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     

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     

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.     

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     

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     

Posterior Cramer-Rao bounds for discrete-time nonlinear filtering

A mean-square error lower bound for the discrete-time nonlinear filtering problem is derived based on the van Trees (1968) (posterior) version of the Cramer-Rao inequality. This lower bound is applicable to multidimensional nonlinear, possibly non-Gaussian, dynamical systems and is more general than the previous bounds in the literature. The case of singular conditional distribution of the one-step-ahead state vector given the present state is considered. The bound is evaluated for three important examples: the recursive estimation of slowly varying parameters of an autoregressive process, tracking a slowly varying frequency of a single cisoid in noise, and tracking parameters of a sinusoidal frequency with sinusoidal phase modulation     

Analytical derivation of finite-data-record performance of Wong-Lok-Lehnert-Zoltowski's DS-CDMA "Blind" space-time receiver

Finite-data-record performance and breakdown behaviors are analytically derived for a space-time "blind" rake-receiver algorithm in a previous proposed by Wong, Lok, Lehnert, and Zoltowski (WLLZ) for uplink direct sequence-code division multiple access (DS-CDMA) cellular wireless communications using only single-user-type "conventional" detectors with either short or long spreading sequences. WLLZ is significant because it needs no prior knowledge nor explicit estimation of 1) the fading channel's multipaths' arrival angles/delays/amplitudes/complex-phases, 2) the receiver's nominal or actual (i.e., calibrated) antenna-array manifold, and 3) the other CDMA users' signature spreading-codes. This analysis a) reveals how the multiuser access cellular system's various parameters influence WLLZs "blind" beamformer's output SINR. These herein-derived quantitative relationships are explicit, closed-form, and accurate to within 1/2-2 dB for the examined scenarios if WLLZ does not break down . This analysis also b) explains WLLZ's breakdown, which can occur for channels with large delay-spreads, due to a matrix rank deficiency, explicitly in closed-form and in terms of the fading-channel's delay spread and temporal variability. It also c) proposes a simple algorithmic modification to WLLZ to avert its breakdown.     

Quasi-fluid-mechanics-based quasi-Bayesian Crame/spl acute/r-Rao bounds for deformed towed-array direction finding

New quasi-Bayesian (hybrid) Crame/spl acute/r-Rao bound (CRB) expressions are herein derived for far-field deep-sea direction-of-arrival (DOA) estimation with a nominally linear towed-array that 1) is deformed by spatio-temporally correlated oceanic currents, which have been previously overlooked in the towed-array shape-deformation statistical analysis literature, 2) is deformed by temporally correlated motion of the towing vessel, which is modeled only as temporally uncorrelated in prior literature, and 3) suffers gain-uncertainties and phase-uncertainties in its constituent hydrophones. This paper attempts to bridge an existing literature gap in deformed towed-array DOA-estimation performance analysis, by simultaneously a) incorporating several essential fluid-mechanics considerations to produce a shape-deformation statistical model physically more realistic than those previously used for DOA performance analysis and b) rigorously derive a mathematical analysis to characterize quantitatively and qualitatively the DOA estimation's statistical performance. The derived CRB expressions are parameterized in terms of the towed-array's physically measurable nonidealities for the single-source case. The new hybrid-CRB expressions herein derived are numerically more stable than those in the current literature.     

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     

Performance analysis of the FastICA algorithm and Crame/spl acute/r-rao bounds for linear independent component analysis

The FastICA or fixed-point algorithm is one of the most successful algorithms for linear independent component analysis (ICA) in terms of accuracy and computational complexity. Two versions of the algorithm are available in literature and software: a one-unit (deflation) algorithm and a symmetric algorithm. The main result of this paper are analytic closed-form expressions that characterize the separating ability of both versions of the algorithm in a local sense, assuming a "good" initialization of the algorithms and long data records. Based on the analysis, it is possible to combine the advantages of the symmetric and one-unit version algorithms and predict their performance. To validate the analysis, a simple check of saddle points of the cost function is proposed that allows to find a global minimum of the cost function in almost 100% simulation runs. Second, the Crame/spl acute/r-Rao lower bound for linear ICA is derived as an algorithm independent limit of the achievable separation quality. The FastICA algorithm is shown to approach this limit in certain scenarios. Extensive computer simulations supporting the theoretical findings are included.