Knowledge-aided adaptive detection in partially homogeneous clutter: Joint exploitation of persymmetry and symmetric spectrum

In this paper, we address the problem of detecting a point-like target embedded in clutter characterized by a symmetrically structured power spectral density and persymmetric covariance matrix. In particular, we consider the so-called partially homogeneous environment, where the cell under test and the training samples share the same covariance matrix up to an unknown power scaling factor. At the design stage, we jointly exploit the spectral properties of the clutter and the persymmetric structure of the clutter covariance matrix to reformulate the decision problem in terms of real variables with an increased number of training samples. Then, we derive two adaptive detectors relying on the Rao test and a suitable modification of the generalized likelihood ratio test (GLRT). The performance analysis, conducted on both simulated and real radar data, confirms the superiority of the newly proposed receivers over the traditional state-of-the-art counterparts which ignore either the persymmetry or the symmetric spectrum.     

Model-based Rao test for adaptive range-spread target detection

This paper deals with the problem of detecting range-spread target in Gaussian disturbance with unknown covariance matrix. A model-based Rao detector is derived by modeling the disturbance as an autoregressive (AR) process with unknown parameters. Meanwhile, the asymptotic expressions for the probabilities of false alarm and detection are derived in closed form, which show that the newly proposed detector is asymptotically constant false alarm rate with respect to the disturbance covariance matrix. The performance assessment conducted by resorting to the simulated data, also in comparison to the previously proposed detectors, has confirmed the effectiveness of the newly proposed detectors.     

Persymmetric adaptive subspace detectors for range-spread targets

This paper investigates the problem of adaptive detection of a range-spread target in colored Gaussian disturbance. The range-spread target is described by a multi-rank subspace model, which lies in a subspace but with unknown coordinates. The disturbance, usually including clutter and thermal noise, has an unknown covariance matrix. Under the above assumption, we design the Rao and generalized likelihood ratio test (GLRT) detectors by the two-step procedure, which incorporates persymmetric structure of received data. The two detectors are shown to coincide with each other. Remarkably, the proposed detector ensures constant false alarm rate property. Experimental results conducted by both simulation and real data verify that the proposed detector outperforms the existing counterparts in training-limited scenarios.     

Empirical Bayes estimators of the random intercept in multilevel analysis: Performance of the classical, Morris and Rao version

For a linear multilevel model with 2 levels, with equal numbers of level-1 units per level-2 unit and a random intercept only, different empirical Bayes estimators of the random intercept are examined. Studied are the classical empirical Bayes estimator, the Morris version of the empirical Bayes estimator and Rao's estimator. It is unclear which of these estimators performs best in terms of Bayes risk. Of these three, the Rao estimator is optimal in case the covariance matrix of random coefficients may be negative definite. However, in the multilevel model this matrix is restricted to be positive semi-definite. The Morris version, replaces the weights of the empirical Bayes estimator by unbiased estimates. This correction, however, is based on known level-1 variances, which in many empirical settings are unknown. A fourth estimator is proposed, a variant of Rao's estimator which restricts the estimated covariance matrix of random coefficients to be positive semi-definite. Since there are no closed-form expressions for estimators involved in the empirical Bayes estimators (except for the Rao estimator), Monte Carlo simulations are done to evaluate the performance of these different empirical Bayes estimators. Only for small sample sizes there are clear differences between these estimators. As a consequence, for larger sample sizes the formula for the Bayes risk of the Rao estimator can be used to calculate the Bayes risk for the other estimators proposed.     

非均匀杂波中的直接变换域STAP算法研究

降维空时自适应处理和降秩空时自适应处理均需要已知杂波协方差矩阵,或者通过参考单元对杂波协方差矩阵进行估计,在非均匀杂波环境中无法获取足够多的有效样本,使得算法性能急剧下降。提出一种直接变换域空时自适应处理算法,不需要对杂波协方差矩阵估计,在角度-多普勒域中的通道之间进行自适应处理,采用最小均方准则求解,能够适用于非均匀杂波环境中目标检测。仿真结果表明,提出的算法相比于直接数据域算法,抑制杂波能力更强,对于目标角度偏差更具稳健性。     

Knowledge-based target detection in compound Gaussian clutter with inverse Gaussian texture

This paper addresses the problem of adaptive detection of radar targets embedded in heterogeneous compound-Gaussian clutter environments. Based on the Bayesian theory, a priori knowledge of clutter is utilized to improve detection performance. The clutter texture is modeled by the inverse Gaussian distribution to describe the heavy-tailed clutter. Furthermore, clutter's heterogeneity results in insufficient secondary data, and the inverse complex Wishart distribution is exploited to model the speckle covariance matrix. Based on a priori distributions of clutter, a novel detector without using secondary data is derived via the generalized likelihood ratio test (GLRT). Monte Carlo experiments are performed to evaluate the detection performance of the proposed detector. Experimental results illustrate that the proposed detector outperforms its competitors in scenarios with limited secondary data.     

