Multi-sensor information fusion estimators for stochastic uncertain systems with correlated noises

The information fusion estimation problems are investigated for multi-sensor stochastic uncertain systems with correlated noises. The stochastic uncertainties caused by correlated multiplicative noises exist in the state and observation matrices. The process noise and the observation noises are one-step auto-correlated and two-step cross-correlated, respectively. While the observation noises of different sensors are one-step cross-correlated. The optimal centralized fusion filter, predictor and smoother are proposed in the linear minimum variance sense via an innovative analysis approach. To enhance the robustness and flexibility, a distributed fusion filter is put forward, which requires the calculation of filtering error cross-covariance matrices between any two local filters. To avoid the calculation of cross-covariance matrices, another distributed fusion filter is also presented by using the covariance intersection (CI) fusion algorithm, which can reduce the computational cost. A simulation example is given to show the effectiveness of the proposed algorithms.     

Optimal linear filter design for systems with correlation in the measurement matrices and noises: recursive algorithm and applications

This paper addresses the optimal least-squares linear estimation problem for a class of discrete-time stochastic systems with random parameter matrices and correlated additive noises. The system presents the following main features: (1) one-step correlated and cross-correlated random parameter matrices in the observation equation are assumed; (2) the process and measurement noises are one-step autocorrelated and two-step cross-correlated. Using an innovation approach and these correlation assumptions, a recursive algorithm with a simple computational procedure is derived for the optimal linear filter. As a significant application of the proposed results, the optimal recursive filtering problem in multi-sensor systems with missing measurements and random delays can be addressed. Numerical simulation examples are used to demonstrate the feasibility of the proposed filtering algorithm, which is also compared with other filters that have been proposed.     

A new approach to distributed fusion filtering for networked systems with random parameter matrices and correlated noises

This paper is concerned with the distributed filtering problem for a class of discrete-time stochastic systems over a sensor network with a given topology. The system presents the following main features: (i) random parameter matrices in both the state and observation equations are considered; and (ii) the process and measurement noises are one-step autocorrelated and two-step cross-correlated. The state estimation is performed in two stages. At the first stage, through an innovation approach, intermediate distributed least-squares linear filtering estimators are obtained at each sensor node by processing available output measurements not only from the sensor itself but also from its neighboring sensors according to the network topology. At the second stage, noting that at each sampling time not only the measurement but also an intermediate estimator is available at each sensor, attention is focused on the design of distributed filtering estimators as the least-squares matrix-weighted linear combination of the intermediate estimators within its neighborhood. The accuracy of both intermediate and distributed estimators, which is measured by the error covariance matrices, is examined by a numerical simulation example where a four-sensor network is considered. The example illustrates the applicability of the proposed results to a linear networked system with state-dependent multiplicative noise and different network-induced stochastic uncertainties in the measurements; more specifically, sensor gain degradation, missing measurements and multiplicative observation noises are considered as particular cases of the proposed observation model.     

Gaussian approximate filter for stochastic dynamic systems with randomly delayed measurements and colored measurement noises带随机延迟量测和有色量测噪声随机动态系统的高斯近似滤波器

In this paper, a new Gaussian approximate (GA) filter for stochastic dynamic systems with both one-step randomly delayed measurements and colored measurement noises is presented. For linear systems, a Kalman filter can be obtained to include one-step randomly delayed measurements and colored measurement noises. On the other hand, for nonlinear stochastic dynamic systems, different GA filters can be developed which exploit numerical methods to compute Gaussian weighted integrals involved in the proposed Bayesian solution. Existing GA filter with one-step randomly delayed measurements and existing GA filter with colored measurement noises are special cases of the proposed GA filter. The efficiency and superiority of the proposed method are illustrated in a numerical example concerning a target tracking problem.     

带随机量测时滞和随机丢包的改进无迹卡尔曼滤波

经典卡尔曼滤波要求量测值可实时获取,且仅适用于线性系统.然而,在工程实际应用中,系统多为非线性系统,量测值也会发生滞后或者丢失等现象,此时经典卡尔曼滤波已不适用.因此,本文针对一类带有随机量测一步时滞和随机丢包的非线性离散系统的状态估计问题,用两个满足伯努利分布的独立随机变量来描述随机量测一步滞后和随机丢包的现象.当量测丢失时,用量测值的一步预测值来代替零输入进行补偿.在此基础上应用正交投影理论和无迹变换的方法提出了一种改进的无迹卡尔曼滤波算法.最后,通过仿真例子验证在考虑随机量测一步时滞和随机丢包的情况下,所提出的改进算法相比于经典无迹卡尔曼滤波算法具有更高的精度.     

