Approximate maximum likelihood hyperparameter estimation for Gibbspriors

The parameters of the prior, the hyperparameters, play an important role in Bayesian image estimation. Of particular importance for the case of Gibbs priors is the global hyperparameter, beta, which multiplies the Hamiltonian. Here we consider maximum likelihood (ML) estimation of beta from incomplete data, i.e., problems in which the image, which is drawn from a Gibbs prior, is observed indirectly through some degradation or blurring process. Important applications include image restoration and image reconstruction from projections. Exact ML estimation of beta from incomplete data is intractable for most image processing. Here we present an approximate ML estimator that is computed simultaneously with a maximum a posteriori (MAP) image estimate. The algorithm is based on a mean field approximation technique through which multidimensional Gibbs distributions are approximated by a separable function equal to a product of one-dimensional (1-D) densities. We show how this approach can be used to simplify the ML estimation problem. We also show how the Gibbs-Bogoliubov-Feynman (GBF) bound can be used to optimize the approximation for a restricted class of problems. We present the results of a Monte Carlo study that examines the bias and variance of this estimator when applied to image restoration.     

Maximum-likelihood versus maximum a posteriori parameter estimation of physiological system models: the C-peptide impulse response case study

Maximum-likelihood (ML), also given its connection to least-squares (LS), is widely adopted in parameter estimation of physiological system models, i.e., assigning numerical values to the unknown model parameters from the experimental data. A more sophisticated but less used approach is maximum a posteriori (MAP) estimation. Conceptually, while ML adopts a Fisherian approach, i.e., only experimental measurements are supplied to the estimator, MAP estimation is a Bayesian approach, i.e., a priori available statistical information on the unknown parameters is also exploited for their estimation. In this paper, after a brief review of the theory behind ML and MAP estimators, we compare their performance in the solution of a case study concerning the determination of the parameters of a sum of exponential model which describes the impulse response of C-peptide (CP), a key substance for reconstructing insulin secretion. The results show that MAP estimation always leads to parameter estimates with a precision (sometimes significantly) higher than that obtained through ML, at the cost of only a slightly worse fit. Thus, a three exponential model can be adopted to describe the CP impulse response model in place of the two exponential model usually identified in the literature by the ML/LS approach. Simulated case studies are also reported to evidence the importance of taking into account a priori information in a data poor situation, e.g., when a few or too noisy measurements are available. In conclusion, our results show that, when a priori information on the unknown model parameters is available, Bayes estimation can be of relevant interest, since it can significantly improve the precision of parameter estimates with respect to Fisher estimation. This may also allow the adoption of more complex models than those determinable by a Fisherian approach.     

Performance analysis of direction finding with large arrays andfinite data

This paper considers analysis of methods for estimating the parameters of narrow-band signals arriving at an array of sensors. This problem has important applications in, for instance, radar direction finding and underwater source localization. The so-called deterministic and stochastic maximum likelihood (ML) methods are the main focus of this paper. A performance analysis is carried out assuming a finite number of samples and that the array is composed of a sufficiently large number of sensors. Several thousands of antennas are not uncommon in, e.g., radar applications. Strong consistency of the parameter estimates is proved, and the asymptotic covariance matrix of the estimation error is derived. Unlike the previously studied large sample case, the present analysis shows that the accuracy is the same for the two ML methods. Furthermore, the asymptotic covariance matrix of the estimation error coincides with the deterministic Cramer-Rao bound. Under a certain assumption, the ML methods can be implemented by means of conventional beamforming for a large enough number of sensors. We also include a simple simulation study, which indicates that both ML methods provide efficient estimates for very moderate array sizes, whereas the beamforming method requires a somewhat larger array aperture to overcome the inherent bias and resolution problem     

