基于自适应固定滞后卡尔曼平滑器的状态观测器在假手上的应用

针对以电位计为角度传感器的假手系统,提出了一种基于自适应固定滞后卡尔曼平滑器的状态观测器以观测手指的当前位置、速度和加速度信息.首先,分析了卡尔曼滤波器滤除电位计热噪声并观测速度与加速度的合理性,进而建立了其系统的离散状态转移矩阵.其次,相比卡尔曼滤波器,卡尔曼平滑器在参数相同的情况下具有更好的平滑效果,据此提出一种基于固定滞后卡尔曼平滑器的状态观测器,并通过引入渐消因子以提高动态响应特性.同时给出了一种将本文算法滞后特性降至一个控制周期的有效实现方式.最后,在HIT-V仿人假手实验平台上进行了实验验证.实验结果表明,相比对原始数据直接进行差分,该方法将速度噪声降低了20倍以上,加速度噪声降低了10 000倍以上.相比标准卡尔曼滤波器和固定滞后卡尔曼平滑器,该方法在动态响应方面具有更好的效果.     

New Kalman filter and smoother consistency tests

We derive three new tests that can be applied to a Kalman filter to check for inconsistencies. The Filter Residual Test can detect observations that are outliers but would be missed by a basic residual test because the uncertainty of the expected observation is large relative to the uncertainty of the observation. The Smoother Residual Test uses the output from a Modified Bryson–Frazier (MBF) smoother to detect observations that are outliers. The Smoother State Test compares the state estimates from the filter and MBF smoother to detect model inconsistencies, in particular insufficient process noise.     

Robust Kalman filter and smoother for errors‐in‐variables state space models with observation outliers based on the minimum‐covariance determinant estimator

In this paper, we propose a robust Kalman filter and smoother for the errors‐in‐variables (EIV) state space models subject to observation noise with outliers. We introduce the EIV problem with outliers and then present the minimum covariance determinant (MCD) estimator which is a highly robust estimator in terms of protecting the estimate from the outliers. Then, we propose the randomized algorithm to find the MCD estimate. However, the uniform sampling method has a high computational cost and may lead to biased estimates, therefore we apply the sub‐sampling method. A Monte Carlo simulation result shows the efficiency of the proposed algorithm. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Bayesian robust linear dynamic system approach for dynamic process monitoring

In this paper, a Bayesian robust linear dynamic system approach is proposed for process modeling. Traditional linear dynamic system (LDS) constructed with Kalman filter is designed by Gaussian assumption which can be easily violated in non-Gaussian modeling situations, especially those with outliers. To deal with this issue, the conventional Gaussian-based Kalman filter is modified with heavy tailed Student's t-distribution so as to deal with the non-Gaussian noise and modeling outliers. Then, a variational Bayesian expectation maximization (VBEM) algorithm is developed for learning parameters of the robust linear dynamic system. For process monitoring, traditional monitoring scheme are discussed and the residual space monitoring mechanism has been improved. To explore the feasibility and effectiveness, the proposed method is applied for fault detection, with detailed comparative studies with several other methods through the Tennessee Eastman benchmark.     

On stable, forward, filtering and fixed-lag smoothing in a class of systems with time delays

The problem of optimal estimation (filtering and fixed-lag smoothing) for linear continuous time systems containing multiple time delays can be considerably simplified in the absence of state excitation noise. The optimal filter and fixed-lag smoother can be computed forward in time and are asymptotically stable.     

