Maximum likelihood localization of diversely polarized sources bysimulated annealing

The maximum likelihood estimator of the angle-of-arrival of sources having diverse polarization is derived and computed via the simulated annealing optimization technique. The estimator is applicable equally well to the case of coherent signals appearing, for example, in multipath propagation problems and to the case of a single snapshot. Simulation results that demonstrate the performance of the algorithm are included     

Maximum likelihood estimation of the parameters of discretefractionally differenced Gaussian noise process

A maximum-likelihood estimation procedure is constructed for estimating the parameters of discrete fractionally differenced Gaussian noise from an observation set of finite size N. The procedure does not involve the computation of any matrix inverse or determinant. It requires N²/2+O(N) operations. The expected value of the loglikelihood function for estimating the parameter d of fractionally differenced Gaussian noise (which corresponds to a parameter of the equivalent continuous-time fractional Brownian motion related to its fractal dimension) is shown to have a unique maximum that occurs at the true value of d. A Cramer-Rao bound on the variance of any unbiased estimate of d obtained from a finite-sized observation set is derived. It is shown experimentally that the maximum-likelihood estimate of d is unbiased and efficient when finite-size data sets are used in the estimation procedure. The proposed procedure is extended to deal with noisy observations of discrete fractionally differenced Gaussian noise     

Maximum likelihood trend estimation in exponential noise

This paper considers the problem of estimating a linear trend in noise, where the noise is modeled as independent and identically distributed (i.i.d.) random process with exponential distribution. The corresponding maximum likelihood parameter estimator of the trend and noise parameters is derived, and its performance is analyzed. It turns out that the resulting maximum likelihood estimator has to solve a linear programming problem with number of constraints equal to the number of received data. A recursive form of the maximum likelihood estimator, which makes it suitable for implementation in real-time systems, is then proposed. The memory requirements of the recursive algorithm are data dependent and are investigated by simulations using both computer-generated and recorded data sets     

Maximum likelihood estimation of signals in autoregressive noise

Time series modeling as the sum of a deterministic signal and an autoregressive (AR) process is studied. Maximum likelihood estimation of the signal amplitudes and AR parameters is seen to result in a nonlinear estimation problem. However, it is shown that for a given class of signals, the use of a parameter transformation can reduce the problem to a linear least squares one. For unknown signal parameters, in addition to the signal amplitudes, the maximization can be reduced to one over the additional signal parameters. The general class of signals for which such parameter transformations are applicable, thereby reducing estimator complexity drastically, is derived. This class includes sinusoids as well as polynomials and polynomial-times-exponential signals. The ideas are based on the theory of invariant subspaces for linear operators. The results form a powerful modeling tool in signal plus noise problems and therefore find application in a large variety of statistical signal processing problems. The authors briefly discuss some applications such as spectral analysis, broadband/transient detection using line array data, and fundamental frequency estimation for periodic signals     

Maximum likelihood time delay estimation in non-Gaussian noise

In a non-Gaussian noise environment, it is theoretically possible to design a delay estimator that performs significantly better than the conventional linear correlator. We study the maximum likelihood estimator for passive time delay in non-Gaussian noise. We show that the form of the best estimator depends strongly on signal-to-noise ratio (SNR), and the estimator optimal at low SNR can fail catastrophically at high values of SNR. The paper uses simulations to examine this sensitivity problem and proposes an ad hoc instrumentation that is reasonably robust over a wide range of SNR values     

Maximum likelihood estimation for array processing in colored noise

Direction of arrival estimation of multiple sources, using a uniform linear array, in noise with unknown covariance is considered. The noise is modeled as a spatial autoregressive process with unknown parameters. Both stochastic and deterministic signal models are considered. For the random signal case, an approximate maximum likelihood estimator of the signal and noise parameters is derived. It requires numerical maximization of a compressed likelihood function over the unknown arrival angles. Analytical expressions for the MLEs of the signal covariance and the AR parameters are given. Similar results for the case of deterministic signals are also presented     

Maximum likelihood array processing for stochastic coherent sources

Maximum likelihood (ML) estimation in array signal processing for the stochastic noncoherent signal case is well documented in the literature. We focus on the equally relevant case of stochastic coherent signals. Explicit large-sample realizations are derived for the ML estimates of the noise power and the (singular) signal covariance matrix. The asymptotic properties of the estimates are examined, and some numerical examples are provided. In addition, we show the surprising fact that the ML estimates of the signal parameters obtained by ignoring the information that the sources are coherent coincide in large samples with the ML estimates obtained by exploiting the coherent source information. Thus, the ML signal parameter estimator derived for the noncoherent case (or its large-sample realizations) asymptotically achieves the lowest possible estimation error variance (corresponding to the coherent Cramer-Rao bound)     

Maximum likelihood estimation for multivariate observations of Markov sources

Parameter estimation for multivariate functions of Markov chains, a class of versatile statistical models for vector random processes, is discussed. The model regards an ordered sequence of vectors as noisy multivariate observations of a Markov chain. Mixture distributions are a special case. The foundations of the theory presented here were established by Baum, Petrie, Soules, and Weiss. A powerful representation theorem by Fan is employed to generalize the analysis of Baum, {em et al.} to a larger class of distributions.     

