Expected likelihood support for deterministic maximum likelihood DOA estimation

In this paper, a solution quality assessment method referred to as the “expected likelihood” (EL) approach, previously introduced for the stochastic (unconditional) Gaussian model, is extended over the deterministic (conditional) Gaussian model. This model is applied for arbitrary temporally correlated (narrowband) waveforms, emitted by point sources impinging upon an antenna array. Performance of direction of arrival (DOA) estimation is then examined.     

引入蝙蝠算法的最大似然DOA估计

DOA估计理论的传统算法中,最大似然DOA估计方法能准确地估计出目标方向角度,性能优良,并且具有很好的稳定性。与MUSIC及其他的子空间分解类算法相比,在信噪比较低、小快拍信号时,最大似然DOA估计算法优势更为突出。但是由于其自身算法复杂度较高的缺陷而碍于工程上的应用。针对这一问题,将蝙蝠算法与最大似然算法相结合,应用于信号的DOA估计,利用蝙蝠搜索算法搜索路径优、寻优能力强的优点,快速搜索到似然函数的全局最优值,优化多维非线性的估计谱函数。仿真结果表明,蝙蝠搜索算法有效地克服最大似然DOA估计中存在的运算量大,计算复杂度高等问题,通过与其他经典的仿生智能优化算法相比较,该方法体现出更好的收敛性。     

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.     

Fast maximum likelihood DOA estimation in the two-target case with applications to automotive radar

Direction-of-arrival (DOA) estimation of two targets using a single snapshot plays an important role in automotive radar for advanced driver assistance systems. Conventional Fourier methods have a limited resolution and generally yield biased estimates. Subspace methods involve a numerically complex eigendecomposition and require multiple snapshots or a suboptimal pre-processing for reliable estimation. We therefore consider the maximum likelihood (ML) DOA estimator, which is applicable with a single snapshot and shows good statistical properties. To reduce the computational burden, we propose a grid search procedure with a simplified calculation of the objective function. The required projection operators are pre-calculated off-line and stored. To save storage space and computations, we further propose a rotational shift of the field-of-view such that the relevant angular sector, which has to be evaluated, is delimited and centered with respect to broadside. The final estimates are obtained using a quadratic interpolation. The developed method is demonstrated with an example. Simulations are designed to assess the performance of the considered ML estimator with grid search and interpolation, and to compare it among selected representative methods. We further present results obtained with experimental data from a typical application in automotive radar.     

Nonlinear maximum likelihood estimation of autoregressive timeseries

Describes an algorithm for finding the exact, nonlinear, maximum likelihood (ML) estimators for the parameters of an autoregressive time series. The authors demonstrate that the ML normal equations can be written as an interdependent set of cubic and quadratic equations in the AR polynomial coefficients. They present an algorithm that algebraically solves this set of nonlinear equations for low-order problems. For high-order problems, the authors describe iterative algorithms for obtaining a ML solution     

New perspectives for maximum likelihood time-delay estimation

This paper introduces a new realization for maximum likelihood time-delay estimation (TDE) that illuminates the relationships between maximum likelihood TDE and other methods. We obtain the result by deriving the likelihood function using a fundamental method that appears to be new to the field of array processing. This method is a natural complement to the generalized Karhunen-Loeve expansion     

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.     

Application of maximum likelihood estimation to radar imaging

An efficient maximum likelihood (ML) estimator to obtain the scattering center locations of a target and the relative scattering level of these scattering centers from the scattered field data is described. In the proposed method, ML estimation is carried out in the image domain rather than in the frequency-aspect domain. A two-dimensional (2-D) inverse Fourier transform is used to transfer the scattered field data from frequency-aspect domain to the image domain (down-range/cross-range). As expected, the scattered field data in the image domain has some regions with high energy. The samples in the high-energy regions are used to obtain the initial guess for the ML estimator as well as for ML estimation. The ML estimator in the image domain is applied to both simulated and experimental scattered fields of some targets     