Robust fusion time‐varying Kalman estimators for multisensor networked systems with mixed uncertainties

This paper addresses the problem of designing robust fusion time‐varying Kalman estimators for a class of multisensor networked systems with mixed uncertainties including multiplicative noises, missing measurements, packet dropouts, and uncertain‐variance linearly correlated measurement and process white noises. By the augmented approach, the original system is converted into a stochastic parameter system with uncertain noise variances. Furthermore, applying the fictitious noise approach, the original system is converted into one with constant parameters and uncertain noise variances. According to the minimax robust estimation principle, based on the worst‐case system with the conservative upper bounds of the noise variances, the five robust fusion time‐varying Kalman estimators (predictor, filter, and smoother) are presented by using a unified design approach that the robust filter and smoother are designed based on the robust Kalman predictor, which include three robust weighted state fusion estimators with matrix weights, diagonal matrix weights, and scalar weights, a modified robust covariance intersection fusion estimator, and robust centralized fusion estimator. Their robustness is proved by using a combination method, which consists of Lyapunov equation approach, augmented noise approach, and decomposition approach of nonnegative definite matrix, such that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. The accuracy relations among the robust local and fused time‐varying Kalman estimators are proved. A simulation example is shown with application to the continuous stirred tank reactor system to show the effectiveness and correctness of the proposed results.     

Robust weighted state fusion Kalman estimators for networked systems with mixed uncertainties

This paper is concerned with robust weighted state fusion estimation problem for a class of time-varying multisensor networked systems with mixed uncertainties including uncertain-variance multiplicative and linearly correlated additive white noises, and packet dropouts. By augmented state method and fictitious noise technique, the original system is converted into one with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst-case system with the conservative upper bounds of uncertain noise variances, four weighted state fusion robust Kalman estimators (filter, predictor and smoother) are presented in a unified form that the robust filter and smoother are designed based on the robust Kalman predictor. Their robustness is proved by the Lyapunov equation approach in the sense that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. Their accuracy relations are proved. The corresponding robust local and fused steady-state Kalman estimators are also presented, and the convergence in a realization between the time-varying and steady-state robust Kalman estimators is proved by the dynamic error system analysis (DESA) method. Finally, a simulation example applied to uninterruptible power system (UPS) shows the correctness and effectiveness of the proposed results.     

A new finite-time linear smoothing filter

A new time-invariant linear smoothing filter is derived for finite data records. The message generating process is assumed to be represented by constant state equations driven by stationary white noise. The smoothing filter transfer function matrix is obtained by solving the finite-time Wiener-Hopf equation in the ε-domain. The filter has the property that it produces an optimal state estimate [xcirc](T₁ |T) at the end of a fixed interval of length [0, T], At other times within the interval the filtor acts as a fixed-lag smoother and gives a sub-optimal state estimate [xcirc](t ₁|t). At times t< T the filter has a fixed memory length. The more conventional optimal time-varying smoother may also be calculated using the expression for the time-invariant smoother impulse response matrix. The major advantage of the time-invariant smoother lies in the ease of implementation. The stability of these smoothing filters is discussed and examples are given of the calculation procedure.     

An adaptive robustizing approach to kalman filtering

The performance of a linear Kalman filter will degrade when the dynamic noise is not Gaussian. A robust Kalman filter based on the m-interval polynomial approximation (MIPA) method for unknown non-Gaussian noise is proposed. Two situations are considered: (a) the state is Gaussian and the observation noise is non-Gaussian; (b) the state is non-Gaussian and the observation noise is Gaussian. It is shown, as compared with other non-Gaussian filters, the MIPA Kalman filter is computationally feasible, unbiased, more efficient and robust. For the scalar model, Monte Carlo simulations are given to demonstrate the ideas involved.     

鲁棒高斯和集合卡尔曼滤波及其在纯角度跟踪中的应用

针对纯角度目标跟踪中量测信息易受异常值和非高斯噪声干扰的问题,提出了一种新的非线性滤波算法–鲁棒高斯和集合卡尔曼滤波(robust Gaussian-sum ensemble Kalman filter,RGSEnKF)算法.首先,采用Huber技术重塑集合卡尔曼滤波的量测更新过程,能够有效地处理量测中的异常值.随后,将改进的集合卡尔曼滤波在高斯和框架下进行扩展,得到RGSEnKF算法,可以进一步解决受非高斯噪声干扰的非线性系统的状态估计问题.此外,新算法中包含距离参数化初始化策略和高斯分量融合策略.前者是为了减小纯角度跟踪中距离信息不可观测的影响,而后者可以避免高斯分量数目随时间不断增长.大量仿真结果验证了新算法的有效性和鲁棒性.     