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.     

Maximum likelihood estimation of direction-of-arrival and detectionfor broad-band sources via dynamic programming

An analysis is presented to estimate the number of broadband sources by sensor arrays and to compute the maximum likelihood estimator (MLE) of their direction-of-arrival (DOA) based on the dynamic programming algorithm. The approach is devised in the frequency domain. With proper selection of the number of elements, the distance between elements, and the step size, the global maximum for the log-likelihood function can be obtained. Otherwise, the global maximum is not guaranteed. Simulation results for broadband sources that demonstrate the performance of the proposed method are presented and compared with that of the MUSIC algorithm which employs coherent signal-subspace processing     

Maximum likelihood DOA estimation and asymptotic Cramer-Rao boundsfor additive unknown colored noise

This paper is devoted to the maximum likelihood estimation of multiple sources in the presence of unknown noise. With the spatial noise covariance modeled as a function of certain unknown parameters, e.g., an autoregressive (AR) model, a direct and systematic way is developed to find the exact maximum likelihood (ML) estimates of all parameters associated with the direction finding problem, including the direction-of-arrival (DOA) angles Θ, the noise parameters α, the signal covariance Φ_s, and the noise power σ². We show that the estimates of the linear part of the parameter set Φ_s and σ² can be separated from the nonlinear parts Θ and α. Thus, the estimates of Φ_s and σ² become explicit functions of Θ and α. This results in a significant reduction in the dimensionality of the nonlinear optimization problem. Asymptotic analysis is performed on the estimates of Θ and α, and compact formulas are obtained for the Cramer-Rao bounds (CRB's). Finally, a Newton-type algorithm is designed to solve the nonlinear optimization problem, and simulations show that the asymptotic CRB agrees well with the results from Monte Carlo trials, even for small numbers of snapshots     

Maximum likelihood estimation and MUSIC in array localization signal processing: A review

Algorithms to treat the maximum likelihood (ML) estimation problem in array localization signal processing are reviewed, including the alternating projection method, the iterative quadratic maximum likelihood method and the expectation-maximization method. The relationship of ML estimators and the MUSIC algorithm is presented. The Cramer-Rao bounds for the deterministic and stochastic models in array localization are summarized. Finally, the problem of the estimation of the number of sources is discussed.     

Passive localization of 3-D near-field sources in coexisted multiplicative noise and additive noise

By exploiting thvorable characteristics of a uniIbrm cross-array, a passive localization algorithm of narrowband sources in the spherical coordinates （azimuth, elevation and range） is proposed. Based on the properly chosen sensor outputs, we compute the third-order cyclic moment matrices, and exploit a pre-calibration technique to eliminate multiplicative noise. Then, we construct a parallel factor （PARAFAC） model, and adopt trilinear altemating least squares regression （TALS） to estimate three-dimensional （3-D） near-field parameters. The investigated algorithm is efficient in the sense that it can eliminate multiplicative noise and additive noise, provide the improved estimation accuracy, as well as avoid the parameter-pairing procedure. Simulation results are carried out to demonstrate the performance of the proposed algorithm.     

Maximum likelihood detection of PPM signals governed by arbitrarypoint-process plus additive Gaussian noise

The maximum likelihood decision statistic for pulse-position modulated (PPM) signals governed by an arbitrary discrete point process in the presence of additive Gaussian noise is derived. Sufficient conditions are given for determining when the optimum PPM symbol detection strategy is to choose the PPM symbol corresponding to the maximum slot statistic. In particular, it is shown that for the important case of Webb distributed avalanche photodiode output electrons in the presence of Gaussian noise, the optimum decision rule is to choose the largest slot observable     

Maximum likelihood multiple-source localization using acoustic energy measurements with wireless sensor networks

A maximum likelihood (ML) acoustic source location estimation method is presented for the application in a wireless ad hoc sensor network. This method uses acoustic signal energy measurements taken at individual sensors of an ad hoc wireless sensor network to estimate the locations of multiple acoustic sources. Compared to the existing acoustic energy based source localization methods, this proposed ML method delivers more accurate results and offers the enhanced capability of multiple source localization. A multiresolution search algorithm and an expectation-maximization (EM) like iterative algorithm are proposed to expedite the computation of source locations. The Crame/spl acute/r-Rao Bound (CRB) of the ML source location estimate has been derived. The CRB is used to analyze the impacts of sensor placement to the accuracy of location estimates for single target scenario. Extensive simulations have been conducted. It is observed that the proposed ML method consistently outperforms existing acoustic energy based source localization methods. An example applying this method to track military vehicles using real world experiment data also demonstrates the performance advantage of this proposed method over a previously proposed acoustic energy source localization method.     