Optimal state estimation for networked systems with random parameter matrices,correlated noises and delayed measurements

In this paper, the optimal least-squares state estimation problem is addressed for a class of discrete-time multisensor linear stochastic systems with state transition and measurement random parameter matrices and correlated noises. It is assumed that at any sampling time, as a consequence of possible failures during the transmission process, one-step delays with different delay characteristics may occur randomly in the received measurements. The random delay phenomenon is modelled by using a different sequence of Bernoulli random variables in each sensor. The process noise and all the sensor measurement noises are one-step autocorrelated and different sensor noises are one-step cross-correlated. Also, the process noise and each sensor measurement noise are two-step cross-correlated. Based on the proposed model and using an innovation approach, the optimal linear filter is designed by a recursive algorithm which is very simple computationally and suitable for online applications. A numerical simulation is exploited to illustrate the feasibility of the proposed filtering algorithm.     

Optimal distributed Kalman filtering fusion for a linear dynamic system with cross-correlated noises

In this article, we study the distributed Kalman filtering fusion problem for a linear dynamic system with multiple sensors and cross-correlated noises. For the assumed linear dynamic system, based on the newly constructed measurements whose measurement noises are uncorrelated, we derive a distributed Kalman filtering fusion algorithm without feedback, and prove that it is an optimal distributed Kalman filtering fusion algorithm. Then, for the same linear dynamic system, also based on the newly constructed measurements, a distributed Kalman filtering fusion algorithm with feedback is proposed. A rigorous performance analysis is dedicated to the distributed fusion algorithm with feedback, which shows that the distributed fusion algorithm with feedback is also an optimal distributed Kalman filtering fusion algorithm; the P matrices are still the estimate error covariance matrices for local filters; the feedback does reduce the estimate error covariance of each local filter. Simulation results are provided to demonstrate the validity of the newly proposed fusion algorithms and the performance analysis.     

网络化不确定系统集中式融合鲁棒稳态估值器

对于一类在状态转移阵和系统观测阵中带相同的状态依赖乘性噪声、带噪声依赖乘性噪声、一步随机观测滞后、丢包和不确定噪声方差的多传感器网络化系统,文章研究其鲁棒集中式融合稳态滤波问题.应用增广方法将系统转换为带随机参数矩阵、相同过程和观测噪声的集中式融合系统.应用去随机化方法和虚拟噪声技术,系统进一步转化为仅带不确定噪声方差的集中式融合系统.根据极大极小鲁棒估计原理,本文提出了鲁棒集中式融合稳态Kalman估值器(预报器、滤波器和平滑器),证明了所提出的集中式融合估值器的鲁棒性,给出了鲁棒局部与集中式融合估值器之间的精度关系.本文提出了应用于多传感器多通道滑动平均(MA)信号估计的一个实例,给出了相应的鲁棒局部和集中式融合信号估值器.仿真实验验证了所提出方法的有效性和正确性.     

Distributed optimal fusion steady-state Kalman filter for systems with coloured measurement noises

Based on the optimal fusion criterion weighted by matrices in the linear minimum variance sense, an optimal information fusion steady-state Kalman filter is given for the discrete time-invariant linear stochastic control system measured by multiple sensors with coloured measurement noises, which is equivalent to an optimal information fusion steady-state Kalman predictor with a two-layer fusion structure for system with correlated noises. Furthermore, the steady-state optimal fusion predictor can be obtained only by fusing once after all local subsystems enter the steady-state predictions. The solution of steady-state prediction error cross-covariance matrix between any two subsystems can be obtained by iteration with an arbitratry initial value, whose convergence is proved. Applying it to a tracking system with three sensors shows its effectiveness.     

带有色观测噪声系统多传感器标量加权最优信息融合稳态Kalman滤波器

基于标量加权多传感器线性最小方差最优信息融合准则,对被多传感器观测的带有色观测噪声的离散线性随机控制系统,提出了一种具有两层融合结构的标量加权信息融合稳态Kalman滤波器,它等价于相应的带相关噪声系统的最优信息融合稳态Kalman预报器.最优信息融合稳态预报器可在所有局部预报器达到稳态时,通过一次融合获得,且任两个子系统之间的稳态预报误差互协方差阵可通过任选初值迭代求得,并证明了它的收敛性.通过将它应用到带三个传感器的雷达跟踪系统验证了其有效性.     

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.     

统一的快速次优固定区间白噪声Wiener平滑算法

对带相关噪声的线性离散随机控制系统,应用Kalman滤波方法,基于CARMA新息模型导出了统一的最优固定区间白噪声递推Wiener平滑器,它带有系数阵指数衰减到零的高阶多项式矩阵.进一步用截断方法提出了相应的快速次优固定区间自噪声Wiener平滑算法,它显著地减小了计算负担.给出了平滑误差公式和选择截断指数的公式.一个Bernoulli-Gaussian白噪声的仿真例子说明了所提出的结果的有效性.     

