Institute for Systems Research
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Item Signal Detection Games with Power Constraints(1993) Sauder, D.; Geraniotis, Evaggelos A.; ISRIn this paper we formulate mathematically and solve maximin and minimax detection problems for signals with power constraints. These problems arise whenever it is necessary to distinguish between a genuine signal and a spurious on designed by an adversary with the principal goal of deceiving the detector. The spurious (or deceptive) signal is usually subject to certain constraints, such as limited power, which preclude it from replicating the genuine signal exactly.The detection problem is formulated as a zero-sum game involving two players: the detector designer and the deceptive signal designer. The payoff is the probability of error of the detector which the detector designer tries to minimize and the deceptive signal designer to maximize. For this detection game, saddle point solutions --- whenever possible --- or otherwise maximin and minimax solutions are derived under three distinct constraints on the deceptive signal power; these distinct constraints involves bounds on (i) the peak power, (ii) the probabilistic average power, and (iii) the time average power. The cases of i.i.d. and correlated signals are both considered.
Item One-Step Memory Nonlinearities for Signal Detection and Discrimination from Correlated Observations(1992) Sauder, D.; Geraniotis, Evaggelos A.; ISRNew detectors employing test statistics which are formed by passing pairs of consecutive observations through one-step memory nonlinearities g(x, y) and summing the resulting terms are introduced. Problems of discrimination between two arbitrary stationary m-dependent or mixing noise are considered in this context. For each problem, the nonlinearity g is optimized for performance criteria, such as the generalized signal-to-noise ratio and the efficacy and is obtained as the solution to an appropriate linear integral equation. Moreover, the schemes considered can be robustified to statistical uncertainties determined by 2-alternating capacity classes, for the second- order joint pdfs of the observations, and by bounds on the correlation coefficients of time-shifts of the observation sequence, for the third - and fourth-order joint pdfs. Evaluation of the performance of the new schemes via simulation reveals significant gains over that of detectors employing memoryless nonlinearities or the i.i.d. nonlinearity.Item Neural Networks for Sequential Discrimination of Radar Targets(1991) Haimerl, Joseph A.; Geraniotis, Evaggelos A.; ISRIn this paper, perceptron neural networks are applied to the problem of discriminating between two classes of radar returns. The perceptron neural networks are used as nonlinearities in two threshold sequential discriminators which act upon samples of the radar return. The test statistic compared to the n - K + 1, thresholds is of the form T n (Z) = j = 1 g ( Z j , Z J + 1, ...., Z j + K - 1 ) where, Z i, i = 1, 2, 3, ..... are the radar samples and g () is the nonlinearity formed by the neural network. Numerical results are presented and compared to existing discrimination schemes.Item Robust Sequential Tests for Memoryless Discrimination from Dependent Observations(1991) Geraniotis, Evaggelos A.; ISRThe problem of robust sequential discrimination from two dependent observation sequences with uncertain statistics is addressed. As in Part I ([1]) of this study, which treated asymptotically optimal sequential discrimination for stationary observations characterized by m - dependent or mixing type of dependence, sequential tests based on memoryless nonlinearities are employed. In particular, the sequential tests robustified in this paper employ linear test _ n _ n, statistics of the form Sn = A g (Xi ) + Bn, , where {Xi } i = 1 is the observation _ i = 1 _, sequence, the coefficients A and B are selected so that the normalized drifts of S n are antipodal under the two hypotheses, and the nonlinearity g solves a linear integral equation. As shown in Part I, the performance of these tests is very close to that of the asymptotically optimal memoryless sequential tests when the statistics of the observations are known. The above tests are robustified in terms of the error probabilities and the expected sample numbers under the two hypotheses, for statistical uncertainty determined by 2-alternating capacity classes for the marginal (univariate) pdfs and upper bounds on the correlation coefficients of time-shifts of the observations sequence for the bivariate pdfs. Finally, the robustification of sequential tests based on a test statistic similar to Sn defined above is carried out for detecting a weak-signal in stationary m - dependent or mixing noise with uncertainty in the univariate and bivariate pdfs.