Performance loss and design method of Kalman filters for discrete-time linear systems with uncertainties†

This paper is divided into two parts. The first part is concerned with the performance loss of the discrete-time Kalman filter designed on the basis of the model with errors in both dynamical and observation systems. The difference equation which describes the evolution of the covariance matrix of actual estimation error is derived. Some numerical results are shown as the illustration of the technique.

The second half is devoted to the development of the method of designing the unbiased minimum variance linear filter for the random system whose elements of both the transition and observation matrices are Gaussian white noises. For this purpose the result of the first part is utilized.     

低复杂度非相干分布源参数估计方法

提出了一种低复杂度的非相干分布源参数估计方法,证明了在小角度扩展下,无噪声协方差矩阵的元素能够被分离成幅度信息和相位信息两部分。基于此性质,利用样本协方差矩阵次对角线上元素的相位信息首先估计出分布源的中心波达方向。根据无噪声协方差矩阵列矢量和采样伪噪声子空间之间的近似正交性构造代价函数,并通过一维搜索估计出分布源的角度扩展参数。该方法避免了对样本协方差矩阵进行特征分解,不需要确定伪信号子空间的维数,而这是现有子空间方法的主要困难。此外,它估计分布源的两个角度参数时仅需要完成一次一维谱搜索,计算复杂度较低。仿真结果证实了所提方法的有效性。     

应用于状态监测的多传感器融合估计

在状态监测的工程实际中, 使用多个同类传感器进行在线测量可以得到更为准确的状态估计．但各传感器测量噪声会出现相关的情况, 而且很难得到相关测量噪声的方差矩阵的精确值, 测量系统往往是不确定的．本文根据系统测量将系统分解为确定和不确定扰动两部分, 分别进行估计, 然后将两者的融合估计结果相加得到了最优鲁棒的融合估计．针对确定部分, 利用同类传感器的测量方差为Pei-Radman矩阵的特性, 通过求解测量噪声方差矩阵的最大特征值得到了一种简便的最优融合估计算法, 该算法避免了求解方差矩阵的逆的过程．针对不确定     

Accuracy analysis of a covariance matching approach for identifying errors-in-variables systems

A system identification method for errors-in-variables problems based on covariance matching was recently proposed. In the first step, a small amount of covariances of noisy input–output data are computed, and then a parametric model is fitted to these covariances. In this paper, the method is further analyzed and the asymptotic accuracy of the parameter estimates is derived. An explicit algorithm for computing the asymptotic covariance matrix of the parameter estimates is given, and the identification method is shown to be asymptotically statistically efficient assuming that the given information is the computed covariances. As an important byproduct, an efficient algorithm is presented for computing the covariance matrix of the computed input–output covariances.     

Non-parametric identification of continuous-time Hammerstein systems using Gaussian process model and particle swarm optimization

This paper deals with a non-parametric identification of continuous-time Hammerstein systems using Gaussian process (GP) models. A Hammerstein system consists of a memoryless non-linear static part followed by a linear dynamic part. The identification model is derived using the GP prior model which is described by the mean function vector and the covariance matrix. This prior model is trained by the separable least-squares (LS) approach combining the linear LS method with particle swarm optimization to minimize the negative log marginal likelihood of the identification data. Then the non-linear static part is estimated by the predictive mean function of the GP, and the confidence measure of the estimated non-linear static part is evaluated by the predictive covariance function of the GP. Simulation results are shown to illustrate the proposed method.     

Improved Stein-type shrinkage estimators for the high-dimensional multivariate normal covariance matrix

Many applications require an estimate for the covariance matrix that is non-singular and well-conditioned. As the dimensionality increases, the sample covariance matrix becomes ill-conditioned or even singular. A common approach to estimating the covariance matrix when the dimensionality is large is that of Stein-type shrinkage estimation. A convex combination of the sample covariance matrix and a well-conditioned target matrix is used to estimate the covariance matrix. Recent work in the literature has shown that an optimal combination exists under mean-squared loss, however it must be estimated from the data. In this paper, we introduce a new set of estimators for the optimal convex combination for three commonly used target matrices. A simulation study shows an improvement over those in the literature in cases of extreme high-dimensionality of the data. A data analysis shows the estimators are effective in a discriminant and classification analysis.     