Source localization in a waveguide using polynomial rooting

Source localization in acoustic waveguides involves a multidimensional search procedure. We propose a new algorithm in which the search in the depth direction is replaced by polynomial rooting. Using the proposed algorithm, range and depth estimation by a vertical array requires a 1-D search procedure. For a 3-D localization problem (i.e., range, depth, and direction-of-arrival (DOA) estimation), the algorithm involves a 2-D search procedure. Consequently, the proposed algorithm requires significantly less computation than other methods that are based on a brute-force search procedure over the source location parameters. In order to evaluate the performance of the algorithm, an error analysis is carried out, and Monte-Carlo simulations are performed. The results are compared with the Cramer-Rao bound (CRB) and to the maximum likelihood (ML) simulation performance. The algorithm is shown to be efficient, while being computationally simpler than the ML or the Bartlett processors. The disadvantage of the algorithm is that its SNR threshold occurs in lower SNR than in the ML algorithm     

Asymptotically Efficient Reduced Complexity Frequency Offset and Channel Estimators for Uplink MIMO-OFDMA Systems

In this paper, we address the joint data-aided estimation of frequency offsets and channel coefficients in uplink multiple-input multiple-output orthogonal frequency-division multiple access (MIMO-OFDMA) systems. As the maximum-likelihood (ML) estimator is impractical in this context, we introduce a family of suboptimal estimators with the aim of exhibiting an attractive tradeoff between performance and complexity. The estimators do not rely on a particular subcarrier assignment scheme and are, thus, valid for a large number of OFDMA systems. As far as complexity is concerned, the computational cost of the proposed estimators is shown to be significantly reduced compared to existing estimators based on ML. As far as performance is concerned, the proposed suboptimal estimators are shown to be asymptotically efficient, i.e., the covariance matrix of the estimation error achieves the Cramer-Rao bound when the total number of subcarriers increases. Simulation results sustain our claims.     

Threshold region performance of maximum likelihood direction of arrival estimators

This paper presents a performance analysis of the maximum likelihood (ML) estimator for finding the directions of arrival (DOAs) with a sensor array. The asymptotic properties of this estimator are well known. In this paper, the performance under conditions of low signal-to-noise ratio (SNR) and a small number of array snapshots is investigated. It is well known that the ML estimator exhibits a threshold effect, i.e., a rapid deterioration of estimation accuracy below a certain SNR or number of snapshots. This effect is caused by outliers and is not captured by standard techniques such as the Crame/spl acute/r-Rao bound and asymptotic analysis. In this paper, approximations to the mean square estimation error and probability of outlier are derived that can be used to predict the threshold region performance of the ML estimator with high accuracy. Both the deterministic ML and stochastic ML estimators are treated for the single-source and multisource estimation problems. These approximations alleviate the need for time-consuming computer simulations when evaluating the threshold region performance. For the special case of a single stochastic source signal and a single snapshot, it is shown that the ML estimator is not statistically efficient as SNR/spl rarr//spl infin/ due to the effect of outliers.     

Application of natural computing algorithms to maximum likelihood estimation of direction of arrival

This work presents a study of the performance of populational meta-heuristics belonging to the field of natural computing when applied to the problem of direction of arrival (DOA) estimation, as well as an overview of the literature about the use of such techniques in this problem. These heuristics offer a promising alternative to the conventional approaches in DOA estimation, as they search for the global optima of the maximum likelihood (ML) function in a framework characterized by an elegant balance between global exploration and local improvement, which are interesting features in the context of multimodal optimization, to which the ML-DOA estimation problem belongs. Thus, we shall analyze whether these algorithms are capable of implementing the ML estimator, i.e., finding the global optima of the ML function. In this work, we selected three representative natural computing algorithms to perform DOA estimation: differential evolution, clonal selection algorithm, and the particle swarm. Simulation results involving different scenarios confirm that these methods can reach the performance of the ML estimator, regardless of the number of sources and/or their nature. Moreover, the number of points evaluated by such methods is quite inferior to that associated with a grid search, which gives support to their application.     

