L. L. Scharf and B. Friedlander, Matched subspace detectors, IEEE Trans. on Signal Processing, vol. 42, pp. 2146-2157, August 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....whiten the data prior to application of a standard matched filter detector. In the sequel, we will refer to this class of algorithms as Space Time Autoregressive (STAR) filtering. In this paper, we will present a new algorithm for STAR processing based on the concept of matched subspace filtering [9]. In the proposed approach, instead of using the estimated parametric filter to whiten the data prior to detection, the parameters are used to construct a subspace that is orthogonal to the interference. Detection is then performed after this subspace has been projected out of the data. A ....

L. Scharf and B. Friedlander, "Matched subspace detectors," IEEE Trans. on Sig. Proc., vol. 42, pp. 2146-2157, August 1994.

.... ratio test (GLRT) statistic to determine if the components of a complex gaussian random vector are independent and that the GC estimate arises as the test statistic in the uni formly most powerful invariant matched subspace detector for a class of multiple channel detection problems [6] [7]. A significant limitation encountered in application of the GC estimate is that its distribution within the framework of a useful signal present (H) model is not known except in the two channel (i.e. MSC) case. Consequently, all per A. Clausen is with the Telecommunications Research Center, ....

L.L. Scharf and B. Friedlander, "Matched subspace detectors," IEEE Transactions on Signal Processing, vol. SP-42(8), pp. 2t46- 2157, August 1994.

....principles give CFAR tests with higher power than the GLR test (for a simple but nontrivial example see [227, Ex. 6. 18] Despite the difficulty in finding maximal invariants and their statistical distributions the payoff for the extra effort in signal processing applications can be high [356, 354, 357, 36, 35], where often the invariant LR test significantly outperforms the GLR or approximate GLR test. 2.2 The EM Algorithm for Parametric Estimation The Expectation Maximization (EM) algorithm has generated much recent interest in the signal processing community due to its ability to reliably compute ....

L. Scharf and B. Friedlander, "Matched subspace detectors," IEEE Transactions on Signal Processing, vol. 42, no. 8, pp. 2146--2157, 1994.

....ratio (GLR) detector, where the parameters (i) occurring in the likelihood ratio are replaced by their (conditional) maximum likelihood (ML) estimates [1, 3] 2 author: title AE U Int. J. Electron. Commun. 53 (1999) No. 6, 1 6 Matched Subspace Detector. The matched subspace detector [2, 11] is given by the detection statistic 3 S (r) hP S r; ri = kP S rk 2 ; 3) where P S denotes the orthogonal projection operator on S. Note that S (r) is a quadratic detection statistic as in (1) however with H = P S . For the special case of our detection problem where s 0 (t) 0 (or ....

....; 3) where P S denotes the orthogonal projection operator on S. Note that S (r) is a quadratic detection statistic as in (1) however with H = P S . For the special case of our detection problem where s 0 (t) 0 (or equivalently (0) 0) and = 0, the matched subspace detector was shown in [2, 11] to be (i) maximally invariant to observation components in the orthogonal complement space S and to rotations within S, ii) UMP, and (iii) the GLR detector. This result can be shown to be true also in the general case where s 0 (t) 6= 0 and 6= 0. Indeed, the maximal invariance proof in [2] ....

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L. L. Scharf and B. Friedlander, "Matched subspace detectors, " IEEE Trans. Signal Processing, vol. 42, pp. 2146--2157, Aug. 1994.

.... of the target [2] 3] 4] 5] This statistic is called the maximal invariant and, if one is lucky, the form of the most powerful (MP) LR test based on the maximal invariant does not depend on the nuisance parameters, resulting in a uniformly most powerful invariant (UMPI) test [6] [7]. When properly applied, the invariance principle can yield adaptive target detection algorithms which outperform the GLR test, sometimes by a significant margin. As we will show in this paper, for the problem of target detection in unknown but structured clutter background, this margin of ....

L. L. Scharf and B. Friedlander, "Matched subspace detectors," IEEE Transactions on Signal Processing, vol. 42, no. 8, pp. 2146-2157, August 1994.

....in this case Theta 0 = a oe 2 ] and Theta 1 = a b oe 2 ] Bear in mind that this approximation does not accurately model the data in cases in which a=oe is relatively small as we shall see later in some examples. The GLRT for this problem is based on the following test statistic [23] [24]: t 1 (y) N Gamma 1) k P r P 1 y k 2 k P r P 1 y k 2 = N Gamma 1) L 1 (y) Gamma 1] 5) where L 1 (y) k P 1 y k 2 k P 1r y k 2 : If t 1 (y) j 1 , then we decide H 1 , otherwise we choose H 0 . We call this test the magnitude correlation (MC) test, because the ....

