaptive secure state estimation (CTASSE) algorithm for state estimation and attack detection. Taking advantage of Kalman filters, attack signal together with process noise or measurement noise are described as total white Gaussian noise with uncertain covariance matrix. The chi-square test method is used in the adaptation of the total noise covariance and attack detection. Then, a standard adaptive unscented Kalman filter (UKF) is used for the state estimation. Finally, simulation results show that the proposed CTASSE algorithm performs better than other UKFs in state estimation and is also effective in real-time attack detection.     

Interacting multiple model estimation-based adaptive robust unscented Kalman filter

The unscented Kalman filter (UKF) is a promising approach for the state estimation of nonlinear dynamic systems due to its simple calculation process and superior performance in highly nonlinear systems. However, its solution will be degraded or even divergent when the system model involves uncertainty. This paper presents an interacting multiple model (IMM) estimation-based adaptive robust UKF to address this problem. This method combines the merits of the adaptive fading UKF and robust UKF and discards their demerits to inhibit the disturbance of system model uncertainty on the filtering solution. An adaptive fading UKF for the case of process model uncertainty and a robust UKF for the case of measurement model uncertainty are established based on the principle of innovation orthogonality. Subsequently, an IMM estimation is developed to fuse the adaptive fading UKF and robust UKF as sub-filters according to the mode probability. The system state estimation is achieved as a probabilistic weighted sum of the estimation results from the two sub-filters. Simulations, experiments and comparison analysis validate the efficacy of the proposed method.     

On the iterated forms of Kalman filters using statistical linearization

The extended Kalman filter (EKF) is a suboptimal estimator of the conditional mean and covariance for nonlinear state estimation. It is based on first order Taylor series approximation of nonlinear state functions. The unscented Kalman filter (UKF) and the ensemble Kalman filter (EnKF) are suboptimal estimators that are termed as Jacobian free because they do not require the existence of the Jacobian of the nonlinearity. The iterated form of EKF is an estimator of the conditional mode that employs an approximate Newton–Raphson iterative scheme to solve the maximization of the conditional probability density function. In this paper, the iterated forms of UKF and EnKF are presented that perform Newton–Raphson iteration without explicitly differentiating the nonlinear functions. The use of statistical linearization in iterated UKF and EnKF is a nondifferentiable optimization method when the measurement function is nonsmooth or discontinuous. All three iterated forms can be shown to be conditional mean estimators after the first iteration. A simple numerical example involving continuous and discontinuous measurment functions is included to evaluate the performance of the algorithms for the estimation of conditional mean, covariance and mode. A batch reactor simulation is shown for estimating both the states and unknown parameters.