Performance of normalized correlation estimators for complexprocesses

Direct and fast techniques for estimating normalized second-order moments of complex processes are discussed. First, the accuracy of the direct estimate is explicitly given in terms of bias and covariance for the Gaussian processes. Then, a class of estimators based on the complex invariance property is considered. Their theoretical accuracy is given for some cases of paramount interest from a computational point of view in the Gaussian case. In particular, applications in the areas of autoregressive spectrum analysis and spectral centroid estimation are presented. General analytic results and simple expression for immediate evaluation are provided     

Discrete time techniques for time delay estimation

Basic aspects of time delay estimation (TDE) based on sampled signals are investigated. The direct cross-correlation method is analyzed and compared to the average square difference function (ASDF) and the (addition only based) average magnitude difference function (AMDF) estimators, Their relative accuracy is theoretically evaluated, and previous empirical results are explained. It is shown that both the ASDF- and the AMDF-based estimators outperform the direct cross-correlation based estimator for medium-high signal-to-noise ratios. Moreover, the AMDF-based estimator, which avoids any multiplications, significantly reduces the computational complexity of the estimation procedure while offering only a moderate performance loss with respect to the ASDF based estimator     

Hybrid nonlinear moments in array processing and spectrum analysis

The aim of this paper is to provide a theoretical basis for the use of hybrid nonlinear (HNL) moments in array processing and spectrum analysis. These moments are defined as the expected value of the product of one random variable times a nonlinear function of another random variable. They generalize a class of twofold higher order moments, and their additional flexibility can be exploited for optimization purposes or for computational convenience. A number of properties beyond the classical Bussgang's (1952) and Price's (1958) theorems are found for HNL moments and matrices, making these statistics suitable for harmonic analysis and bearing estimation. Covariance based and higher order moments based methods are extended to the HNL moments domain, and a new class of Gaussian noise rejecting statistics is added to cumulants. The properties of some classes of matrices of HNL moments of practical interest are analyzed in detail     

Texture synthesis-by-analysis with hard-limited Gaussian processes

A twin stage texture synthesis-by-analysis method is presented. It aims to approximate first- and second-order distributions of the texture, accordingly to the Julesz conjecture. In the first stage, the binary textural behavior of a given prototype is represented by means of a hard-limited Gaussian process. In the second stage, the texture is synthesized by passing the binary hard-limited Gaussian process through a linear filter followed by a zero memory histogram equalizer.     

Bandpass nonlinear systems identification by higher order crosscorrelation

Nonlinear systems constituted by a zero-memory nonlinearity cascaded with linear filters can be identified by input-output cross correlation using a Gaussian input signal. The method is extended to complex systems through a pair of complex invariance theorems. The stated properties allow identifying the linear parts of systems characterized by magnitude/phase nonlinearities with the joint use of second- and third-order input-output moments. The method can be employed for a wide class of communication bandpass circuits when signals are represented by complex envelopes     

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.     

Parameter estimation of an SSR amplitude comparison monopulse extractor

The letter summarises the results of an investigation on the monopulse receiver used in the ADSEL (selectively addressed secondary radar system). The results are the bias and the variance of the error as a function of the off-boresight angle and of the channels' mismatching.