黎曼流形上的保局投影在图像集匹配中的应用

目的提出了黎曼流形上局部结构特征保持的图像集匹配方法。方法该方法使用协方差矩阵建模图像集合,利用对称正定的非奇异协方差矩阵构成黎曼流形上的子空间,将图像集的匹配转化为流形上的点的匹配问题。通过基于协方差矩阵度量学习的核函数将黎曼流形上的协方差矩阵映射到欧几里德空间。不同于其他方法黎曼流形上的鉴别分析方法,考虑到样本分布的局部几何结构,引入了黎曼流形上局部保持的图像集鉴别分析方法,保持样本分布的局部邻域结构的同时提升样本的可分性。结果在基于图像集合的对象识别任务上测试了本文算法,在ETH80和YouTube Celebrities数据库分别进行了对象识别和人脸识别实验,分别达到91.5%和65.31%的识别率。结论实验结果表明,该方法取得了优于其他图像集匹配算法的效果。     

Solving a part classification problem using simulated annealing-like hybrid algorithm

Part classification and coding is still considered as laborious and time-consuming exercise. Keeping in view, the crucial role, which it plays, in developing automated CAPP systems, the attempts have been made in this article to automate a few elements of this exercise using a shape analysis model. In this study, a 24-vector directional template is contemplated to represent the feature elements of the parts (candidate and prototype). Various transformation processes such as deformation, straightening, bypassing, insertion and deletion are embedded in the proposed simulated annealing (SA)-like hybrid algorithm to match the candidate part with their prototype. For a candidate part, searching its matching prototype from the information data is computationally expensive and requires large search space. However, the proposed SA-like hybrid algorithm for solving the part classification problem considerably minimizes the search space and ensures early convergence of the solution.The application of the proposed approach is illustrated by an example part. The proposed approach is applied for the classification of 100 candidate parts and their prototypes to demonstrate the effectiveness of the algorithm.     

Robust space time processing based on bi-iterative scheme of secondary data selection and PSWF method

Prolate spheroidal wave function (PSWF) method could improve the target detection performance for space-time adaptive processing (STAP) in nonhomogeneous environment. However, it may be ineffective with system parameter error. In this paper, we correct the system parameter with clutter spectrum analysis. Since contaminated samples contained in the secondary data set have detrimental impact on this spectrum analysis, the traditional sample selection method of generalized inner production (GIP) is combined with PSWF method, and then a bi-iterative scheme is proposed. Firstly, the system parameter for PSWF is estimated via the analysis of spectrum image, which is constructed with the secondary data set. Then, the covariance matrix is derived by PSWF method with the estimated parameter. Thirdly, the GIP sample selection technique is implemented with the PSWF covariance matrix, and the secondary data set would be updated. Repeat these steps until a stable parameter is obtained. Several vital issues such as how to estimate the parameter with real data and why the precision of covariance matrix could be improved during the iteration are analyzed. In the end, the validity of the proposed algorithm is substantiated by practical and simulation results.     

An effective localization method for mixed far-field and near-field strictly non-circular sources

In this paper, an effective direction-of-arrival (DOA) and range estimations method for mixed far-field and near-field non-circular sources is proposed based on a large centrosymmetric uniform linear array (ULA). By exploiting the non-circularity of the sources, an extended signal is generated by concatenating the received array data and its conjugate counterparts. Then the DOAs of far-field signals are estimated based on the extended covariance matrix with the traditional MUSIC algorithm. After eliminating the far-field components from the extended signal subspace, the extended covariance matrix of the near-field signals is obtained. Thus a near-field estimator is constructed based on symmetric property of the extended array manifold where the generalized ESPRIT method is adopted to estimate the DOAs of near-field sources. Finally, the range estimator is derived using the DOA estimations of near-field sources. Simulation results are provided to validate that the proposed method has achieved a better performance than existing ones and is quite suitable for massive MIMO (multiple-input multiple-out) system.     

