James P. Reilly

On information theoretic criteria for determining the number of signals in high resolution array processing

An important problem in high-resolution array processing is the determination of the number of signals arriving at the array. Information theoretic criteria provide a means to achieve this. Two commonly used criteria are the Akaike information criterion (AIC) and minimum descriptive length (MDL) criterion. While the AIC tends to overestimate even at a high signal-to-noise ratio (SNR), the MDL criterion tends to underestimate at low or moderate SNR. By excluding irrelevant parameters, a new log likelihood function has been chosen. Utilizing this new log likelihood function gives a set of more accurate estimates of the eigenvalues and in the establishment of modified information theoretic criteria which moderate the performance of the AIC and the MDL criterion. Computer simulations confirm that the modified criteria have superior performance. >

Statistical analysis of the performance of information theoretic criteria in the detection of the number of signals in array processing

The performances of the Akaike (1974) information criterion and the minimum descriptive length criterion methods are examined. The events which lead to erroneous decisions are considered, and, on the basis of these events, the probabilities of error for the two criteria are derived. The probabilities of the first two events are derived based on the asymptotic distribution of the sample eigenvalues of an estimated Hermitian matrix. It is further shown that the probabilities of missing and false alarm for these two criteria can be evaluated to a close approximation. Although the derivation of the probabilities of error is based on an asymptotic analysis, the results are confirmed to be in very close agreement with computer simulation results. >

A frequency domain method for blind source separation of convolutive audio mixtures

In this paper, we propose a new frequency domain approach to blind source separation (BSS) of audio signals mixed in a reverberant environment. We propose a joint diagonalization procedure on the cross power spectral density matrices of the signals at the output of the mixing system to identify the mixing system at each frequency bin up to a scale and permutation ambiguity. The frequency domain joint diagonalization is performed using a new and quickly converging algorithm which uses an alternating least-squares (ALS) optimization method. The inverse of the mixing system is then used to separate the sources. An efficient dyadic algorithm to resolve the frequency dependent permutation ambiguities that exploits the inherent nonstationarity of the sources is presented. The effect of the unknown scaling ambiguities is partially resolved using an initialization procedure for the ALS algorithm. The performance of the proposed algorithm is demonstrated by experiments conducted in real reverberant rooms. Performance comparisons are made with previous methods.

Detection of the number of signals: a predicted eigen-threshold approach

A novel method for detecting the number of signals incident upon an array of sensors is described. The method is based on finding upper thresholds for the observed eigenvalues of the correlation matrix of the array output. The asymptotic normality of the multifold eigenvalue estimate is used to derive a prediction formula for the thresholds. Due to the fact that the detection error of the method can be controlled by a parameter t, the performance of the method is superior to the MDL (minimum description length) under low SNR (signal-to-noise ratio) and superior to an AIC (Akaike information criterion) under high SNR. The distribution functions of both missing and false alarm errors are evaluated so that the performance of the method can be analyzed and so that t can be chosen. Simulation results are presented to confirm the analysis. >

Estimation of the directions of arrival of signals in unknown correlated noise. I. The MAP approach and its implementation

The authors propose a method of direction of arrival (DOA) estimation of signals in the presence of noise whose covariance matrix is unknown and arbitrary, other than being positive definite. They examine the projection of the data onto the noise subspace. The conditional probability density function (PDF) of the projected data given the signal parameters and the unknown projected noise covariance matrix is first formed. The a posteriori PDF of the signal parameters alone is then obtained by assigning a noninformative a priori PDF to the unknown noise covariance matrix and integrating out this quantity. A simple criterion for the maximum a posteriori (MAP) estimate of the DOAs of the signals is established. Some properties of this criterion are discussed, and an efficient numerical algorithm for the implementation of this criterion is developed. The advantage of this method is that the noise covariance matrix does not have to be known, nor must it be estimated. >

Particle filters for tracking an unknown number of sources

This paper addresses the application of sequential importance sampling (SIS) schemes to tracking directions of arrival (DOAs) of an unknown number of sources, using a passive array of sensors. This proposed technique has significant advantages in this application, including the ability to detect a changing number of signals at arbitrary times throughout the observation period and that the requirement for quasistationarity over a limited interval may be relaxed. We propose the use of a reversible jump Monte Carlo Markov chain (RJMCMC) step to enhance the statistical diversity of the particles. This step also enables us to introduce two novel moves that significantly enhance the performance of the algorithm when the DOA tracks cross. The superior performance of the method is demonstrated by examples of application of the particle filter to sequential tracking of the DOAs of an unknown and nonstationary number of sources and to a scenario where the targets cross. Our results are compared with the PASTd method.

