Shawn Kraut

Adaptive subspace detectors

We use the theory of generalized likelihood ratio tests (GLRTs) to adapt the matched subspace detectors (MSDs) of Scharf (1991) and of Scharf and Frielander (1994) to unknown noise covariance matrices. In so doing, we produce adaptive MSDs that may be applied to signal detection for radar, sonar, and data communication. We call the resulting detectors adaptive subspace detectors (ASDs). These include Kellys (1987) GLRT and the adaptive cosine estimator (ACE) of Kaurt and Scharh (see ibid., vol.47, p.2538-41, 1999) and of Scharf and McWhorter (see Proc. 30th Asilomar Conf. Signals, Syst., Comput., Pacific Grove, CA, 1996) for scenarios in which the scaling of the test data may deviate from that of the training data. We then present a unified analysis of the statistical behavior of the entire class of ASDs, obtaining statistically identical decompositions in which each ASD is simply decomposed into the nonadaptive matched filter, the nonadaptive cosine or t-statistic, and three other statistically independent random variables that account for the performance-degrading effects of limited training data.

The adaptive coherence estimator: a uniformly most-powerful-invariant adaptive detection statistic

We show that the Adaptive Coherence Estimator (ACE) is a uniformly most powerful (UMP) invariant detection statistic. This statistic is relevant to a scenario appearing in adaptive array processing, in which there are auxiliary, signal-free, training-data vectors that can be used to form a sample covariance estimate for clutter and interference suppression. The result is based on earlier work by Bose and Steinhardt, who found a two-dimensional (2-D) maximal invariant when test and training data share the same noise covariance. Their 2-D maximal invariant is given by Kellys Generalized Likelihood Ratio Test (GLRT) statistic and the Adaptive Matched Filter (AMF). We extend the maximal-invariant framework to the problem for which the ACE is a GLRT: The test data shares the same covariance structure as the training data, but the relative power level is not constrained. In this case, the maximal invariant statistic collapses to a one-dimensional (1-D) scalar, which is also the ACE statistic. Furthermore, we show that the probability density function for the ACE possesses the property of total positivity, which establishes that it has monotone likelihood ratio. Thus, a threshold test on the ACE is UMP-invariant. This means that it has a claim to optimality, having the largest detection probability out of the class of detectors that are also invariant to affine transformations on the data matrix that leave the hypotheses unchanged. This requires an additional invariance not imposed by Bose and Steinhardt: invariance to relative scaling of test and training data. The ACE is invariant and has a Constant False Alarm Rate (CFAR) with respect to such scaling, whereas Kellys GLRT and the AMF are invariant, and CFAR, only with respect to common scaling.

A generalized Karhunen-Loeve basis for efficient estimation of tropospheric refractivity using radar clutter

In this paper, we consider the problem of obtaining a reduced-dimension parameterization of a propagation medium for the purpose of estimating the medium from transmission data. The application addressed is microwave remote sensing of tropospheric index-of-refraction profiles over the sea surface, using radar clutter returns. The proposed parameterization balances the desire to represent features prominent in the a priori statistics of the profiles versus the need to capture elements of the profile that significantly affect the observed clutter data. In linear estimation problems, basis vectors for the unknown parameter vector that optimizes this tradeoff have been derived as the reduced-rank Wiener filter or, equivalently, the generalized Karhunen-Loeve transform (GKLT). In this paper, we reinterpret the linear result, producing an extension to the nonlinear refractivity estimation problem. The resulting procedure produces basis vectors for tropospheric refractivity that are less dependent on features that have little effect on the clutter measurements. This results in a more efficient parameterization and reduces mean-square estimation error relative to an approach driven purely by the statistical prior. Application of the generalized KL technique to finding efficient basis vectors for refractivity profiles taken off the southern California coast is presented.