Enhanced knowledge-aided space–time adaptive processing exploiting inaccurate prior knowledge of the array manifold

The accuracy of the prior knowledge of the clutter environments is critical to the clutter suppression performance of knowledge-aided space–time adaptive processing (KA-STAP) algorithms in airborne radar applications. In this paper, we propose an enhanced KA-STAP algorithm to estimate the clutter covariance matrix considering inaccurate prior knowledge of the array manifold for airborne radar systems. The core idea of this algorithm is to incorporate prior knowledge about the range of the measured platform velocity and the crab angle, and other radar parameters into the assumed clutter model to obtain increased robustness against inaccuracies of the data. It first over-samples the space–time subspace using prior knowledge about the range values of parameters and the inaccurate array manifold. By selecting the important clutter space–time steering vectors from the over-sampled candidates and computing the corresponding eigenvectors and eigenvalues of the assumed clutter model, we can obtain a more accurate clutter covariance matrix estimate than directly using the prior knowledge of the array manifold. Some extensions of the proposed algorithm with existing techniques are presented and a complexity analysis is conducted. Simulation results illustrate that the proposed algorithms can obtain good clutter suppression performance, even using just one snapshot, and outperform existing KA-STAP algorithms in presence of the errors in the prior knowledge of the array manifold.     

Novel Rao–Blackwellized jump Markov CBMeMBer filter for multi-target tracking

The jump Markov cardinality balanced multi-target multi-Bernoulli (JM–CBMeMBer) filter can estimate both state and number of targets from uncertain measurements. To deal with high computational complexity and imprecise estimations of the existing JM–CBMeMBer filters, we put forward a novel Rao–Blackwellized JM–CBMeMBer filter and its sequential Monte Carlo implementation in this paper. Different from the previous works, we first divide target state space into the nonlinear and linear components based on the Rao–Blackwellized theory, where the linear component is estimated by the Kalman filter (KF) and the results are applied to extract the nonlinear component in lower dimension state space. Moreover, the track management scheme is considered to simplify tracking parameters and distinguish target track. After analysis on computational complexity, the optimised Rao–Blackwellized filtering scheme is presented to reduce the number of the KF recursions. As a result, the computational complexity is reduced and the estimation accuracy is improved owing to small estimation covariance during the whole filtering process. Finally, the numerical simulation results are provided to show the reliability and efficiency of the proposed filter.     

A distribution independent data-driven design scheme of optimal dynamic fault detection systems

In this paper, design issues of data-driven optimal dynamic fault detection systems for stochastic linear discrete-time processes are addressed without precise distribution knowledge of unknown inputs and faults. Concerning a family of faults with different distribution profiles in mean and covariance matrix, we introduce a bank of parameter vectors of parity space and construct the parity relation based residual generators using process input and output data. In the context of minimizing the missed detection rate for a prescribed false alarm rate, the design of fault detection system is formulated as a bank of distribution independent optimization problems without posing specific distribution assumption on unknown inputs and faults. It is proven that the optimal selection of individual parameter vector can be formulated as a generalized eigenvalue–eigenvector problem in terms of the means and covariance matrices of residuals in fault-free and each faulty cases, and is thus solved via singular value decomposition. The tight upper bounds of false alarm rate and missed detection rate are simultaneously achieved quantitatively. Besides, the existence condition of the optimal solutions is investigated analytically. Experimental study on a three-tank system illustrates the application of the proposed scheme.     

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.     

Adaptive parameter estimation for a general dynamical system with unknown states

This paper is concerned with the design of a state filter for a time‐delay state‐space system with unknown parameters from noisy observation information. The key is to investigate new identification algorithms for interactive state and parameter estimation of the considered system. Firstly, an observability canonical state‐space model is derived from the original model by linear transformation for the purpose of simplifying the model structure. Secondly, a direct state filter is formulated by minimizing the state estimation error covariance matrix on the basis of the Kalman filtering principle. Thirdly, once the unknown states are estimated, a state filter–based recursive least squares algorithm is proposed for parameter estimation using the least squares principle. Then, a state filter–based hierarchical least squares algorithm is derived by decomposing the original system into several subsystems for improving the computational efficiency. Finally, the numerical examples illustrate the effectiveness and robustness of the proposed algorithms.     

Projection based MIMO control performance monitoring: I—covariance monitoring in state space

In this paper we propose a new control performance monitoring method based on subspace projections. We begin with a state space model of a generally non-square process and derive the minimum variance control (MVC) law and minimum achievable variance in a state feedback form. We derive a multivariate time delay (MTD) matrix for use with our extended state space formulation, which implicitly is equivalent to the interactor matrix. We show how the minimum variance output space can be considered an optimal subspace of the general closed-loop output space and propose a simple control performance calculation which uses orthogonal projection of filtered output data onto past closed-loop data. Finally, we propose a control performance monitoring technique based on the output covariance and diagnose the cause of suboptimal control performance using generalized eigenvector analysis. The proposed methods are demonstrated on a few simulated examples and an industrial wood waste burning power boiler.     

