非均匀噪声背景下混合信号DOA估计算法

针对非均匀噪声背景下非相关信源与相干信源并存时波达方向(DOA)估计问题，提出了基于迭代最小二乘和空间差分平滑的混合信号DOA估计算法。首先，该算法利用迭代最小二乘方法得到噪声协方差矩阵估计，然后对数据协方差矩阵进行“去噪”处理，利用子空间旋转不变技术实现非相关信源DOA估计；其次，基于空间差分法消除非相关信号并构造新矩阵进行前后向空间平滑，利用求根MUSIC算法估计相干信源DOA。相比于传统算法，该算法能估计更多的信源数，在低信噪比情况下DOA估计性能更优越。仿真实验结果验证了该算法的有效性。      

Maximum likelihood direction-of-arrival estimation in unknown noise fields using sparse sensor arrays

We address the problem of maximum likelihood (ML) direction-of-arrival (DOA) estimation in unknown spatially correlated noise fields using sparse sensor arrays composed of multiple widely separated subarrays. In such arrays, intersubarray spacings are substantially larger than the signal wavelength, and therefore, sensor noises can be assumed to be uncorrelated between different subarrays. This leads to a block-diagonal structure of the noise covariance matrix which enables a substantial reduction of the number of nuisance noise parameters and ensures the identifiability of the underlying DOA estimation problem. A new deterministic ML DOA estimator is derived for this class of sparse sensor arrays. The proposed approach concentrates the ML estimation problem with respect to all nuisance parameters. In contrast to the analytic concentration used in conventional ML techniques, the implementation of the proposed estimator is based on an iterative procedure, which includes a stepwise concentration of the log-likelihood (LL) function. The proposed algorithm is shown to have a straightforward extension to the case of uncalibrated arrays with unknown sensor gains and phases. It is free of any further structural constraints or parametric model restrictions that are usually imposed on the noise covariance matrix and received signals in most existing ML-based approaches to DOA estimation in spatially correlated noise.     

Direction estimation in partially unknown noise fields

The problem of direction of arrival estimation in the presence of colored noise with unknown covariance is considered. The unknown noise covariance is assumed to obey a linear parametric model. Using this model, the maximum likelihood directions parameter estimate is derived, and a large sample approximation is formed. It is shown that a priori information on the source signal correlation structure is easily incorporated into this approximate ML (AML) estimator. Furthermore, a closed form expression of the Cramer-Rao bound on the direction parameter is provided. A perturbation analysis with respect to a small error in the assumed noise model is carried out, and an expression of the asymptotic bias due to the model mismatch is given. Computer simulations and an application of the proposed technique to a full-scale passive sonar experiment is provided to illustrate the results     

Maximum-likelihood bearing estimation with partly calibrated arraysin spatially correlated noise fields

The problem of using a partly calibrated array for maximum likelihood (ML) bearing estimation of possibly coherent signals buried in unknown correlated noise fields is shown to admit a neat solution under fairly general conditions. More exactly, this paper assumes that the array contains some calibrated sensors, whose number is only required to be larger than the number of signals impinging on the array, and also that the noise in the calibrated sensors is uncorrelated with the noise in the other sensors. These two noise vectors, however, may have arbitrary spatial autocovariance matrices. Under these assumptions the many nuisance parameters (viz., the elements of the signal and noise covariance matrices and the transfer and location characteristics of the uncalibrated sensors) can be eliminated from the likelihood function, leaving a significantly simplified concentrated likelihood whose maximum yields the ML bearing estimates. The ML estimator introduced in this paper, and referred to as MLE, is shown to be asymptotically equivalent to a recently proposed subspace-based bearing estimator called UNCLE and rederived herein by a much simpler approach than in the original work. A statistical analysis derives the asymptotic distribution of the MLE and UNCLE estimates, and proves that they are asymptotically equivalent and statistically efficient. In a simulation study, the MLE and UNCLE methods are found to possess very similar finite-sample properties as well. As UNCLE is computationally more efficient, it may be the preferred technique in a given application     

Maximum-likelihood diversity combining in partial-band noise

Maximum-likelihood diversity combining is investigated for an FFH/MFSK spread spectrum system in partial-band noise (PBN). The structure of maximum-likelihood diversity reception in PBN plus white Gaussian noise is derived. It is shown that signal-to-noise ratio and the noise variance at each hop have to be known to implement this optimum diversity combiner. Several suboptimum diversity combining schemes are also considered. The performance of the optimum combining scheme is evaluated. It is shown that adaptive gain control diversity combining actually achieves the optimum performance when interference is not very weak     