An LMI approach to periodic discrete-time unbiased filtering

The problem of unbiased filtering for a discrete-time linear periodic system is faced by means of linear matrix inequality techniques. As leading case, we derive the synthesis conditions to obtain an unbiased filter and an unbiased fixed-lag smoother enforcing a bound on the H_∞ performance on the error dynamics.     

Robust ε-contaminated gaussian filtering of discrete-time linear systems

A robust slate estimation of multi-input single-output discrete-time linear systems is considered, where both the system disturbance and observation noise sequences contain outliers. The robust estimation problem is mathematically formulated for a special case assuming that the samples of the system disturbance and observation noise are from a known ε-contaminated gaussian density and a partially known ε-contaminated gaussian density, respectively. Through Monte Carlo simulations, the performance of the proposed robust filter is compared with that of the gaussian sum filter, which is the best non-linear filter when the densities of the underlying uncertainties are completely known. Comparison is also made between the proposed filter and some other available candidates.     

Discrete-time complementary models and smoothing algorithms: The correlated noise case

The concept of complementary models for discrete-time linear finite-dimensional systems with correlated observation and process noise is developed. Using this concept, a new algorithm for the fixed interval smoothing problem is obtained. The new algorithm offers great flexibility with respect to changes in the initial state variancePi_{0}. Next, the relationship among the new smoothing algorithm, the two-filter smoother, and the reversed-time Kalman filter is explored. It is shown that a similarity transformation on the Hamiltonian system simultaneously produces the new smoothing algorithm, as well as the reversed-time Kalman filter.     

Robust centralized and weighted measurement fusion Kalman estimators for uncertain multisensor systems with linearly correlated white noises

This paper addresses the design of robust centralized fusion (CF) and weighted measurement fusion (WMF) Kalman estimators for a class of uncertain multisensor systems with linearly correlated white noises. The uncertainties of the systems include multiplicative noises, missing measurements, and uncertain noise variances. By introducing the fictitious noises, the considered system is converted into one with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst-case system with the conservative upper bounds of uncertain noise variances, the robust CF and WMF time-varying Kalman estimators (predictor, filter, and smoother) are presented in a unified framework. Applying the Lyapunov equation approach, their robustness is proved in the sense that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. Using the information filter, their equivalence is proved. Their accuracy relations are proved. The computational complexities of their algorithms are analyzed and compared. Compared with CF algorithm, the WMF algorithm can significantly reduce the computational burden when the number of sensors is larger. A robust weighted least squares (WLS) measurement fusion filter is also presented only based on the measurement equation, and it is proved that the robust accuracy of the robust CF or WMF Kalman filter is higher than that of robust WLS filter. The corresponding robust fused steady-state estimators are also presented, and the convergence in a realization between the time-varying and steady-state robust fused estimators is proved by the dynamic error system analysis (DESA) method. A simulation example shows the effectiveness and correctness of the proposed results.     

考虑星间测量的航天器自主导航并行滤波器

针对基于星间测量的航天器自主导航问题,本文考虑测量中存在野值的情况,提出了一种轨道根数辅助估计的并行无迹卡尔曼滤波算法.系统由两个并行滤波器组成,通过副滤波器的状态估计识别观测野值,进而在主滤波器中修正导航定位结果.文章选择了星间相对观测两卫星编队的基本构型,研究了算法的阈值参数选择,对不同参数条件下的滤波结果进行了对比.数值仿真说明了该算法在观测量变化率较大时能够有效降低连续野值对自主导航系统的影响,和传统算法相比具有更高的滤波精度和收敛速度.     