Tensor-based methods for blind spatial signature estimation under arbitrary and unknown source covariance structure

Spatial signature estimation is a problem encountered in several applications in signal processing such as mobile communications, sonar, radar, astronomy and seismology. In this paper, we propose higher-order tensor methods to solve the blind spatial signature estimation problem using planar arrays. By assuming that sources' powers vary between successive time blocks, we recast the spatial and spatiotemporal covariance models for the received data as third-order PARATUCK2 and fourth-order Tucker4 tensor decompositions, respectively. Firstly, by exploiting the multilinear algebraic structure of the proposed tensor models, new iterative algorithms are formulated to blindly estimate the spatial signatures. Secondly, in order to achieve a better spatial resolution, we propose an expanded form of spatial smoothing that returns extra spatial dimensions in comparison with the traditional approaches. Additionally, by exploiting the higher-order structure of the resulting expanded tensor model, a multilinear noise reduction preprocessing step is proposed via higher-order singular value decomposition. We show that the increase on the tensor order provides a more efficient denoising, and consequently a better performance compared to existing spatial smoothing techniques. Finally, a solution based on a multi-stage Khatri–Rao factorization procedure is incorporated as the final stage of our proposed estimators. Our results demonstrate that the proposed tensor methods yield more accurate spatial signature estimates than competing approaches while operating in a challenging scenario where the source covariance structure is unknown and arbitrary (non-diagonal), which is actually the case when sample covariances are computed from a limited number of snapshots.     

A generative model for graph matching and embedding

This paper shows how to construct a generative model for graph structure through the embedding of the nodes of the graph in a vector space. We commence from a sample of graphs where the correspondences between nodes are unknown ab initio. We also work with graphs where there may be structural differences present, i.e. variations in the number of nodes in each graph and their edge structure. We characterise the graphs using the heat-kernel, and this is obtained by exponentiating the Laplacian eigensystem with time. The idea underpinning the method is to embed the nodes of the graphs into a vector space by performing a Young-Householder decomposition of the heat-kernel into an inner product of node co-ordinate matrices. The co-ordinates of the nodes are determined by the eigenvalues and eigenvectors of the Laplacian matrix, together with a time-parameter which can be used to scale the embedding. Node correspondences are located by applying Scott and Longuet-Higgins algorithm to the embedded nodes. We capture variations in graph structure using the covariance matrix for corresponding embedded point positions. We construct a point-distribution model for the embedded node positions using the eigenvalues and eigenvectors of the covariance matrix. We show how to use this model to both project individual graphs into the eigenspace of the point position covariance matrix and how to fit the model to potentially noisy graphs to reconstruct the Laplacian matrix. We illustrate the utility of the resulting method for shape analysis using data from the Caltech–Oxford and COIL databases.     

Local fuzzy PCA based GMM with dimension reduction on speaker identification

To reduce the high dimensionality required for training of feature vectors in speaker identification, we propose an efficient GMM based on local PCA with fuzzy clustering. The proposed method firstly partitions the data space into several disjoint clusters by fuzzy clustering, and then performs PCA using the fuzzy covariance matrix on each cluster. Finally, the GMM for speaker is obtained from the transformed feature vectors with reduced dimension in each cluster. Compared to the conventional GMM with diagonal covariance matrix, the proposed method shows faster result with less storage maintaining same performance.     

Impact of unknown covariance structures in semiparametric models for longitudinal data: An application to Wisconsin diabetes data

Semiparametric models are becoming increasingly attractive for longitudinal data analysis. Often there is lack of knowledge of the covariance structure of the response variable. Although it is still possible to obtain consistent estimators for both parametric and nonparametric components of a semipatrametric model by assuming an identity structure for the covariance matrix, the resulting estimators may not be efficient. We conducted extensive simulation studies to investigate the impact of an unknown covariance structure on estimators in semiparametric models for longitudinal data. In some situations the loss of efficiency could be substantial. A two-step estimator is thus proposed to improve the efficiency. Our study was motivated by a population based data analysis to examine the temporal relationship between systolic blood pressure and urinary albumin excretion.     