Universal prediction of individual binary sequences in the presenceof noise

The problem of predicting the next outcome of an individual binary sequence, based on noisy observations of the past, is considered. The goal of the predictor is to perform, for each individual sequence, “almost” as well as the best in a set of experts, where performance is evaluated using a general loss function. A comprehensive approach to prediction in this noisy setting is presented and proven generally efficient under appropriate conditions. As an illustration of the applicability of the approach suggested for concrete situations, two important special cases are explicitly treated. The first is the case where the data-corrupting noise process is binary-valued (where the observed bit is the bitwise XOR of the clean bit and the noise bit). The second case is that of real-valued additive noise. It is shown that even in this more challenging situation, where the information available to the predictor regarding the past sequence is incomplete, a predictor can be guaranteed to successfully compete with a whole set of experts in considerably strong senses     

Resolving manifold ambiguities in direction-of-arrival estimationfor nonuniform linear antenna arrays

This paper addresses the problem of ambiguities in direction of arrival (DOA) estimation for nonuniform (sparse) linear arrays. Usually, DOA estimation ambiguities are associated with linear dependence among the points on the antenna array manifold, that is, the steering vectors degenerate so that each may be expressed as a linear combination of the others. Most nonuniform array geometries, including the so-called “minimum redundancy” arrays, admit such manifold ambiguities. While the standard subspace algorithms such as MUSIC fail to provide unambiguous DOA estimates under these conditions, we demonstrate that this failure does not necessarily imply that consistent and asymptotically effective DOA estimates do not exist. We demonstrate that in most cases involving uncorrelated Gaussian sources, manifold ambiguity does not necessarily imply nonidentifiability; most importantly, we introduce algorithms designed to resolve manifold ambiguity. We also show that for situations where the number of sources exceeds the number of array sensors, a new class of locally nonidentifiable scenario exists     

Adaptive estimation in linear systems with unknown Markovian noise statistics

The asymptotic behavior of a Bayes optimal adaptive estimation scheme for a linear discrete-time dynamical system with unknown Markovian noise statistics is investigated. Noise influencing the state equation and the measurement equation is assumed to come from a group of Gaussian distributions having different means and covariances, with transitions from one noise source to another determined by a Markov transition matrix. The transition probability matrix is unknown and can take values only from a finite set. An example is simulated to illustrate the convergence.     

一种波达方向估计的快速算法

提出一种波达方向估计的快速算法.为了估计到信号子空间,该方法只需要多级维纳滤波器的前向递推,不需要估计样本协方差矩阵和对其作特征值分解,也不需要多级维纳滤波器的后向递推.从而使得该方法具有小运算量和低复杂度的特点,易于实时处理.由于不需要估计样本协方差矩阵,所以该方法可以应用在小样本和快时变的信号环境中.仿真结果证明了该方法的有效性.     

Subspace-based direction-of-arrival estimation using nonparametricstatistics

The problem of subspace estimation using multivariate nonparametric statistics is addressed. We introduce new high-resolution direction-of-arrival (DOA) estimation methods that have almost optimal performance in nominal conditions and are robust in the face of heavy-tailed noise. The extensions of the techniques for the case of coherent sources are considered as well. The proposed techniques are based on spatial sign and rank concepts. We show that spatial sign and rank covariance matrices can be used to obtain convergent estimates of the signal and noise subspaces. In the proofs, the noise is assumed to be spherically symmetric. Moreover, we illustrate how the number of signals may be determined using the proposed covariance matrix estimates and a robust estimator of variance. The performance of the algorithms is studied using simulations in a variety of noise conditions including noise that is not spherically symmetric. The results show that the algorithms perform near optimally in the case of Gaussian noise and highly reliably if the noise is non-Gaussian     

A novel approach for DOA estimation in unknown correlated noise fields

The key of the subspace-based Direction Of Arrival （DOA） estimation lies in the estimation of signal subspace with high quality. In the case of uncorrelated signals while the signals are temporally correlated, a novel approach for the estimation of DOA in unknown correlated noise fields is proposed in this paper. The approach is based on the biorthogonality between a matrix and its Moore-Penrose pseudo inverse, and made no assumption on the spatial covariance matrix of the noise. The approach exploits the structural information of a set of spatio-temporal correlation matrices, and it can give a robust and precise estimation of signal subspace, so a precise estimation of DOA is obtained. Its performances are confirmed by computer simulation results.     