一种提高无迹卡尔曼滤波精确度的方法

无迹卡尔曼滤波是通过确定性采样,以无迹变换为基础,用卡尔曼线性滤波框架而建立起来的,对非线性系统有很好的滤波效果,但当噪声的影响较大时,精确度将会减低。为解决上述问题,提出了一种提高无迹卡尔曼滤波(UKF)精确度的方法,它将观测噪声和系统噪声引入到采样点中,对噪声进行对称采样处理,同时改进了算法过程,增加了无迹卡尔曼滤波的抗干扰性,与常规无迹卡尔曼滤波(UKF)相比,不仅保持了系统的稳定性,而且提高了精确度,最后通过仿真进行了验证。     

Filtering for discrete-time linear noise delay systems

Optimal state estimation problem for discrete-time systems with delays in noise sequence is investigated. Predictor similar to the traditional Kalman ones is derived based on projection formula in Hilbert space. Filter and fixed-lag smoother are obtained at the same time. The estimators are presented by solving two coupled Riccati-type difference equations. One example shows the effectiveness of the proposed approach.     

Robust fusion steady‐state filtering for multisensor networked systems with one‐step random delay,missing measurements,and uncertain‐variance multiplicative and additive white noises

The robust fusion steady‐state filtering problem is investigated for a class of multisensor networked systems with mixed uncertainties including multiplicative noises, one‐step random delay, missing measurements, and uncertain noise variances, the phenomena of one‐step random delay and missing measurements occur in a random way, and are described by two Bernoulli distributed random variables with known conditional probabilities. Using a model transformation approach, which consists of augmented approach, derandomization approach, and fictitious noise approach, the original multisensor system under study is converted into a multimodel multisensor system with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst‐case subsystems with conservative upper bounds of uncertain noise variances, the robust local steady‐state Kalman estimators (predictor, filter, and smoother) are presented in a unified framework. Applying the optimal fusion algorithm weighted by matrices, the robust distributed weighted state fusion steady‐state Kalman estimators are derived for the considered system. In addition, by using the proposed model transformation approach, the centralized fusion system is obtained, furthermore the robust centralized fusion steady‐state Kalman estimators are proposed. The robustness of the proposed estimators is proved by using a combination method consisting of augmented noise approach, decomposition approach of nonnegative definite matrix, matrix representation approach of quadratic form, and Lyapunov equation approach, such that for all admissible uncertainties, the actual steady‐state estimation error variances of the estimators are guaranteed to have the corresponding minimal upper bounds. The accuracy relations among the robust local and fused steady‐state Kalman estimators are proved. An example with application to autoregressive signal processing is proposed, which shows that the robust local and fusion signal estimation problems can be solved by the state estimation problems. Simulation example verifies the effectiveness and correctness of the proposed results.     

带不确定方差乘性和加性噪声系统鲁棒加权 融合稳态Kalman估值器

本文研究带不确定方差乘性和加性噪声和带状态相依及噪声相依乘性噪声的多传感器系统鲁棒加权融合估计问题.通过引入虚拟噪声补偿乘性噪声的不确定性,将原系统化为带确定参数和不确定加性噪声方差的系统,进而利用Lyapunov方程方法提出在统一框架下的按对角阵加权融合极大极小鲁棒稳态Kalman估值器(预报器、滤波器和平滑器),其中基于预报器设计滤波器和平滑器,并给出每个融合器的实际估值误差方差的最小上界.证明了融合器的鲁棒精度高于每个局部估值器的鲁棒精度.应用于不间断电源(uninterruptible power system,UPS)系统鲁棒融合滤波的仿真例子说明了所提结果的正确性和有效性.     

基于自适应抗差滤波的WSNs节点跟踪算法

针对无线传感器网络定位误差大、有色噪声影响严重等问题,提出一种基于自适应抗差Kalman滤波的无线传感器网络节点跟踪算法.先采用直线拟合削弱初始点位观测值的横向误差,然后通过构造自适应因子和等价权函数来控制未知有色噪声和观测值粗差的影响,并利用观测环境构造可信度因子干预滤波计算.在低速、高速运动模型下,分别以直线运动和...