An enhanced classification approach for reliability estimation of structural systems

The accuracy of a classification-based surrogate model for reliability assessment can be improved by augmenting the training data (labeled data or data with known responses) with a large number of unlabeled data (data with unknown responses) in semi-supervised learning methods. In this research, an enhanced Probabilistic Neural Network (PNN) algorithm is proposed where the Gaussians at each labeled point are not assumed to be spherical. Each of the Gaussians has a ‘full’ covariance matrix instead of simply assuming the Gaussian with a ‘spherical’ covariance matrix. First, the Expectation-Maximization algorithm is applied on the labeled and unlabeled data while assuming that the number of ‘full’ Gaussians is equal to the number of labeled datapoints. The contribution of each of these ‘full’ Gaussians at a particular datapoint is found by using the Bayes Theorem. The Bayes decision criterion is then used in the final output layer of the PNN to classify test patterns into either the safe or the failure class. The primary benefit of the proposed method comes from utilizing unlabeled data for better estimation of ‘full’ covariance matrices of constituting Gaussian clusters of underlying data, which are then used to estimate the Probability Density Functions of classes for classification. This procedure does not require additional computational costs to improve the accuracy of the classification results since the cost of unlabeled data is negligible in general. Two examples including an analytic problem and a truss problem are presented in order to validate the proposed reliability estimation process. The results reflect considerable improvements of the classifier performance for estimating reliability while maintaining sufficient accuracy.     

Localization of multiple disjoint sources with prior knowledge on source locations in the presence of sensor location errors

Sensor location errors are known to be able to degrade the source localization accuracy significantly. This paper considers the problem of localizing multiple disjoint sources where prior knowledge on the source locations is available to mitigate the effect of sensor location uncertainty. The error in the priorly known source location is assumed to follow a zero-mean Gaussian distribution. When a source location is completely unknown, the covariance matrix of its prior location would go to infinity. The localization of multiple disjoint sources is achieved through exploring the time difference of arrival (TDOA) and the frequency difference of arrival (FDOA) measurements. In this work, we derive the Cramér–Rao lower bound (CRLB) of the source location estimates. The CRLB is shown analytically to be able to unify several CRLBs introduced in literature. We next compare the localization performance when multiple source locations are determined jointly and individually. In the presence of sensor location errors, the superiority of joint localization of multiple sources in terms of greatly improved localization accuracy is established. Two methods for localizing multiple disjoint sources are proposed, one for the case where only some sources have prior location information and the other for the scenario where all sources have prior location information. Both algorithms can reach the CRLB accuracy when sensor location errors are small. Simulations corroborate the theoretical developments.     

A non-homogeneous dynamic Bayesian network with a hidden Markov model dependency structure among the temporal data points

In the topical field of systems biology there is considerable interest in learning regulatory networks, and various probabilistic machine learning methods have been proposed to this end. Popular approaches include non-homogeneous dynamic Bayesian networks (DBNs), which can be employed to model time-varying regulatory processes. Almost all non-homogeneous DBNs that have been proposed in the literature follow the same paradigm and relax the homogeneity assumption by complementing the standard homogeneous DBN with a multiple changepoint process. Each time series segment defined by two demarcating changepoints is associated with separate interactions, and in this way the regulatory relationships are allowed to vary over time. However, the configuration space of the data segmentations (allocations) that can be obtained by changepoints is restricted. A complementary paradigm is to combine DBNs with mixture models, which allow for free allocations of the data points to mixture components. But this extension of the configuration space comes with the disadvantage that the temporal order of the data points can no longer be taken into account. In this paper I present a novel non-homogeneous DBN model, which can be seen as a consensus between the free allocation mixture DBN model and the changepoint-segmented DBN model. The key idea is to assume that the underlying allocation of the temporal data points follows a Hidden Markov model (HMM). The novel HMM–DBN model takes the temporal structure of the time series into account without putting a restriction onto the configuration space of the data point allocations. I define the novel HMM–DBN model and the competing models such that the regulatory network structure is kept fixed among components, while the network interaction parameters are allowed to vary, and I show how the novel HMM–DBN model can be inferred with Markov Chain Monte Carlo (MCMC) simulations. For the new HMM–DBN model I also present two new pairs of MCMC moves, which can be incorporated into the recently proposed allocation sampler for mixture models to improve convergence of the MCMC simulations. In an extensive comparative evaluation study I systematically compare the performance of the proposed HMM–DBN model with the performances of the competing DBN models in a reverse engineering context, where the objective is to learn the structure of a network from temporal network data.     

杂波协方差矩阵结构的融合估计方法

针对特定杂波背景下的最优或次优杂波协方差矩阵估计方法难以适应过渡杂波环境的问题,提出协方差矩阵结构的融合估计方法,通过调整参数涵盖现有的3种杂波协方差矩阵估计方法,并分析所提出方法对应的自适应归一化匹配滤波器的自适应特性.其次,确定了控制参数的经验公式,经验公式符合数值结果.最后,从估计精度、恒虚警率特性和检测性能3个方面对所提出方法和已有方法进行对比分析.仿真结果表明,在过渡杂波环境中,所提出方法的精度更高、检测效果更好,对实际杂波非高斯程度时空渐变性具有较强的适应能力.