The error performance of digital subscriber lines in the presenceof impulse noise

This paper describes the error performance of the ISDN basic access digital subscriber line (DSL), the high bit rate digital subscriber line (HDSL), and the asymmetric digital subscriber line (ADSL) in the presence of impulse noise. Results are found by using data from the 1986 NYNEX impulse noise survey in simulations. It is shown that a simple uncoded ADSL would have an order of magnitude more errored seconds than DSL and HDSL     

Maximum-likelihood estimation of Rician distribution parameters

The problem of parameter estimation from Rician distributed data (e.g., magnitude magnetic resonance images) is addressed. The properties of conventional estimation methods are discussed and compared to maximum-likelihood (ML) estimation which is known to yield optimal results asymptotically. In contrast to previously proposed methods, ML estimation is demonstrated to be unbiased for high signal-to-noise ratio (SNR) and to yield physical relevant results for low SNR     

Fast algorithm for minimum-norm direction-of-arrival estimation

The original minimum-norm direction-of-arrival estimator, proposed by Kumaresan and Tufts, employs the noise-subspace projection matrix, calculated by the eigendecomposition of spatial covariance matrix. The present authors propose a novel noneigenvector fast algorithm, which calculates the required minimum-norm function using the special power basis instead of eigenvector basis. The proposed algorithm provides a substantial saving as compared with computational loads of the eigendecomposition-based minimum-norm algorithm in cases when the number of multiple sources is much lower than the number of array sensors. Some computer simulation results, verifying the high performance and accuracy of the proposed algorithm, are presented     

Maximum-likelihood image estimation using photon-correlated beams

A theory is presented addressing the fundamental limits of image estimation in a setup that uses two photon-correlated beams. These beams have the property that their photon arrivals, as a point process, are ideally synchronized in time and space. The true image represents the spatial distribution of the optical transmittance (or reflectance) of an object. In this setup, one beam is used to probe the image while the other is used as a reference providing additional information on the actual number of photons impinging on the object. This additional information is exploited to reduce the effect of quantum noise associated with the uncertainty in the number of photons per pixel. A stochastic model for the joint statistics of the two observation matrices is developed and used to obtain a local maximum-likelihood estimator of the image. The model captures the nonideal nature of the correlation between the photons of the beams by means of a simple random translation model. The mean-square error of the estimator is evaluated and compared to the corresponding conventional techniques. Conditions for the performance advantage of the proposed estimator are examined in terms of key system parameters. The theoretical predictions are demonstrated by means of simulation.     

一种基于循环互相关的非相干源信号方向估计方法

给出了基于循环互相关运算的阵列信号模型,根据该信号模型,运用MUSIC算法得到了对空间非相干源信号方向进行估计的有效方法—CCC-MUSIC算法,定性的分析及仿真实验均说明了所给方法具有较好的抑制噪声和选择信号的能力。该算法将为利用天线阵列提取具有循环平稳特性的源信号方向这一问题提供较好的实现方法。     

A conjugate augmented approach to direction-of-arrival estimation

In this paper, we propose a new Direction-of-Arrival (DOA) estimator called Conjugate Augmented MUSIC (CAM). The basic idea of CAM is to use the second-order statistics of the received signals to get the conjugate steering matrix. This, together with the steering matrix, is used to find the fourth-order cumulants. From that the source directions are obtained using the MUSIC-like algorithm. CAM can resolve two times the number of directions when compared to MUSIC-like estimator. Moreover, simulation results show that the estimation capacity, angle resolution, immunity to noise, and the number of required snapshots are all better than MUSIC-like algorithm.     

Off-grid direction-of-arrival estimation for wideband noncircular sources

Researchers have recently shown an increased interest in estimating the direction-of-arrival (DOA) of wideband noncircular sources, but existing studies have been restricted to subspace-based methods. An off-grid sparse recovery-based algorithm is proposed in this paper to improve the accuracy of existing algorithms in low signal-to-noise ratio situations. The covariance and pseudo covariance matrices can be jointly represented subject to block sparsity constraints by taking advantage of the joint sparsity between signal components and bias. Furthermore, the estimation problem is transformed into a single measurement vector problem utilizing the focused operation, resulting in a significant reduction in computational complexity. The proposed algorithm's error threshold and the Cramer–Rao bound for wideband noncircular DOA estimation are deduced in detail. The proposed algorithm's effectiveness and feasibility are demonstrated by simulation results.     

Maximum-likelihood based estimation of the Nakagami m parameter

Maximum-likelihood estimation of the Nakagami (1960) m parameter is considered. Two new estimators are proposed and examined. The sample mean and the sample variance of the new estimators are compared with the best reported estimator. The new estimators offer superior performance.     

基于非圆信号的二维测向算法

提出了一种基于窄带非圆信号的二维测向算法,利用非圆信号的椭圆协方差矩阵非零特性将阵列有效阵元数和孔径同时扩展,提高多信号检测的能力。进一步通过利用L阵的几何性质和两子阵间的互相关来滤除噪声,提高角度估计精度,并采用快速算法获得信号方位角和俯仰角。最后计算机仿真结果验证了该方法由于利用非圆信号特性比传统测向算法的估计性能更高。