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Sequential joint signal detection and signal-to-noise ratio estimation | IEEE Conference Publication | IEEE Xplore

Sequential joint signal detection and signal-to-noise ratio estimation


Abstract:

The sequential analysis of the problem of joint signal detection and signal-to-noise ratio (SNR) estimation for a linear Gaussian observation model is considered. The pro...Show More

Abstract:

The sequential analysis of the problem of joint signal detection and signal-to-noise ratio (SNR) estimation for a linear Gaussian observation model is considered. The problem is posed as an optimization setup where the goal is to minimize the number of samples required to achieve the desired (i) type I and type II error probabilities and (ii) mean squared error performance. This optimization problem is reduced to a more tractable formulation by transforming the observed signal and noise sequences to a single sequence of Bernoulli random variables; joint detection and estimation is then performed on the Bernoulli sequence. This transformation renders the problem easily solvable, and results in a computationally simpler sufficient statistic compared to the one based on the (untransformed) observation sequences. Experimental results demonstrate the advantages of the proposed method, making it feasible for applications having strict constraints on data storage and computation.
Date of Conference: 05-09 March 2017
Date Added to IEEE Xplore: 19 June 2017
ISBN Information:
Electronic ISSN: 2379-190X
Conference Location: New Orleans, LA, USA

1. Introduction

The joint problem of distinguishing between different hypotheses and estimating the unknown parameters based on the outcome of the hypotheses test has received considerable attention in the literature [1]–[6]. Such a problem arises in a wide range of applications, including (i) radiographic inspection for detecting anomalies in manufactured objects and estimating their position and size [7], (ii) retrospective changepoint hypotheses testing to detect change in the statistics and simultaneously estimate the time of change [8], [9], (iii) jointly detecting the presence of multiple objects and estimating their states using image observations [10], and (iv) distinguishing between two hypotheses and at the same time estimating the unknown parameters in the accepted hypothesis in a distributed framework [11]. Some popular techniques to address this problem include reformulating the composite detection problem as a pure estimation problem [12], while the maximum a posteriori estimate was shown to provide a solution to the joint detection and estimation problem in a Bayesian context [13]. The problem has also been addressed in a sequential setting, where the objective is to minimize the number of samples subject to a constraint on the combined detection and estimation cost [14], [15]. The generalized sequential probability ratio test was presented in [16], where a decision was obtained using the maximum likelihood estimate of the unknown parameter.

References

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