基于图像强度最优的SAR高精度运动补偿方法

由于载体平台的不稳定性和测量传感器的精度限制,运动误差成为了提高合成孔径雷达(SAR)成像质量的一个瓶颈。基于图像锐度最优的自聚焦后向投影算法通过估计相位误差进行运动补偿,具有较高精度,但这种方法假设场景中所有像素点相位误差相同,即没有考虑运动误差的空变性,导致大部分像素点仍存在残留误差,造成成像质量下降。针对运动误差空变性的问题,该文提出一种高精度运动补偿方法,该方法在图像强度最大准则下,采用最优化技术估计天线相位中心测量误差,随后利用该测量误差估计量校正天线相位中心并进行后向投影成像。由于估计天线相位中心等效于估计每个像素点的距离历史,因此该方法可以对每个像素点进行高精度相位补偿。点目标仿真和实测数据处理结果均验证了所提方法的有效性。      

Maximum-likelihood direction-of-arrival estimation in the presenceof unknown nonuniform noise

We consider the problem of estimating directions of arrival (DOAs) of multiple sources observed on the background of nonuniform white noise with an arbitrary diagonal covariance matrix. A new deterministic maximum likelihood (ML) DOA estimator is derived. Its implementation is based on an iterative procedure which includes a stepwise concentration of the log-likelihood (LL) function with respect to the signal and noise nuisance parameters and requires only a few iterations to converge. New closed-form expressions for the deterministic and stochastic direction estimation Cramer-Rao bounds (CRBs) are derived for the considered nonuniform model. Our expressions can be viewed as an extension of the well-known results by Stoica and Nehorai (1989, 1990) and Weiss and Friedlander (1993) to a more general noise model than the commonly used uniform one. In addition, these expressions extend the results obtained by Matveyev et al. (see Circuits, Syst., Signal Process., vol.18, p.479-87, 1999) to the multiple source case. Comparisons with the above-mentioned earlier results help to discover several interesting properties of DOA estimation in the nonuniform noise case. To compare the estimation performance of the proposed ML technique with the results of our CRB analysis and with the performance of conventional “uniform” ML, simulation results are presented. Additionally, we test our technique using experimental seismic array data. Our simulations and experimental results both validate essential performance improvements achieved by means of the approach proposed     

On rate-constrained distributed estimation in unreliable sensor networks

We study the problem of estimating a physical process at a central processing unit (CPU) based on noisy measurements collected from a distributed, bandwidth-constrained, unreliable, network of sensors, modeled as an erasure network of unreliable "bit-pipes" between each sensor and the CPU. The CPU is guaranteed to receive data from a minimum fraction of the sensors and is tasked with optimally estimating the physical process under a specified distortion criterion. We study the noncollaborative (i.e., fully distributed) sensor network regime, and derive an information-theoretic achievable rate-distortion region for this network based on distributed source-coding insights. Specializing these results to the Gaussian setting and the mean-squared-error (MSE) distortion criterion reveals interesting robust-optimality properties of the solution. We also study the regime of clusters of collaborative sensors, where we address the important question: given a communication rate constraint between the sensor clusters and the CPU, should these clusters transmit their "raw data" or some low-dimensional "local estimates"? For a broad set of distortion criteria and sensor correlation statistics, we derive conditions under which rate-distortion-optimal compression of correlated cluster-observations separates into the tasks of dimension-reducing local estimation followed by optimal distributed compression of the local estimates.     

Signal waveform estimation in the presence of uncertainties about the steering vector

We consider the problem of signal waveform estimation using an array of sensors where there exist uncertainties about the steering vector of interest. This problem occurs in many situations, including arrays undergoing deformations, uncalibrated arrays, scattering around the source, etc. In this paper, we assume that some statistical knowledge about the variations of the steering vector is available. Within this framework, two approaches are proposed, depending on whether the signal is assumed to be deterministic or random. In the former case, the maximum likelihood (ML) estimator is derived. It is shown that it amounts to a beamforming-like processing of the observations, and an iterative algorithm is presented to obtain the ML weight vector. For random signals, a Bayesian approach is advocated, and we successively derive an (approximate) minimum mean-square error estimator and maximum a posteriori estimators. Numerical examples are provided to illustrate the performances of the estimators.     