Efficient design of oversampled NPR GDFT filterbanks

We propose a flexible, efficient design technique for the prototype filter of an oversampled near perfect reconstruction (NPR) generalized discrete Fourier transform (GDFT) filterbank. Such filterbanks have several desirable properties for subband processing systems that are sensitive to aliasing, such as subband adaptive filters. The design criteria for the prototype filter are explicit bounds (derived herein) on the aliased components in the subbands and the output, the distortion induced by the filterbank, and the imaged subband errors in the output. It is shown that the design of an optimal prototype filter can be transformed into a convex optimization problem, which can be efficiently solved. The proposed design technique provides an efficient and effective tool for exploring many of the inherent tradeoffs in the design of the prototype filter, including the tradeoff between aliasing in the subbands and the distortion induced by the filterbank. We calculate several examples of these tradeoffs and demonstrate that the proposed method can generate filters with significantly better performance than filters obtained using current design methods.

An EM Algorithm for Nonlinear State Estimation With Model Uncertainties

In most solutions to state estimation problems, e.g., target tracking, it is generally assumed that the state transition and measurement models are known a priori. However, there are situations where the model parameters or the model structure itself are not known a priori or are known only partially. In these scenarios, standard estimation algorithms like the Kalman filter and the extended Kalman Filter (EKF), which assume perfect knowledge of the model parameters, are not accurate. In this paper, the nonlinear state estimation problem with possibly non-Gaussian process noise in the presence of a certain class of measurement model uncertainty is considered. It is shown that the problem can be considered as a special case of maximum-likelihood estimation with incomplete data. Thus, in this paper, we propose an EM-type algorithm that casts the problem in a joint state estimation and model parameter identification framework. The expectation (E) step is implemented by a particle filter that is initialized by a Monte Carlo Markov chain algorithm. Within this step, the posterior distribution of the states given the measurements, as well as the state vector itself, are estimated. Consequently, in the maximization (M) step, we approximate the nonlinear observation equation as a mixture of Gaussians (MoG) model. During the M-step, the MoG model is fit to the observed data by estimating a set of MoG parameters. The proposed procedure, called EM-PF (expectation-maximization particle filter) algorithm, is used to solve a highly nonlinear bearing-only tracking problem, where the model structure is assumed unknown a priori. It is shown that the algorithm is capable of modeling the observations and accurately tracking the state vector. In addition, the algorithm is also applied to the sensor registration problem in a multi-sensor fusion scenario. It is again shown that the algorithm is successful in accommodating an unknown nonlinear model for a target tracking scenario.

Reversible jump MCMC for joint detection and estimation of sources in colored noise

This paper presents a novel Bayesian solution to the difficult problem of joint detection and estimation of sources impinging on a single array of sensors in spatially colored noise with arbitrary covariance structure. Robustness to the noise covariance structure is achieved by integrating out the unknown covariance matrix in an appropriate posterior distribution. The proposed procedure uses the reversible jump Markov chain Monte Carlo (MCMC) method to extract the desired model order and direction-of-arrival parameters. We show that the determination of model order is consistent, provided a particular hyperparameter is within a specified range. Simulation results support the effectiveness of the method.

A Space Mapping Methodology for Defect Characterization From Magnetic Flux Leakage Measurements

We present an inversion methodology for defect characterization using the data from magnetic flux leakage (MFL) measurements. We use a single tangential component of the leakage field as the MFL response. The inversion procedure employs the space mapping methodology. Space mapping is an efficient technique that shifts the optimization burden from a computationally expensive accurate (fine) model to a less accurate (coarse) but fast model. Here the fine model is a finite-element method (FEM) simulation, while the coarse model is based on analytical formulas. We achieve good estimation of the defect parameters using just a few FEM simulations, which leads to substantial savings in computational cost as compared to other optimization approaches. We examine the efficiency of the proposed inversion technique in estimating the shape parameters of rectangular and cylindrical defects in steel pipes. Our results show good agreement between the actual and estimated defect parameters.