Robust maximum likelihood bearing estimation in contaminatedGaussian noise

A robust maximum likelihood (ML) direction-of-arrival (DOA) estimation method that is insensitive to outliers and distributional uncertainties in Gaussian noise is presented. The algorithm has been shown to perform much better than the Gaussian ML algorithm when the underlying noise distribution deviates even slightly from Gaussian while still performing almost as well in pure Gaussian noise. As with the Gaussian ML estimation, it is still capable of handling correlated signals as well as single snapshot cases. Performance of the algorithm is analyzed using the unique resolution test procedure which determines whether a DOA estimation algorithm, at a given confidence level, can resolve two dominant sources with very close DOAs     

Computationally efficient maximum likelihood estimation ofstructured covariance matrices

By invoking the extended invariance principle (EXIP), we present herein a computationally efficient method that provides asymptotic (for large samples) maximum likelihood (AML) estimation for structured covariance matrices and is referred to as the AML algorithm. A closed-form formula for estimating the Hermitian Toeplitz covariance matrices that makes AML computationally simpler than most existing Hermitian Toeplitz matrix estimation algorithms is derived. Although the AML covariance matrix estimator can be used in a variety of applications, we focus on array processing. Our simulation study shows that AML enhances the performance of angle estimation algorithms, such as MUSIC, by making them very close to the corresponding Cramer-Rao bound (CRB) for uncorrelated signals. Numerical comparisons with several structured and unstructured covariance matrix estimators are also presented     

An exact forward-backward maximum likelihood autoregressiveparameter estimation method

A method for obtaining an exact maximum likelihood estimate (MLE) of the autoregressive (AR) parameters is proposed. The method is called the forward-backward maximum likelihood algorithm. Based on a new form of the log likelihood function for a Gaussian AR process, an iterative maximization is used to obtain an MLE of the inverse covariance matrix. The AR parameters are then determined via the normal equations. Experimental results comparing the new method with other popular AR spectrum estimation methods indicate the new method achieves low bias and low variance AR parameter estimates comparable with the existing methods     

Exact maximum likelihood estimation using masked system data

This work estimates component reliability from masked series-system life data, viz, data where the exact component causing system failure might be unknown. The authors extend the results of Usher and Hodgson (1988) by deriving exact maximum likelihood estimators (MLE) for the general case of a series system of three exponential components with independent masking. Their previous work shows that closed-form MLE are intractable, and they propose an iterative method for the solution of a system of three nonlinear likelihood equations     

Diversity improvement estimation from rain Radar databases using maximum likelihood estimation

This research examines route diversity as a fade mitigation technique in the presence of rain, for terrestrial microwave links. The improvement in availability due to diversity depends upon the complex spatio-temporal properties of rainfall. To produce a general model to predict the advantage due to route diversity it is necessary to be able to predict the correlation of rain attenuation on arbitrary pairs of microwave links. This is achieved by examination of a database of radar derived rain rate fields. Given a representative sample of rain field images, the joint rain attenuation statistics of arbitrary configurations of terrestrial links can be estimated. Existing rain field databases often yield very small numbers of high joint attenuation events. Consequently, estimates of the probability of joint high attenuation events derived from ratios of the number of occurrences can be highly inaccurate. This paper assumes that pairs of terrestrial microwave links have joint rain attenuation distributions that are bi-lognormally distributed. Four of the five distribution parameters can be estimated from ITU-R models. A maximum likelihood estimation (MLE) method is used to estimate the fifth parameter, i.e., the covariance or correlation. The predicted diversity statistics vary smoothly and yield plausible extrapolations into low probability situations.     

基于NC-MUSIC算法的均匀圆阵DOA估计及性能分析

近年来基于非圆信号的DOA估计算法由于其优良的估计性能,受到越来越多的关注。在接收阵列为均匀圆阵的情况下,对入射信号进行方位角和俯仰角的联合估计。依据非圆信号的DOA估计数学模型及阵列模型,采用NC-MUSIC算法完成对均匀圆阵方位角和俯仰角的联合估计。通过计算机仿真,得出该算法对均匀圆阵方位角和俯仰角的估计是比较准确的,并且通过NC-MUSIC与MUSIC算法仿真性能的分析比较,得出在接收阵列为均匀圆阵的情况下,NC-MUSIC算法也优于MUSIC。     

Vector-extrapolated fast maximum likelihood estimation algorithms for emission tomography