非均匀噪声环境下宽带近场源定位的两种改进方法

研究了宽带近场信号源基于最大似然方法和相关信号子空间方法在非均匀噪声下的被动定位算法，并进行了比较。这两种算法均可在传感器任意分布的情况下有效地进行信号源定位。最大似然法采用了迭代的方法来估计噪声的协方差矩。而信号子空间法给出了聚焦阵构造的新方法。仿真试验证明了方法的有效性和稳健性。     

平坦衰落信道下基于变分贝叶斯的多天线信号联合符号检测算法

该文针对平坦衰落信道下存在信道参数差异的多天线接收信号联合参数估计和符号检测问题,提出一种基于变分贝叶斯的联合处理算法。算法直接利用多个接收数据流进行信息符号的估计,抑制传统信号合成与解调解耦处理带来的性能损失。将问题建模为已知多组观测数据条件下发送符号、信道传输时延、信道增益和噪声功率的联合最大后验估计问题。基于变分贝叶斯理论对该最大后验进行近似求解,在相对熵最小化的准则下,推导得到了各个待估参数解析形式的近似后验分布——变分分布。所提算法无需计算各参数精确的点估计值,而是采用信道参数和信息符号变分分布迭代处理的方式进行联合求解。仿真结果表明,所提算法通过多信号、多参数的联合处理能够获得优于经典解耦处理和部分联合处理技术的系统误码率性能,且在接收天线数目较多和观测数据长度较短时性能优势体现更加明显。     

Landmine detection and localization using chemical sensor arrayprocessing

We develop methods for automatic detection and localization of landmines using chemical sensor arrays and statistical signal processing techniques. The transport of explosive vapors emanating from buried landmines is modeled as a diffusion process in a two-layered system consisting of ground and air. Measurement and statistical models are then obtained from the associated concentration distribution. We derive two detectors (the generalized likelihood ratio (GLR) test and the mean detector) and determine their performance in terms of the probabilities of false alarm and detection. To determine the unknown location of a landmine, we derive a maximum likelihood (ML) estimation algorithm and evaluate its performance by computing the Cramer-Rao bound (CRB). The results are applied to the design of chemical sensor arrays, satisfying criteria specified in terms of detection and estimation performance measures and for optimally selecting the number and positions of sensors and the number of time samples. To illustrate the potential of the proposed techniques in a realistic demining scenario, we derive a moving-sensor algorithm in which the stationary sensor array is replaced by a single moving sensor. Numerical examples are given to demonstrate the applicability of our results     

Estimation of chirp radar signals in compound-Gaussian clutter: acyclostationary approach

Signal detection of known (within a complex scaling) rank one waveforms in non-Gaussian distributed clutter has received considerable attention. We expand on published solutions to consider the case of rank one waveforms that have some unknown parameters, i.e., signal amplitude, initial phase, Doppler shift, and Doppler rate of change. The contribution of this paper is the derivation and performance analysis of two joint estimators of Doppler shift and Doppler rate-the chirp embedded in correlated compound-Gaussian clutter. One solution is based on the maximum likelihood (ML) principle and the other one on target signal second-order cyclostationarity. The hybrid Cramer-Rao lower bounds (HCRLBs) and a large sample closed-form expression for the mean square estimation error (only for the Doppler shift) are also derived. Numerical examples are provided to show the behavior of the proposed estimator under different non-Gaussian clutter scenarios     

