A bayesian approach to adaptive detection in nonhomogeneous environments

We consider the adaptive detection of a signal of interest embedded in colored noise, when the environment is nonhomogeneous, i.e., when the training samples used for adaptation do not share the same covariance matrix as the vector under test. A Bayesian framework is proposed where the covariance matrices of the primary and the secondary data are assumed to be random, with some appropriate joint distribution. The prior distributions of these matrices require a rough knowledge about the environment. This provides a flexible, yet simple, knowledge-aided model where the degree of nonhomogeneity can be tuned through some scalar variables. Within this framework, an approximate generalized likelihood ratio test is formulated. Accordingly, two Bayesian versions of the adaptive matched filter are presented, where the conventional maximum likelihood estimate of the primary data covariance matrix is replaced either by its minimum mean-square error estimate or by its maximum a posteriori estimate. Two detectors require generating samples distributed according to the joint posterior distribution of primary and secondary data covariance matrices. This is achieved through the use of a Gibbs sampling strategy. Numerical simulations illustrate the performances of these detectors, and compare them with those of the conventional adaptive matched filter

Time-varying autoregressive (TVAR) models for multiple radar observations

©2007 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.We consider the adaptive radar problem where the properties of the (nonstationary) clutter signals can be estimated using multiple observations of radar returns from a number of sufficiently homogeneous range/azimuth resolution cells. We derive a method for approximating an arbitrary Hermitian covariance matrix by a time-varying autoregressive model of order m, TVAR(m), that is based on the Dym-Gohberg band-matrix extension technique which gives the unique TVAR(m) model for any nondegenerate covariance matrix. We demonstrate that the Dym-Gohberg transformation of the sample covariance matrix gives the maximum-likelihood (ML) estimate of the TVAR(m) covariance matrix. We introduce an example of TVAR(m) clutter modeling for high-frequency over-the-horizon radar that demonstrates its practical importanceYuri I. Abramovich, Nicholas K. Spencer, and Michael D. E. Turle

Regularized adaptive long autoregressive spectral analysis

This paper is devoted to adaptive long autoregressive spectral analysis when (i) very few data are available, (ii) information does exist beforehand concerning the spectral smoothness and time continuity of the analyzed signals. The contribution is founded on two papers by Kitagawa and Gersch. The first one deals with spectral smoothness, in the regularization framework, while the second one is devoted to time continuity, in the Kalman formalism. The present paper proposes an original synthesis of the two contributions: a new regularized criterion is introduced that takes both information into account. The criterion is efficiently optimized by a Kalman smoother. One of the major features of the method is that it is entirely unsupervised: the problem of automatically adjusting the hyperparameters that balance data-based versus prior-based information is solved by maximum likelihood. The improvement is quantified in the field of meteorological radar

Adaptive detection of distributed targets in compound-Gaussian noise without secondary data: A Bayesian approach

In this paper, we deal with the problem of adaptive detection of distributed targets embedded in colored noise modeled in terms of a compound-Gaussian process and without assuming that a set of secondary data is available.The covariance matrices of the data under test share a common structure while having different power levels. A Bayesian approach is proposed here, where the structure and possibly the power levels are assumed to be random, with appropriate distributions. Within this framework we propose GLRT-based and ad-hoc detectors. Some simulation studies are presented to illustrate the performances of the proposed algorithms. The analysis indicates that the Bayesian framework could be a viable means to alleviate the need for secondary data, a critical issue in heterogeneous scenarios

Основные характеристики морского клатера, влияющие на обнаружение малоразмерных малоподвижных целей морскими РЛС