Variance results for identification of cascade systems

The objective of this contribution is to analyze statistical properties of estimated models of cascade systems. Models of such systems are important in for example cascade control applications. The aim is to present and analyze some fundamental limitations in the quality of an identified model of a cascade system under the condition that the true subsystems have certain common dynamics. The model quality is analyzed by studying the asymptotic (large data) covariance matrix of the Prediction Error Method parameter estimate. The analysis will focus on cascade systems with three subsystems. The main result is that if the true transfer functions of the first and second subsystem are identical, the output signal information from the second and third subsystems will not affect the asymptotic variance of the estimated model of the first subsystem. This result implies that for a cascade system with two subsystems, where the dynamics of the first subsystem is a factor of the dynamics of the second one, the output signal information from the second subsystem will not improve the asymptotic quality of the estimate of the first subsystem. The results are illustrated by some simple FIR examples.     

Heuristic algorithms for the problem of integer balancing of a three-dimensional matrix with constraints of the second type

The problem of integer balancing of a three-dimensional matrix with constraints of the second type is studied. The elements of the inner part (all three indices are greater than zero) of the three-dimensional matrix are summed in each direction and each section of the matrix; the total sum is also found. These sums are placed into the elements where one or more indices are equal to zero (according to the summing directions). The problem is to find an integer matrix of the same structure, which can be produced from the initial one by replacing the elements of the inner part with the largest previous or the smallest following integer. At the same time, variations of the sums of elements from those in the initial matrix should be less than 2 and an element with three zero indices should be produced with standard rounding-off rules. Heuristic algorithms for this problem are suggested: layering algorithm obtained as a generalization of a similar algorithm for the problem with constraints of the first type and a new matrix algorithm. The latter consists of three parts: search for the basic matrix, search for the maximum matrix, and matrix correction. Each of them is a cyclic change of the integer matrix using from one to three elements from the inner part. A modification of the matrix algorithm is suggested. The algorithm is directed to more uniform filling of the inner part of the integer matrix. Also, the complexity of all three algorithms is estimated. The comparative analysis of matrix algorithms based on the results of computing experiments is adduced.     

一种对称噪声环境下DOA估计的新方法

研究水下目标优化估算精度问题。在满足对称分布的海洋环境噪声中进行波达方向(DOA)估计的方法对于解决水下目标感知问题有重要意义。由于水下存在的海洋噪声等识别目标难度大,提出了一种重构数据协方差矩阵实部的DOA估计。通过消除数据协方差矩阵实部来降低对称噪声的影响,然后对协方差矩阵实部进行重新构造,恢复损失的目标信息,实现精确DOA估计。与传统方法的比较,方法能够有效降低对称噪声影响,避免双边谱的出现,提高了估计精度。仿真结果表明,方法性能优良,对于海洋环境中DOA估计的研究提供了参考。     

一种子空间分解的MIMO-OFDM半盲信道估计方法

信道估计是MIMO-OFDM系统实现优良传输的一项重要环节。半盲信道估计算法是将MIMO-OFDM信道矩阵进行分解,分别利用未知数据和已知导频信息来完成信道估计。在利用未知数据进行估计时,提出一种利用频域子载波分组的子空间分解方法,不仅降低了计算复杂度,而且同时提高了信道估计的精度。利用已知的导频信息和未知数据估计出来的结果,可以求得最后的信道矩阵。相对于传统的频域子空间分解的半盲估计方法,算法可以减小计算复杂度80%,同时提高了估计精度平均1～2dB。仿真结果证明了算法具有良好的性能表现。     

Non-stationary response of large, non-linear finite element systems under stochastic loading