Maximum likelihood filters in spectral estimation problems

This paper begins with a classification of power spectral estimates from the point of view of bank filter analysis. To reinforce the interest of such a classification, a review of the main and most familiar procedures for spectral estimation is included. Starting from the most general approach, due to Frost, we indicate why it is not appropriate to classify Capon's maximum likelihood method as a low resolution procedure.The second part of the paper deals with a modification of the so-called maximum likelihood estimate in order to obtain the resolution which corresponds to a power density estimate. The modification provided here consists in a bandwidth normalization. The resulting estimate shows how the area of application of ML filters (as the data depending filters reported some years ago by Capon and Lacoss could be named) is considerably extended to a reliable procedure for power level and power density level estimation.We also explain in this paper how to get cross-spectral estimates from ML filters. From our point of view, this approach is the only one, among currently reported methods, that enhances the adequate levels of quality in order to compete with classical Fourier analyzers.In addition, the interesting ideas of Pisarenko about power function estimates can also be applied to the new approach presented here. The resulting family of power function estimates can further improve resolution up to the quality provided by SVD like methods, but avoiding the computational burden associated with them.     

Maximum pseudo likelihood estimation in network tomography

Network monitoring and diagnosis are key to improving network performance. The difficulties of performance monitoring lie in today's fast growing Internet, accompanied by increasingly heterogeneous and unregulated structures. Moreover, these tasks become even harder since one cannot rely on the collaboration of individual routers and servers to measure network traffic directly. Even though the aggregative nature of possible network measurements gives rise to inverse problems, existing methods for solving inverse problems are usually computationally intractable or statistically inefficient. A pseudo likelihood approach is proposed to solve a group of network tomography problems. The basic idea of pseudo likelihood is to form simple subproblems and ignore the dependences among the subproblems to form a product likelihood of the subproblems. As a result, this approach keeps a good balance between the computational complexity and the statistical efficiency of the parameter estimation. Some statistical properties of the pseudo likelihood estimator, such as consistency and asymptotic normality, are established. A pseudo expectation-maximization (EM) algorithm is developed to maximize the pseudo log-likelihood function. Two examples, with simulated or real data, are used to illustrate the pseudo likelihood proposal: 1) inference of the internal link delay distributions through multicast end-to-end measurements; 2) origin-destination matrix estimation through link traffic counts.     

MAXIMUM LIKELIHOOD SOURCE SEPARATION FOR FINITE IMPULSE RESPONSE MULTIPLE INPUT—MULTIPLE OUTPUT CHANNELS IN THE PRESENCE OF ADDITIVE NOISE

Blind identification-blind equalization for finite Impulse Response(FIR)Multiple Input-Multiple Output(MIMO)channels can be reformulated as the problem of blind sources separation.It has been shown that blind identification via decorrelating sub-channels method could recover the input sources.The Blind Identification via Decorrelating Sub-channels(BIDS)algorithm first constructs a set of decorrelators,which decorrelate the output signals of subchannels,and then estimates the channel matrix using the transfer functions of the decorrelators and finally recovers the input signal using the estimated channel matrix.In this paper,a new qpproximation of the input source for FIR-MIMO channels based on the maximum likelihood source separation method is proposed.The proposed method outperforms BIDS in the presence of additive white Garssian noise.     

Maximum likelihood estimation of object location in diffractiontomography

The problem is formulated within the context of diffraction tomography, where the complex phase of the diffracted wavefield is modeled using the Rytov approximation and the measurements consist of noisy renditions of this complex phase at a single frequency. The log likelihood function is computed for the case of additive zero mean Gaussian white noise and shown to be expressible in the form of the filtered backpropagation algorithm of diffraction tomography. In this form however, the filter function is no longer the rho filter appropriate to least square reconstruction but is now the generalized projection (propagation) of the object (centered at the origin) onto the line(s) parallel to the measurement line(s), but passing through the origin. This result allows the estimation problem to be solved via a diffraction tomographic imaging procedure where the noisy data is filtered and backpropagated in a first step, and the point of maximum value of the resulting image is then the maximum likelihood (ML) estimate of the object's location. The authors include a calculation of the Cramer-Rao bound for the estimation error and a computer simulation study illustrating the estimation procedure     

Maximum likelihood localization of 2-D patterns in the Gauss-Laguerre transform domain: theoretic framework and preliminary results

Usual approaches to localization, i.e., joint estimation of position, orientation and scale of a bidimensional pattern employ suboptimum techniques based on invariant signatures, which allow for position estimation independent of scale and orientation. In this paper a Maximum Likelihood method for pattern localization working in the Gauss-Laguerre Transform (GLT) domain is presented. The GLT is based on an orthogonal family of Circular Harmonic Functions with specific radial profiles, which permits optimum joint estimation of position and scale/rotation parameters looking at the maxima of a "Gauss-Laguerre Likelihood Map." The Fisher information matrix for any given pattern is given and the theoretical asymptotic accuracy of the parameter estimates is calculated through the Cramer Rao Lower Bound. Application of the ML estimation method is discussed and an example is provided.