Separating Function Estimation Tests: A New Perspective on Binary Composite Hypothesis Testing

Ghobadzadeh, Ali; Gazor, Saeed; Taban, Mohammad Reza; Tadaion, Aliakbar; Gazor, Majid

doi:10.1109/tsp.2012.2211594

Cited by 33 publications

(28 citation statements)

References 34 publications

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“…which are two separating functions (SFs) [35] and convert test (4) into H 1 :g i (α, e, A, Q) > 0 against H 0 :g i (α, e, A, Q) = 0, i = 1, 2. Obviously, we have L 1S = g 1 (â 1S ,ê 1S ), L 2S = g 2 (â 2S ,ê 2S ,Â,Q), thus both (25) and (34) are SF-estimator tests.…”

Section: Ad Hoc Detectormentioning

confidence: 99%

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Parametric space–time detection and range estimation of a small target

Chen

Gazor

Orlando³

et al. 2015

IET Radar, Sonar & Navigation

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In this study, the authors deal with the problem of parametric detection for relatively small targets using space-time adaptive processing (STAP). In contrast to the existing parametric STAP detectors, the proposed detectors perform range estimation by exploiting the spillover of the target energy between consecutive samples. To this end, the authors assume that the received useful signal is known up to a complex unknown deterministic factor parameter and the disturbance signal is modelled as a multichannel autoregressive Gaussian process. Moreover, the authors assume that a set of secondary data is available which are free of signal components, but have the same unknown parameters as the disturbance in the cells under test. Using these assumptions, the so-called simplified generalised likelihood ratio test (GLRT) and the two-step GLRT are derived and assessed. It is worth noting that the simplified GLRT is based on an asymptotic ML estimate of the amplitude, which leads to a simple and closed-form detection statistic. The performance assessment, conducted resorting to both simulated dataset and KASSPER dataset, has shown that the proposed decision schemes can provide accurate estimates of the target position within the cell under test and ensure enhanced detection performance compared with their natural competitors.

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Section: Ad Hoc Detectormentioning

confidence: 99%

“…Note that for plain GLRT, oncê a 1S andê 1S are available,Â andQ can be obtained accordingly [18]. According to [35,Theorem 8], tests (25) and (34) asymptotically tend to the uniformly most powerful unbiased test as K → ∞.…”

Section: Ad Hoc Detectormentioning

confidence: 99%

Parametric space–time detection and range estimation of a small target

Chen

Gazor

Orlando³

et al. 2015

IET Radar, Sonar & Navigation

View full text Add to dashboard Cite

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“…The SFET is a suboptimal test based on the estimation of an SF and comparison it with a threshold provided by the false alarm probability [24]. In this paper, an SF using the induced maximal invariant is proposed.…”

Section: Sfets Using Induced Maximal Invariantmentioning

confidence: 99%

“…It is shown that the set of unknown parameters after applying the maximal invariant statistic is reduced to the induced maximal invariant. In [24], it is shown that the separating function estimation test (SFET) based on estimating the induced maximal invariant provides a robust detector. Interestingly, in [25] it is shown that the GLRT is an invariant test.…”

Section: Introductionmentioning

confidence: 99%

Separating function estimation tests for narrowband signal activity detection using linear array

Ghobadzadeh

Taban

2015

IET Radar, Sonar & Navigation

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This study addresses the narrowband signal detection with unknown frequency, direction of arrival, complex amplitude and noise variance. The authors find a separating function (SF) using the maximal invariant of induced group of transformations. Then three separating function estimation tests (SFETs) are proposed which called SFET 1 , SFET 2 and SFET 3 . It is shown that the SFET 1 using the maximum likelihood estimation (MLE) of SF is equal to the generalised likelihood ratio test. The SFET 2 and SFET 3 are proposed to reduce the computational complexity of SFET 1 , based on a proposed estimation named by averaged MLE. The authors show that the proposed tests are constant false alarm rate. Moreover it is shown that the proposed tests are asymptotically optimal by increasing the number of snapshots and antennas. The simulation results show that the SFET 3 outperforms the SFET 1 and SFET 2 and the decreasing rate of miss detection against the number of snapshots for SFET 3 is higher than that for SFET 1 and SFET 2 .

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“…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].…”

Section: Introductionmentioning

confidence: 99%

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

Fauß

Nagananda

Zoubir

et al. 2017

2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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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.

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Separating Function Estimation Tests: A New Perspective on Binary Composite Hypothesis Testing

Cited by 33 publications

References 34 publications

Parametric space–time detection and range estimation of a small target

Parametric space–time detection and range estimation of a small target

Separating function estimation tests for narrowband signal activity detection using linear array

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

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