A new class of fast maximum-likelihood estimation (MLE) algorithms for emission computed tomography (ECT) is developed. In these cyclic iterative algorithms, vector extrapolation techniques are integrated with the iterations in gradient-based MLE algorithms, with the objective of accelerating the convergence of the base iterations. This results in a substantial reduction in the effective number of base iterations required for obtaining an emission density estimate of specified quality. The mathematical theory behind the minimal polynomial and reduced rank vector extrapolation techniques, in the context of emission tomography, is presented. These extrapolation techniques are implemented in a positron emission tomography system. The new algorithms are evaluated using computer experiments, with measurements taken from simulated phantoms. It is shown that, with minimal additional computations, the proposed approach results in substantial improvement in reconstruction.     

被动虚拟阵列的CRB界及最大似然估计方法研究

针对利用机载运动平台对窄带微波信号进行侦测的背景,研究了被动虚拟阵列（PASA）对窄带微波信号的参数估计性能。在考虑方向角、频率和幅度均为未知参数的条件下,推导了方向角估计的克拉美劳界（CRB）的表达式,同时给出了PASA合成孔径长度的选取方案。另外,本文给出了PASA对方位角估计的最大似然（ML）估计算法。研究表明,随着合成孔径长度和信噪比的增加,ML估计误差可以很快地收敛于CRB,但存在阈值效应。计算机仿真结果验证了本文研究结果的正确性。     

Exact maximum likelihood time delay estimation for shortobservation intervals

An exact solution is presented to the problem of maximum likelihood time delay estimation for a Gaussian source signal observed at two different locations in the presence of additive, spatially uncorrelated Gaussian white noise. The solution is valid for arbitrarily small observation intervals; that is, the assumption T≫τ _c, |d| made in the derivation of the conventional asymptotic maximum likelihood (AML) time delay estimator (where τ _c is the correlation time of the various random processes involved and d is the differential time delay) is relaxed. The resulting exact maximum likelihood (EML) instrumentation is shown to consist of a finite-time delay-and-sum beamformer, followed by a quadratic postprocessor based on the eigenvalues and eigenfunctions of a one-dimensional integral equation with nonconstant weight. The solution of this integral equation is obtained for the case of stationary signals with rational power spectral densities. Finally, the performance of the EML and AML estimators is compared by means of computer simulations     

Iterative maximum likelihood displacement field estimation inquantum-limited image sequences

We develop an algorithm for obtaining the maximum likelihood (ML) estimate of the displacement vector field (DVP) from two consecutive image frames of an image sequence acquired under quantum-limited conditions. The estimation of the DVF has applications in temporal filtering, object tracking, stereo matching, and frame registration in low-light level image sequences as well as low-dose clinical X-ray image sequences. In the latter case, a controlled X-ray dosage reduction may be utilized to lower the radiation exposure to the patient and the medical staff. The quantum-limited effect is modeled as an undesirable, Poisson-distributed, signal-dependent noise artifact. A Fisher-Bayesian formulation is used to estimate the DVF and a block component search algorithm is employed in obtaining the solution. Several experiments involving a phantom sequence and a teleconferencing image sequence with realistic motion demonstrate the effectiveness of this estimator in obtaining the DVF under severe quantum noise conditions (20-25 events/pixel).     

A recursive maximum likelihood algorithm for ARMA spectral estimation

A spectral estimation technique is presented for autoregressive moving-average (ARMA) processes. The technique is based on a parameter estimation technique known as the rec ursive maximum likelihood (RML) method. The recursive spectral estimation algorithm is presented and its asymptotic properties are discussed. Simulation results are presented to illustrate the performance of the estimator for various types of data.     

Conditional mean and maximum likelihood approaches to multiharmonicfrequency estimation

The performance of an extended Kalman filter (EKF) applied to the problem of estimating the (assumed constant) parameters (fundamental frequency, harmonic phases, and amplitudes) of a complex multiharmonic signal measured in noise is shown to be asymptotically (i.e., as the number of measurements tends to infinity) efficient. The Cramer-Rao (CR) bounds associated with the estimation problem are derived for the case where the measurements commence at an arbitrary time distinct from zero