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.     

Asymptotic receiver structures for joint maximum likelihood timedelay estimation and channel identification using Gaussian signals

The problem of jointly estimating the relative time delay and the impulse response linking two received discrete-time Gaussian signals is addressed. Using two different methods, possible structures for the joint maximum-likelihood (ML) estimator are proposed, when the observation interval is long compared to both the delay to estimate and the correlation time, of the various random processes involved. These structures generalize the cross-correlation method with prefiltering that implements the ML estimation of pure time delays     

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.     

Asymptotic maximum likelihood estimator performance for chaoticsignals in noise

The performance of the maximum likelihood estimator for a 1-D chaotic signal in white Gaussian noise is derived. It is found that the estimator is inconsistent and therefore the usual asymptotic distribution (large data record length) is invalid. However, for high signal-to-noise ratios (SNRs), the maximum likelihood estimator is asymptotically unbiased and attains the Cramer-Rao lower bound     

Asymptotic equivalence between the unconditional maximum likelihood and the square-law nonlinearity symbol timing estimation

This paper provides a systematic approach to the problem of nondata aided symbol-timing estimation for linear modulations. The study is performed under the unconditional maximum likelihood framework where the carrier-frequency error is included as a nuisance parameter in the mathematical derivation. The second-order moments of the received signal are found to be the sufficient statistics for the problem at hand and they allow the provision of a robust performance in the presence of a carrier-frequency error uncertainty. We particularly focus on the exploitation of the cyclostationary property of linear modulations. This enables us to derive simple and closed-form symbol-timing estimators which are found to be based on the well-known square timing recovery method by Oerder and Meyr. Finally, we generalize the OM method to the case of linear modulations with offset formats. In this case, the square-law nonlinearity is found to provide not only the symbol-timing but also the carrier-phase error.     

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     

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.     

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     

On maximum likelihood estimation for the two parameter Weibull distribution

This paper examines recent results presented on maximum likelihood estimation for the two parameter Weibull distribution. In particular, we seek to explain some recently reported values for estimator bias when the data for analysis contains both times to failure and censored times in operation; our discussion centres on the generation of sample data sets. We conclude that, under appropriate conditions, estimators are asymptotically unbiased, with relatively low bias in small to moderate samples. We then present the results of some further experiments which suggest that the previously reported values for estimator bias can be attributed to the method of generating sample data sets in simulation experiments.     

Two-stage maximum likelihood estimation for diversity combining indigital mobile radio

For space diversity, it is shown that it is related to maximal-ratio combining (MRC). Unlike MRC, it allows the receiver to collect diversity signals without gain adjustments or cophasing. Some worst-case bit error rate (BER) simulation results that show the influence of time delay spread, Doppler, shadow loss, and diversity for a seven-cell cluster using quadrature modulation are presented     

Symmetric adaptive maximum likelihood estimation for noisecancellation and signal separation

The symmetric adaptive maximum likelihood estimation (SAMLE) algorithm is proposed. It is shown to be a generalisation of the symmetric adaptive decorrelation (SAD) algorithm for noise cancellation and signal separation. Both the SAD and SAMLE algorithms are applied to the separation of a mixture of natural speech recorded in a realistic acoustic environment. A comparative simulation confirms that the SAMLE algorithm provides superior separation capabilities     

Cramer-Rao bounds and maximum likelihood estimation for randomamplitude phase-modulated signals

The problem of estimating the phase parameters of a phase-modulated signal in the presence of colored multiplicative noise (random amplitude modulation) and additive white noise (both Gaussian) is addressed. Closed-form expressions for the exact and large-sample Cramer-Rao Bounds (CRBs) are derived. It is shown that the CRB is significantly affected by the color of the modulating process when the signal-to-noise ratio (SNR) or the intrinsic SNR is small. Maximum likelihood type estimators that ignore the noise color and optimize a criterion with respect to only the phase parameters are proposed. These estimators are shown to be equivalent to the nonlinear least squares estimators, which consist of matching the squared observations with a constant amplitude phase-modulated signal when the mean of the multiplicative noise is forced to zero. Closed-form expressions are derived for the efficiency of these estimators and are verified via simulations     

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