В роботі здійснюється пошук математичної моделі морського клатера, придатної для створення на її основі алгоритму виявлення малорозмірних малорухомих цілей морськими РЛС. В результаті аналізу джерел для моделювання стохастичного розподілу амплітуди морського клатера обирається компонована Гаусова модель, оскільки її адекватність підтверджена найбільшою кількістю дослідників. В якості перспективної альтернативи стохастичній моделі обирається обговорювана в останнє десятиліття в літературі модель, основана на теорії хаосу, перевага використання якої для вирішення даного класу задач потребує остаточного підтвердження або заперечення.Searching of the sea clutter mathematical model is carried out in this paper. It is suitable to create based on it algorithm for small slow moving targets detection by marine radars. The compound Gaussian model for modeling sea clutter amplitude stochastic distribution is selected as a result of the sources analysis, because it was confirmed by most of researches. The discussed in the literature model based on chaos theory is choosen as perspective alternative for stochastic model; its advantage of using it for such problems solution must be definitively proved or denied. It was proposed many different distributions for high resolution sea clutter amplitude data modeling. The most frequently reported in the literature are K, Log-Normal and Weibull distributions. K distribution belonging to a compound-Gaussian model has the most significant theoretical and experimental background. This distribution choice is physically explained basing on the processes taking place when electromagnetic waves scattered from capillarity and gravity sea waves create a composed echo. Signal representing this echo is the product of two random components, called texture and speckle. Texture is the result of scattering from gravity waves, has a Gamma pdf (in case of K distribution) and corresponds to slow-varying large-scale structure. Speckle is the result of scattering from isolated scatterers (capillarity waves), has a Rayleigh pdf and corresponds to rapid varying small-scale structure. So, K distribution envelope is a compound distribution consisting of a locally Rayleigh distribution speckle whose mean is modulated by a gamma distribution texture. All researches consider Rayleigh pdf for speckle. The lognormal, generalized Gaussian, inverse gamma and some other distributions were proposed for the texture. Due to literature analyses it is seen that texture distribution depends on radar range resolution, but strong dependence is not proved. Some scientists modified K distribution to K-A distribution consisting of the Rayleigh, gamma and Poisson distributions to describe better spikes appearence caused by whitecaps and bursts. Using of Weibull-Weibull (WW) and KK distributions was proposed for high grazing angle and high resolution sea clutter. Doppler characteristics of the sea clutter has been investigated by many researchers and now we have well developed theory. It is known empirical behavior of sea clutter doppler spectrum for different conditions – grazing angle, resolution, wind speed, polarisation and others. Lee, Walker and Ward models are used for sea clutter doppler spectrum describing. Fast moving targets can be effectively detected in heavy sea clutter by doppler radars. But existing theory cannot improve detection of slow moving small targets in heavy sea clutter, because slow moving targets have doppler shift compared to doppler shift of sea clutter. Correlation properties of high resolution sea clutter cannot be derived from its doppler spectrum. In alternative to stohastic model, many researches prefer deterministic model and use chaos theory to describe sea clutter. This choise is based on the fact that both hydrodynamic and electromagnetic therory relying on deterministic models only. If deterministic theory usefulness in applying to high resolution see clutter description be proved completely, it can lead to great progress for small targets in heavy sea clutter detection; because in this case sea clutter behavior can be predicted if initial conditions are precisely known. Using chaotic model for high resolution sea clutter description is highly disputed in recent years, and many researches have questioned first results of high resolution sea clutter describing with chaotic theory usage by Haykin. But great possibilities can give deterministic model for small targets detection definitively proving its ability to describe high resolution sea clutter data precisely causes different scientists to return to chaos theory again and again. Promising results in this field was obtained by using multifractal theory, but still there are not strong methodological background of using deterministic models for small slow moving targets in sea clutter detection, so it is required to make research to prove or deny deterministic models usefulness for high resolution sea clutter data description.В работе осуществляется поиск математической модели морского клатера, пригодной для создания на ее основе алгоритма обнаружения малоразмерных малоподвижных целей морскими РЛС. В результате анализа источников для моделирования стохастического распределения амплитуды морского клатера избирается составная Гауссова модель, поскольку ее состоятельность подтверждена наибольшим количеством исследователей. В качестве перспективной альтернативы стохастической модели избирается обсуждаемая в литературе модель, основанная на теории хаоса, преимущество использования которой для решения данного класса задач требует окончательного подтверждения или отрицания

The estimation of pointing angle and normalized surface scattering cross section from GEOS-3 radar altimeter measurements

The statistical error of the pointing angle estimation technique is determined as a function of the effective receiver signal to noise ratio. Other sources of error are addressed and evaluated with inadequate calibration being of major concern. The impact of pointing error on the computation of normalized surface scattering cross section (sigma) from radar and the waveform attitude induced altitude bias is considered and quantitative results are presented. Pointing angle and sigma processing algorithms are presented along with some initial data. The intensive mode clean vs. clutter AGC calibration problem is analytically resolved. The use clutter AGC data in the intensive mode is confirmed as the correct calibration set for the sigma computations

