Chair: Boaz Porat, University of California (USA)
Chunming Han, University of Connecticut
Peter Willett, University of Connecticut
Douglas Abraham, Naval Undersea Warfare Center (USA)
The performance of Page's test for the detection of a permanent change in distribution is reasonably well-understood. However, there are few parallel results on its application to the detection of a temporary (i.e., transient) change, and this is the paper's subject. Specifically, a lower bound on detectability is developed using a quantization approach; and a pair of approximations are presented, one based on a Brownian motion analogy, which yields an upper bound in the Gaussian case, and the other again on quantization. The correspondence between these and simulation appears good in both Gaussian and non-Gaussian cases with heavier tail probability.
Scott Enserink, Arizona State University (USA)
Douglas Cochran, Arizona State University (USA)
This paper presents a detector for cyclostationary signals that uses an estimate of spectral autocoherence as a detection statistic. Knowledge of the estimate's statistical behavior in the absence of a cyclostationary signal allows detection thresholds corresponding to particular false alarm probabilities to be established analytically. Computer simulations are used to verify the analytical results and to determine receiver operating characteristic curves for a BPSK signal in additive noise. A detector for polycyclic signals based on generalized coherence estimation is also described, but is not analyzed.
P. Rostaing, Universite de Nice-Sophia Antipolis
E. Thierry, Universite de Nice-Sophia Antipolis
T. Pitarque, Universite de Nice-Sophia Antipolis
M. Le Dard, DCN St. Tropez (FRANCE)
This paper deals with detection of weak cyclostationary signals embedded in colored gaussian noise. We consider the normalized correlation function of the noise to be known and the noise power to be unknown. We propose a temporal structure of the single cycle detector which includes a prewhitening filter. We compare performances of this detector to the classical radiometer and the modified radiometer. The performances are quantified in terms of Receiver Operating Characteristics for two different noise power spectral densities. We compute the theoretical deflection, this measure gives a means to choose the best cyclic frequency used in the single cycle detector. We conclude that cyclic methods outperform radiometric methods when the noise and the signal power spectral densities strongly overlap and for a unknown noise power.
M. Jay Arnold, Queensland University of Technology (AUSTRALIA)
D. Robert Iskander, Queensland University of Technology (AUSTRALIA)
Abdelhak M. Zoubir, Queensland University of Technology (AUSTRALIA)
We wish to formulate a test for the hypothesis of Gaussianity against unspecified alternatives. We assume the components of our sample are independent and identically distributed. This is a problem of universal importance as the assumption of Gaussianity is prevalent and fundamental to many statistical theories and engineering applications. Many such tests exist, the most well-known being the chi-squared goodness-of-fit test with its variants and the Kolmogorov-Smirnov one-sample cumulative probability function test. More powerful modern tests for the hypothesis of Gaussianity include the D'Agostino $K^2$ and Shapiro-Wilk W tests. Recently, tests for Gaussianity have been proposed which use the characteristic function. It is the purpose of this paper to highlight and resolve problems with these tests and to improve performance so that the test is competitive with, and in some cases better than, the most powerful known tests for Gaussianity.
Bulent Baygu, Schlumberger-Doll Research (USA)
We present a methodology to test multiple hypotheses on the distribution of a random variable when the hypotheses are parameterized by fuzzy variables. The proposed approach has a Bayesian flavor in the sense that the objective is to minimize a fuzzy average decision error probability by a proper choice of decision regions. We use a scalar index, called the total distance criterion (TDC) ranking index, in order to rank the fuzzy average decision error probabilities of different decision rules. We derive the optimal decision rule which minimizes the TDC index of the fuzzy average decision error probability. As an example we apply the general approach proposed here to the classification of the fuzzy mean of a Gaussian random variable.
Frederic Champagnat, Ecole Polytechnique (CANADA)
Jerome Idier, LSS/ESE (FRANCE)
Because true Maximum Likelihood (ML) is too expensive, the dominant approach in Bernoulli- Gaussian (BG) myopic deconvolution consists in the joint maximization of a single Generalized Likelihood with respect to the input signal and the hyperparameters. This communication assesses the theoretical properties of a related Maximum Generalized Marginal Likelihood (MGML) estimator in a simplified framework: the filter is reduced to identity, so that the output data is a mixture of Gaussian populations. Our results are three-fold: first, exact MGML estimates can be efficiently computed; second, this estimator performs better than ML in the short sample case whereas it is drastically less expensive; third, asymptotic estimates are significant although biased.
Pan-Tai Liu, University of Rhode Island
Hui Fang, University of Rhode Island
Fu Li, Portland State University (USA)
Heng Xiao, Portland State University (USA)
When a system is unobservable, the error covariance associated with a Kalman filter will be nearly singular. As a consequence, an optimum estimation does not exist. In this paper, we show that this system can be transformed into a nonlinear system with a linear measurement equation. In addition to other useful features, this transformation also serves to decouple the state in such a way that an observable part can be extracted and estimated while no information can be gained and processed for the unobservable part.
Vikram Krishnamurthy, University of Melbourne (AUSTRALIA)
H. Vincent Poor, Princeton University (USA)
Recently we presented a parameter estimation algorithm called the Binary Series Estimation Algorithm (BSEA) for Gaussian auto-regressive (AR) time series given 1-bit quantized noisy measurements. In this paper we carry out an aymptotic analysis of the BSEA for Gaussian AR models. In particular, from a central limit theorem we obtain expressions for the asymptotic covariances of the parameter estimates. From this we: (1) Present an algorithm for estimating the order of an AR series from one-bit quantized measurements. (2) Theoretically justify why BSEA can yield better estimates than the Yule-Walker methods in some cases.
Bernard Picinbono, Supelec (FRANCE)
Optimum mean square estimation of a random variable y in terms of an observation vector x is realized by the conditional expectation value. When x and y are real and jointly normal this expectation is linear in x. This is no longer the case when x and y are complex and jointly normal and the expectation is linear in x and in its complex conjugate x*, which introduces a widely linear procedure. The purpose of this paper is to study the properties of widely linear systems for estimation and prediction. The structure of such systems is calculated and the gain in performance is analyzed. The results are applied to autoregressive signals, which introduces widely linear prediction.
Michael P. Clark, Air Force Institute of Technology (USA)
Consider the problem of finding a lower bound on the signal to noise ratio (SNR) at which any unbiased 2-D harmonic estimation scheme may resolve closely spaced parameters. In particular, consider the Cramer-Rao bounds associated with the parameters. If the parameter estimates are unbiased and normally distributed, the bounds give the smallest possible ellipsoid about each of the parameters which contains a given amount of probability mass. These ellipsoids increase in size with decreasing SNR. This paper presents a method for determining the largest SNR at which any two of the ellipsoids touch. This is deemed the resolution threshold SNR.