....We call this test the magnitude correlation (MC) test, because the test statistic t 1 (y) is proportional to the correlation between the magnitude data y and the reference signal r. The test statistic t 1 (y) under the assumption that y is truly Gaussian, is distributed as F 1; N Gamma1) SNR) [24], where SNR = 2 a 2 =oe 2 . That is SNR is the non centrality parameter of F distribution. Unfortunately, the Gaussian approximation (4) is inaccurate when a=oe 3. In fact, when a=oe is small, we don t know the distribution of MC detector nor whether or not it has CFAR property. So ....

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L. L. Scharf and B. Friedlander. Matched subspace detectors. IEEE Trans. Signal Processing, 42(8):2146--2157, 1994. REFERENCES 37

....that will be viable. When the signal subspace is known, the fundamental method for detection is the matched subspace detector, or in the case of a rank 1 subspace, the matched filter. This detector is optimal for the problem of detecting signals in the presence of random white Gaussian noise, [1] It is also optimal for the problem of Supported by ONR N00014 94 1 0102, NSF MIP 9705349 detecting signals in the presence of noise and structured interference, provided that the signal subspace and the interference subspace are linearly independent, 1] Optimality here means that when the ....

.... presence of random white Gaussian noise, 1] It is also optimal for the problem of Supported by ONR N00014 94 1 0102, NSF MIP 9705349 detecting signals in the presence of noise and structured interference, provided that the signal subspace and the interference subspace are linearly independent, [1]. Optimality here means that when the signal subspace is known, the receiver operating characteristic (ROC) curve of any proposed detection method will be no better than the ROC curve of the matched subspace detector. The matched subspace detector also yields the maximum likelihood estimate of the ....

L. L. Scharf and B. Friedlander, "Matched subspace detectors," IEEE Transactions on Signal Processing, vol. 42, pp. 2146--2157, August 1994.

....tight upper bounds on the error rate are derived and performance relative to the matched filter is analyzed in the high SNR regime. I. Introduction In this paper, we present a non trivial extension of the recent work by Scharf and Friedlander on the problem of matched subspace detection [5, 6]. Matched subspace detection arise naturally whenever only a filtered version of a known signal can be observed and the coefficients are unknown. We extend their work to the case where, on both hypotheses of the detection problem, non zero signals are transmitted. In contrast, in [5, 6] the null ....

....detection [5, 6] Matched subspace detection arise naturally whenever only a filtered version of a known signal can be observed and the coefficients are unknown. We extend their work to the case where, on both hypotheses of the detection problem, non zero signals are transmitted. In contrast, in [5, 6], the null hypothesis was always that no signal was present. This paper begins with some background in which we present the assumptions related to the channel model. When the channel coefficients are unknown, we can consider the detector to be blind. One solution is to estimate the coefficients ....

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L. Scharf and B. Friedlander, "Matched Subspace Detectors," IEEE Trans. on Signal Processing, vol. 42, no. 8, pp. 2146-- 2157, August, 1994.

.... (MSC) estimate, a widely used statistic for detection of a common signal on two noisy channels [4] Recently it has been observed that the GC estimate arises as the test statistic in the uniformly most powerful invariant matched subspace detector for a class of multiple channel detection problems [5, 6]. Explicit knowledge of the GC estimate s probability distribution under the H 0 hypothesis that all M channels contain independent white gaussian noise makes it possible to calculate detection thresholds corresponding to given probabilities of false alarm. Such thresholds are calculated [1] and ....

L.L. Scharf and B. Friedlander, "Matched subspace detectors," IEEE Transactions on Signal Processing, vol. SP-42(8), pp. 2146-2157, August 1994.

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L. L. Scharf and B. Friedlander, Matched subspace detectors, IEEE Trans. on Signal Processing, vol. 42, pp. 2146-2157, August 1994.

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L.L. Scharf and B. Friedlander, "Matched subspace detectors," IEEE Transactions on Signal Processing, vol. 42, no. 8, pp. 2146--2157, 1994.

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Scharf, L. and B. Friedlander, "Matched Subspace Detectors," IEEE Trans. Signal Proc., Vol. 42, No.8, pp. 2146-2157, August 1994.

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L. L. Scharf and B. Friedlander: "Matched Subspace Detectors, " IEEE Trans. on Signal Processing, Vol. 42, No. 8, pp. 2146-2157, August 1994.

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L. Scharf and B. Friedlander, "Matched subspace detectors," IEEE Transactions on Signal Processing 42(8), pp. 2146--2157, 1994.

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L. L. Scharf and B. Friedlander, "Matched subspace detectors," IEEE Trans. Signal Processing, vol. 42, pp. 2146--2157, Aug. 1994.

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L. L. SCHARF AND B. FRIEDLANDER. Corrections to "Matched subspace detectors". IEEE Transactions on Signal Processing, 45(6):1669, June 1997.

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