We consider a well-defined joint detection and parameter estimation problem. By combining the Bayesian formulation of the estimation subproblem with suitable constraints on the detection subproblem, we develop optimum one- and two-step test for the joint detection/estimation setup. The proposed combined strategies have the very desirable characteristic to allow for the trade-off between detection power and estimation quality. Our theoretical developments are, then, applied to the problems of retrospective changepoint detection and multiple-input multiple-output (MIMO) radar. In the former case, we are interested in detecting a change in the statistics of a set of available data and provide an estimate for the time of change, while in the latter in detecting a target and estimating its location. Intense simulations in the MIMO radar example demonstrate that by using jointly optimum schemes, we can experience significant improvement in estimation quality, as compared to generalized the likelihood ratio test or the test that treats the two subproblems separately, with only small sacrifices in detection power.

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Joint Detection and Estimation: Optimum Tests and Applications

This paper addresses the problem of finite sample simultaneous detection and estimation which arises when estimation of signal parameters is desired but signal presence is uncertain. In general, a joint detection and estimation algorithm cannot simultaneously achieve optimal detection and optimal estimation performance. We develop a multihypothesis testing framework for studying the tradeoffs between detection and parameter estimation (classification) for a finite discrete parameter set. Our multihypothesis testing problem is based on the worst case detection and worst case classification error probabilities of the class of joint detection and classification algorithms which are subject to a false alarm constraint. This framework leads to the evaluation of greatest lower bounds on the worst case decision error probabilities and a construction of decision rules which achieve these lower bounds. For illustration, we apply these methods to signal detection, order selection, and signal classification for a multicomponent signal in noise model. For two or fewer signals, an SNR of 3 dB and signal space dimension of N=10 numerical results are obtained which establish the existence of fundamental tradeoffs between three performance criteria: probability of signal detection, probability of correct order selection, and probability of correct classification. Furthermore, based on numerical performance comparisons between our optimal decision rule and other suboptimal penalty function methods, we observe that Rissanen's (1978) order selection penalty method is nearly min-max optimal in some nonasymptotic regimes. >

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Optimal simultaneous detection and estimation under a false alarm constraint

The Statistical Signal and Array Processing Technical Committee (SSAP-TC) deals with signals that are random and processes an array of signals simultaneously. The field of SSAP represents both solid theory and practical applications. Starting with research in spectrum estimation and statistical modeling, study in this field is always full of elegant mathematical tools such as statistical analysis and matrix theory. The area of statistical signal processing expands into estimation and detection algorithms, time-frequency domain analysis, system identification, and channel modeling and equalization. The area of array signal processing also extends into multichannel filtering, source localization and separation, and so on. This article represents an endeavor by the members of the SSAT-TC to review all the significant developments in the field of SSAP. To provide readers with pointers for further study of the field, this article includes a very impressive bibliography-close to 500 references are cited. This is just one of the indications that the field of statistical signals has been an extremely active one in the signal processing community. The article also introduces the recent reorganization of three technical committees of the Signal Processing Society.

Highlights of statistical signal and array processing

In this paper, we present a simultaneous detection and estimation approach for speech enhancement in nonstationary noise environments. A detector for speech presence in the short-time Fourier transform domain is combined with an estimator, which jointly minimizes a cost function that takes into account both detection and estimation errors. Under speech-presence, the cost is proportional to a quadratic spectral amplitude error, while under speech-absence, the distortion depends on a certain attenuation factor. Experimental results demonstrate the advantage of using the proposed simultaneous detection and estimation approach which facilitate suppression of nonstationary noise with a controlled level of speech distortion.

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Speech Enhancement for Nonstationary Noise Environments

In this paper, we present a simultaneous detection and estimation approach for speech enhancement. A detector for speech presence in the short-time Fourier transform domain is combined with an estimator, which jointly minimizes a cost function that takes into account both detection and estimation errors. Cost parameters control the tradeoff between speech distortion, caused by missed detection of speech components and residual musical noise resulting from false-detection. Furthermore, a modified decision-directed a priori signal-to-noise ratio (SNR) estimation is proposed for transient-noise environments. Experimental results demonstrate the advantage of using the proposed simultaneous detection and estimation approach with the proposed a priori SNR estimator, which facilitate suppression of transient noise with a controlled level of speech distortion.

Simultaneous Detection and Estimation Approach for Speech Enhancement

Simultaneous detection and estimation under multiple hypotheses when data from only one observation interval are available, are treated on the basis of statistical decision theory. Estimation is carried out under the assumption that the signal of interest is not present with probability 1, which is necessary if detection is to be a meaningful operation. Also, we consider the case where the operations of detection and estimation are coupled. Specific detector and estimator structures are determined for the case of strong coupling when the cost of estimation error is given by a quadratic function. The detector structures are in general complex nonlinear functions of the received data. However, a detailed analysis of the Gaussian case resulted in a type of correlation detector, which correlates the received data with the least square estimators of the possible signals in the absence of uncertainty. The associated optimum estimator structure is found to be a weighted sum of least square estimators in the absence of uncertainty. Also, joint detection and estimation under multiple hypotheses is discussed for the case of a simple cost function. The estimators that result can be interpreted as generalized maximum-likelihood estimators. Finally, optimum prediction and filtering are briefly considered.

D. Middleton

Papers

Simultaneous signal detection and estimation under multiple hypotheses