A very efficient and straightforward numerical procedure for the computation of statistical second moment characteristics of large, non-linear finite element systems under stochastic loading is presented. For the modeling of both the loading and the response of the system an orthogonal series expansion of the corresponding covariance matrix, the so-called Karhunen-Loève expansion is applied, allowing to incorporate potentially available statistical data of an excitation process directly into the analysis. The non-linear equation of motion is linearized by the method of equivalent statistical linearization. According to the present capabilities of this linearization technique, one-dimensional hysteretic elements are used for modeling the non-linear system behavior. The mode acceleration method is applied in order to reduce significantly the size of the system equation and thus increasing the computational efficiency of the proposed procedure. Contrary to methodologies based on state space formulations, this procedure relies on deterministic step by step integration, implying that the dimension of the system equation is the same as in a purely deterministic analysis.     

一种自适应滤波方法在捷联惯导系统大失准角初始对准中的应用

为了对静基座大失准角捷联惯导系统(SINS)进行初始对准,建立了在静基座下基于四元数的SINS非线性误差模型。该误差模型无需对姿态误差角进行小角度假设。为了在观测噪声方差未知的情况下估计SINS失准角,提出一种在线估计观测噪声方差矩阵的自适应扩展卡尔曼滤波方法。仿真结果表明,该自适应滤波方法能在观测噪声方差未知的情况下有效地对静基座大失准角SINS进行初始对准。     

A Suboptimal Dual Control Method for the Stochastic Systems with Parameters Drifting

This paper proposed a suboptimal dual control method for the stochastic systems with parameters drifting. Based on the consideration of the performance index control and the parameter estimation, the minimum variance of the system output and the estimated covariance matrix of the parameters estimation are both put into the performance index to evaluate the control quality. Furthermore, a dual control strategy is designed which is of the property of learning and control. Simulation results illustrate the effectiveness of the algorithm.     

Choosing an appropriate number of factors in factor analysis with incomplete data

When we conduct factor analysis, the number of factors is often unknown in advance. Among many decision rules for an appropriate number of factors, it is easy to find approaches that make use of the estimated covariance matrix. When data include missing values, the estimated covariance matrix using either complete cases or available cases may not accurately represent the true covariance matrix, and decision based on the estimated covariance matrix may be misleading. We discuss how to apply model selection techniques using AIC or BIC to choose an appropriate number of factors when data include missing values. In the simulation study, it is shown that the suggested methods select the correct number of factors for simulated data with known number of factors.     

基于凹凸区域的断裂面匹配算法

针对破碎刚体复原给出一种断裂面匹配算法。根据平均曲率判断顶点的凹凸性,对凹凸顶点进行聚类将断裂面划分为多个凹凸特征区域;定义特征区域的协方差矩阵,根据其主成分和主方向定义特征区域的尺寸特征和各向异性特征,面积相近、类型相同和特征相近的区域为相似区域对,之后再根据距离主方向约束排除伪区域对;采用穷举法对每3对质心不共线的相似区域对,计算三维变换,将断裂面粗略对齐,再根据最近点迭代算法的收敛程度得到最优匹配,同时将两断裂面精细校准。实验结果表明,该算法能够实现较复杂断裂面的部分和完全匹配。     

Analysis of theoretical surface scattering models for polarimetric microwave remote sensing of bare soils

During the MAESTRO 1 Campaign, mulli-frequency polarimetric SAR data were acquired over the Dutch site ‘Flevoland’. At the same time, an extensive ground data collection took place in order to measure several different bio- and geophysical parameters for bare soils. The SAR data are used to assess the performance of several theoretical surface scattering models for rough surfaces. These models are extended in order to yield all the elements of the covariance matrix, particularly the phase and the correlation factor between the HHand W channels. Using the ground data, input elements such as the soil permittivity and the surface roughness are fed into the models to compute the elements of the covar ance matrix. A comparison for Land C band between the theoretical predictions and the measured backscattering coefficients is then presented and clearly shows that the models predict in a satisfactory manner the elements of the covariance matrix.