电磁矢量传感器原位误差校正方法

 现有基于电磁矢量传感器阵列的信号DOA和极化参数联合估计算法,大都假设电磁矢量传感器的三个电偶极子和三个磁偶极子严格指向参考坐标系的三个坐标轴,即不存在原位误差.然而在实际应用场合,电磁矢量传感器是存在原位误差的,因此其实际极化-角度域导向矢量与理想情况下的极化-角度域导向矢量有一定的偏差,导致现有方法的估计性能显著下降,因此必须对原位误差进行校正.通过对存在偏差的极化-角度域导向矢量进行一阶Taylor近似展开,并利用一个辅助校正源,提出了电磁矢量传感器原位误差校正方法,给出了原位误差估计的CRB界.仿真结果验证了该方法的有效性.     

Underwater acoustic sensor networks: Target size detection and performance analysis

Underwater acoustic sensor network consists of a variable number of sensors and vehicles that are deployed to perform collaborative monitoring tasks over a given area. Scalability concern suggests a hierarchical organization of underwater sensor networks with the lowest level in the hierarchy being a cluster. In this paper, we show that an ultra-wide band (UWB) channel can be used for underwater channel modeling and propose a maximum-likelihood (ML) estimation algorithm for underwater target size detection using collaborative signal processing within a cluster in underwater acoustic sensor networks. Theoretical analysis demonstrates that our underwater sensor network can tremendously reduce the variance of target size estimation. We show that our ML estimator is unbiased and the variance of parameter estimation matches the Cramer–Rao lower bound. Simulations further validate these theoretical results.     

Amplitude spectrum estimation for two-dimensional gapped data

The amplitude and phase estimation (APES) approach to nonparametric spectrum estimation of uniformly sampled data has received considerable interest. We consider the extension of APES to gapped data, i.e., uniformly sampled data with missing samples. It has been shown that the APES estimate of the spectrum is the minimizer of a certain least-squares (LS) criterion, and our extension of APES is based on minimizing this LS criterion with respect to the missing data as well. A computationally efficient method for doing this based on cyclic minimization and the conjugate gradient algorithm is proposed. The new algorithm is called gapped-data APES (GAPES) and is developed for the two-dimensional (2-D) case, with the one-dimensional (1-D) case as a special instance. Numerical examples are provided to demonstrate the performance of the algorithm and to show the advantages of 2-D data processing over 1-D (row or column-wise) data processing, as well as to show the applicability of the algorithm to synthetic aperture radar (SAR) imaging     

二值传感器网络的分布式稀疏LMS算法

在基于无线传感器网络的参数估计中,每个节点在数据采集、存储、处理和传输等方面的能力是有限的。二值传感器网络中的每个节点只能提供低精度1比特测量值,与能够提供模拟测量值（无限精度）的传感器相比,二值传感器有较低的使用成本。如何利用低成本二值传感器网络获得较好的参数估计性能近些年已引起广泛关注,基于该二值传感器网络,论文提出了一种分布式稀疏参数估计的自适应最小均方（LMS）算法。该算法采用稀疏惩罚最大似然优化,并结合期望最大化和LMS方法,获得稀疏信号的在线估计。仿真实验表明,尽管只采用1比特测量,提出的算法仍具有较好的收敛性,并且稳定状态的估计误差接近于非1比特测量的同类算法。      

Decoding space-time codes with BLAST architectures

We introduce a coding/decoding scheme matched to a "vertical" BLAST architecture; a code has its words evenly split among the transmit antennas. The subcodes so transmitted by each antenna are decoded in sequence to cancel the spatial interference while a final decoding step is performed on the whole code. We also examine the behavior of zero-forcing (ZF) and minimum-mean-square error (MMSE) BLAST by comparing their error probabilities with those resulting from optimum, i.e., maximum-likelihood (ML), processing. Since, with vertical BLAST, ordering of the columns of the channel-gain matrix is crucial, we also study the performance of algorithms intended to find an optimal (or mildly suboptimal) ordering.