广义系统Kalman融合器的研究

研究带自回归滑动平均(ARMA)有色观测噪声的多传感器广义离散随机线性系统,根据Kalman滤波方法和白噪声估计理论,在线性最小方差信息融合准则下,应用奇异值分解和增广状态空间模型,为了提高融合器的精度,提出了按矩阵加权降阶稳态广义Kalman融合器,可统一处理稳态滤波、平滑和预报问题,可减少计算负担和改善局部估计精度。并提出最优加权系数的局部估计误差方差和协方差阵的计算公式。用一个Monte Carlo数值仿真实例说明了所提方法的有效性。     

Distributed weighted robust Kalman filter fusion for uncertain systems with autocorrelated and cross-correlated noises

In this paper, the problem of distributed weighted robust Kalman filter fusion is studied for a class of uncertain systems with autocorrelated and cross-correlated noises. The system under consideration is subject to stochastic uncertainties or multiplicative noises. The process noise is assumed to be one-step autocorrelated. For each subsystem, the measurement noise is one-step autocorrelated, and the process noise and the measurement noise are two-step cross-correlated. An optimal robust Kalman-type recursive filter is first designed for each subsystem. Then, based on the newly obtained optimal robust Kalman-type recursive filter, a distributed weighted robust Kalman filter fusion algorithm is derived for uncertain systems with multiple sensors. The distributed fusion algorithm involves a recursive computation of the filtering error cross-covariance matrix between any two subsystems. Compared with the centralized Kalman filter, the distributed weighted robust Kalman filter developed in this paper has stronger fault-tolerance ability. Simulation results are provided to demonstrate the effectiveness of the proposed approaches.     

Maximum Correntropy Kalman Filtering for Non-Gaussian Systems With State Saturations and Stochastic Nonlinearities

This paper tackles the maximum correntropy Kalman filtering problem for discrete time-varying non-Gaussian systems subject to state saturations and stochastic nonlinearities. The stochastic nonlinearities, which take the form of statemultiplicative noises, are introduced in systems to describe the phenomenon of nonlinear disturbances. To resist non-Gaussian noises, we consider a new performance index called maximum correntropy criterion(MCC) which describes the similarity between two stochastic ...     

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.     

相关观测融合Kalman估值器及其全局最优性

对于带相关观测噪声和带不同观测阵的多传感器线性离散时变随机控制系统, 用加权最小二乘法(WLS)提出了两种加权观测融合Kalman估值器, 它们包括状态滤波、状态预报和状态平滑. 基于信息滤波器形式下的Kalman滤波器, 证明了在相同初值下, 它们在数值上恒等于相应的集中式观测融合Kalman估值器, 因而具有全局最优性. 但是它们可明显减轻计算负担. 数值仿真例子验证了它们在功能上等价于集中式观测融合Kalman估值器.     

基于最小均方误差估计的噪声相关UKF设计

传统Unscented卡尔曼滤波器(UKf)要求系统噪声和量测噪声必须是互不相关的.针对此局限性,研究了一类带相关噪声的非线性离散系统UKF设计方法.基于最小均方误差估计和正交变换,给出了噪声相关UKF滤波递推公式,并采用Unscented变换(UT)来计算系统状态的后验分布.所设计的UKF有效解决了传统UKF在噪声相关条件下非线性滤波失效的问题,拓展了UKF的应用范围.最后,仿真实例表明了所设计UKF的有效性.     

改进型平方根无迹卡尔曼滤波及其在无轴承永磁同步电机无速度传感器运行中的应用

平方根无迹卡尔曼滤波(SRUKF)解决了标准无迹卡尔曼滤波(UKF)中由于误差协方差阵负定而引起的滤波发散问题, 保证了算法的数值稳定性, 但仍存在对模型参数变化的鲁棒性差、收敛速度慢及对突变状态的跟踪能力低等缺陷. 因此, 本文提出一种改进SRUKF滤波, 通过引入时变渐消因子和弱化因子, 实时修正滤波增益矩阵和误差协方差平方根矩阵, 实现残差序列正交, 确保SRUKF滤波保持对目标实际状态的准确跟踪. 将该算法在无轴承永磁同步电机无速度传感器矢量控制系统中进行仿真研究. 结果表明: 改进SRUKF非线性近似精度、数值稳定性及滤波精度更高, 在系统状态突变或负载扰动时, 鲁棒性更强, 能够有效实现转速及转子角度的准确估计, 确保转子稳定悬浮运行.     

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.