Frequency rate estimation at high SNR

The problem of estimating the frequency rate-of-change of complex-valued frequency-modulated signals from noisy observations is considered. The performance of four related estimators is studied, both analytically and by means of simulations, and their relationship to the estimators proposed by Djuric and Kay (1990) and Lang and Musicus (1989) is established     

Cross-product algorithms for source tracking using an EM vectorsensor

We present an adaptive cross-product algorithm for tracking the direction to a moving source using an electromagnetic vector sensor and analyze its performance. We then propose a multiple forgetting factor variant of the same algorithm, which has self-tuning capability, numerical examples are included     

A hybrid technique for blind separation of non-gaussian and time-correlated sources using a multicomponent approach.

Blind inversion of a linear and instantaneous mixture of source signals is a problem often encountered in many signal processing applications. Efficient fastICA (EFICA) offers an asymptotically optimal solution to this problem when all of the sources obey a generalized Gaussian distribution, at most one of them is Gaussian, and each is independent and identically distributed (i.i.d.) in time. Likewise, weights-adjusted second-order blind identification (WASOBI) is asymptotically optimal when all the sources are Gaussian and can be modeled as autoregressive (AR) processes with distinct spectra. Nevertheless, real-life mixtures are likely to contain both Gaussian AR and non-Gaussian i.i.d. sources, rendering WASOBI and EFICA severely suboptimal. In this paper, we propose a novel scheme for combining the strengths of EFICA and WASOBI in order to deal with such hybrid mixtures. Simulations show that our approach outperforms competing algorithms designed for separating similar mixtures.     

High-SNR asymptotics for signal-subspace methods in sinusoidalfrequency estimation

High-SNR-limit second-order properties of multiple signal classification (MUSIC), minimum-norm (MN), and subspace rotation (SUR) signal-subspace methods for sinusoidal frequency estimation are discussed. An alternative to large-sample analysis of the methods is presented. The two most important variants of these methods are considered in connection with the choice of the sample covariance matrix: the simpler technique follows the principle of a linear prediction, and the more complex one is based on the idea of a forward-backward prediction. Explicit expressions for the high-SNR covariance elements of the estimation errors associated with all the methods are derived. The expressions for the covariances are used to analyze and compare the statistical performances of MUSIC, MN, and SUR estimation methods in both of the variants, to discuss the problem of the optimal dimension of the data covariance matrix, and to study the limit statistical efficiency of the methods. Performances of the large-sample and high-SNR asymptotics derived using Monte Carlo simulations are presented     

Multicomponent polynomial phase signal analysis using a trackingalgorithm

We describe an efficient technique analyzing signals that comprise a number of polynomial phase components. The technique is based on a previously proposed “multiple frequency tracker”, which is an algorithm for recursive estimation of parameters of multiple sine waves in noise. It has a relatively low SNR threshold and moderate computational complexity     

Near-field/far-field azimuth and elevation angle estimation using asingle vector hydrophone

This paper introduces a new underwater acoustic eigenstructure ESPRIT-based algorithm that yields closed-form direction-of-arrival (DOA) estimates using a single vector hydrophone. A vector hydrophone is composed of two or three spatially co-located but orthogonally oriented velocity hydrophones plus another optional co-located pressure hydrophone. This direction finding algorithm may (under most circumstances) resolve up to four uncorrelated monochromatic sources impinging from the near-field or the far-field, but it assumes that all signal frequencies are distinct. It requires no a priori knowledge of the signals' frequencies, suffers no frequency-DOA ambiguity, and pairs automatically the x-axis direction cosines with the y-axis direction cosines. It significantly outperforms an array of spatially displaced pressure hydrophones of comparable array-manifold size and computational load but may involve more complex hardware. This work also derives new Cramer-Rao bounds (CRBs) for various vector hydrophone constructions of arrival angle estimates for the incident uncorrelated sinusoidal signals corrupted by spatio-temporally correlated additive noise     

Comparative study of four adaptive frequency trackers

We study and compare four algorithms for adaptive retrieval of slowly time-varying multiple cisoids in noise: the adaptive notch filter, the multiple frequency tracker, the adaptive estimation scheme, and the hyperstable adaptive line enhancer. The local behavior of the algorithms in a neighborhood of their equilibrium state [assuming high signal-to-noise ratio (SNR) and large data sample] for a two-cisoid signal is treated in a similar way to the linear filter approximation technique used for a single-cisoid case. The validity of the results is confirmed by computer simulations     

Statistical characterization of sample fourth-order cumulants of anoisy complex sinusoidal process

The paper deals with the statistical characterization of sample estimates of the fourth-order cumulants of a random process consisting of multiple complex sinusoids and additive colored Gaussian noise. In particular, it presents necessary and sufficient conditions for strong consistency of the sample cumulants of arbitrary orders, and derives expressions for the asymptotic covariance of the sample estimates of the fourth-order cumulants. It is shown that the fourth-order cumulant C_4y (τ₁,...,τ₄) can be written as a function of a single argument τ=τ₃+τ₄ -τ₁-τ₂, which implies large flexibility in estimating the cumulant. It is recommended that the estimate be based upon lags such that τ₁ is distant from τ₂ and τ₃ is distant from τ₄, and/or as a linear combination of such terms. The asymptotic variance of a cumulant-based frequency estimator is shown to have the form c₂·SNR^-2+c₃·SNR^-3 +c₄·SNR^-4, where the coefficient c ₂ may possibly vanish. The theory is illustrated via numerical examples. The results of this paper will be useful in analyzing the performance of various cumulant-based frequency estimation algorithms     

Two algorithms for adaptive retrieval of slowly time-varyingmultiple cisoids in noise

Two algorithms for tracking parameters of slowly varying multiple complex sine waves (cisoids) in noise (the multiple frequency tracker and the adaptive notch filter) are described. For high signal-to-noise ratio (SNR), the properties of the algorithms (i.e., stability, noise rejection, and tracking speed) are studied analytically using a linear filter approximation technique. The tradeoff between noise rejection and tracking error for both algorithms is shown to be similar. Different choices of the design variables are discussed, namely (i) minimal mean-square estimation error for random walk modeled frequency variations and (ii) minimal stationary estimation variance subject to a given tracking delay