Order estimation and discrimination between stationary and time-varying (TVAR) autoregressive models

Copyright © 2007 IEEEFor a set of T independent observations of the same N-variate correlated Gaussian process, we derive a method of estimating the order of an autoregressive (AR) model of this process, regardless of its stationary or time-varying nature. We also derive a test to discriminate between stationary AR models of order m,AR(m), and time-varying autoregressive models of order m,TVAR(m). We demonstrate that within this technique the number T of independent identically distributed data samples required for order estimation and discrimination just exceeds the maximum possible order mmax, which in many cases is significantly fewer than the dimension of the problem NYuri I. Abramovich, Nicholas K. Spencer, and Michael D. E. Turle

Spatial--temporal mesoscale modeling of rainfall intensity using gage and radar data

Gridded estimated rainfall intensity values at very high spatial and temporal resolution levels are needed as main inputs for weather prediction models to obtain accurate precipitation forecasts, and to verify the performance of precipitation forecast models. These gridded rainfall fields are also the main driver for hydrological models that forecast flash floods, and they are essential for disaster prediction associated with heavy rain. Rainfall information can be obtained from rain gages that provide relatively accurate estimates of the actual rainfall values at point-referenced locations, but they do not characterize well enough the spatial and temporal structure of the rainfall fields. Doppler radar data offer better spatial and temporal coverage, but Doppler radar measures effective radar reflectivity ($Ze$) rather than rainfall rate ($R$). Thus, rainfall estimates from radar data suffer from various uncertainties due to their measuring principle and the conversion from $Ze$ to $R$. We introduce a framework to combine radar reflectivity and gage data, by writing the different sources of rainfall information in terms of an underlying unobservable spatial temporal process with the true rainfall values. We use spatial logistic regression to model the probability of rain for both sources of data in terms of the latent true rainfall process. We characterize the different sources of bias and error in the gage and radar data and we estimate the true rainfall intensity with its posterior predictive distribution, conditioning on the observed data.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS166 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Covariance matrix estimation with heterogeneous samples

We consider the problem of estimating the covariance matrix Mp of an observation vector, using heterogeneous training samples, i.e., samples whose covariance matrices are not exactly Mp. More precisely, we assume that the training samples can be clustered into K groups, each one containing Lk, snapshots sharing the same covariance matrix Mk. Furthermore, a Bayesian approach is proposed in which the matrices Mk. are assumed to be random with some prior distribution. We consider two different assumptions for Mp. In a fully Bayesian framework, Mp is assumed to be random with a given prior distribution. Under this assumption, we derive the minimum mean-square error (MMSE) estimator of Mp which is implemented using a Gibbs-sampling strategy. Moreover, a simpler scheme based on a weighted sample covariance matrix (SCM) is also considered. The weights minimizing the mean square error (MSE) of the estimated covariance matrix are derived. Furthermore, we consider estimators based on colored or diagonal loading of the weighted SCM, and we determine theoretically the optimal level of loading. Finally, in order to relax the a priori assumptions about the covariance matrix Mp, the second part of the paper assumes that this matrix is deterministic and derives its maximum-likelihood estimator. Numerical simulations are presented to illustrate the performance of the different estimation schemes

Different homogeneity detectors for improving space-time adaptive radar performance in heterogeneous clutter

© Copyright 2006 IEEESecondary data selection for estimation of the clutter covariance matrix in space-time adaptive processing (STAP) is normally obtained from cells (range rings) in close proximity of the cell under test. The aim of this paper is the analysis of performance improvement of Space-Time Adaptive radars when secondary data selection is obtained by discriminating between quasi-homogeneous areas on the ground which generate clutter with different statistics (i.e. clutter edges including littoral, farmland-wooded hills or rural-urban interfaces). The algorithm presented in this paper, referred to as the Different Homogeneity Detector (DHD), has been tested with simulated data obtained by using a general clutter model and a uniform linear array.Massimo Bertacca, Douglas A. Gray, Luke Rosenber