Robust altitude estimation for over-the-horizon radar using a state-space multipath fading model

In previous work, a matched-field estimate of aircraft altitude from multiple over-the-horizon (OTH) radar dwells was presented. This approach exploits the altitude dependence of direct and surface reflected returns off the aircraft and the relative phase changes of these micro-multipath arrivals across radar dwells. Since this previous approach assumed high dwell-to-dwell predictability, it has been found to be sensitive to mismatch between modeled versus observed micro-multipath phase and amplitude changes from dwell-to-dwell. A generalized matched-field altitude estimate is presented here based on a state-space model that accounts for random ionospheric and target-motion effects that degrade the dwell-to-dwell predictability of target returns. The new formulation results in an efficient, robust recursive maximum likelihood (ML) estimation of aircraft altitude. Simulations suggest that the proposed technique can achieve accuracy within 5,000 ft of the true aircraft altitude, even with relatively high levels of uncertainty in modeling of dwell-to-dwell changes in the target return. A real data result is also presented to illustrate the technique.

Application of maximal invariance to the ACE detection problem

Three simple adaptive detection statistics frequently appearing in the radar detection literature, which employ a sample covariance estimate for clutter suppression, are Kellys GLRT (generalized likelihood ratio test): the adaptive matched filter (AMF) and the adaptive cosine estimator (ACE), which is also a GLRT for the problem where the test-data power level is unconstrained relative to the training data. Bose and Steinhardt (1995, 1996) found a two-dimensional maximal invariant statistic for the adaptive detection problem for which Kellys statistic is a GLRT, a one-to-one function of the Kelly GLRT and the AMF. We extend this maximal-invariant framework to the adaptive detection problem for which ACE is a GLRT showing that ACE is a one-dimensional maximal invariant.

Passive localization in range-rate of shallow-water moving targets, by sequential importance sampling

We examine the problem of passive localization of moving targets in shallow-water environments. In contrast with standard Matched Field Processing approaches, we localize targets in range-rate, rather than in range. This approach avoids smearing of target energy across range, and is more robust with respect to uncertainties about the ocean environment. In particular, it depends on the product of the channel-mode horizontal wave numbers and the differential distance traveled in a sampling interval, rather than the horizontal wave numbers and baseline distance to the sensor array. Thus it is less sensitive to errors in specifying the wavenumbers. The technique assumes some target dynamics and physics of the channel modes to hypothesize candidate sequences of mode coefficients. We evaluate the likelihood in range-rate and depth, updating it with a recursive Bayesian state-space model for the mode coefficients. To update the likelihood we employ a method of sequential importance sampling (SIS).

A Partially Adaptive Beamforming with Slepian-Based Quiescent Response

We propose and investigate a partially adaptive beamformer that employs Slepian sequences in both the quiescent weight vector and the signal blocking matrix. This technique maintains robustness in the sense that it preserves low sidelobe levels under conditions of low training data support, signal steering vector mismatch, and moving interference. The adaptive degrees of freedom are chosen based on the properties of Slepian sequences, in order to mitigate the effects of signal self-nulling. Numerical comparisons with adaptive beamformers with Slepian-based and Chebyshev-based quiescent responses support the efficacy of this method

Multitaper scan-free spectrum estimation using a rotational shear interferometer

Multitaper methods for a scan-free spectrum estimation that uses a rotational shear interferometer are investigated. Before source spectra can be estimated the sources must be detected. A source detection algorithm based upon the multitaper F-test is proposed. The algorithm is simulated, with additive, white Gaussian detector noise. A source with a signal-to-noise ratio (SNR) of 0.71 is detected 2.9 degrees from a source with a SNR of 70.1, with a significance level of 10(-4), approximately 4 orders of magnitude more significant than the source detection obtained with a standard detection algorithm. Interpolation and the use of prewhitening filters are investigated in the context of rotational shear interferometer (RSI) source spectra estimation. Finally, a multitaper spectrum estimator is proposed, simulated, and compared with untapered estimates. The multitaper estimate is found via simulation to distinguish a spectral feature with a SNR of 1.6 near a large spectral feature. The SNR of 1.6 spectral feature is not distinguished by the untapered spectrum estimate. The findings are consistent with the strong capability of the multitaper estimate to reduce out-of-band spectral leakage.

UMP invariance in adaptive detection: kernels that preserve monotone likelihood ratio

We consider the question of optimality for the adaptive coherence estimator (ACE), which is an adaptive detection statistic for the problem in which noise in the training data is not constrained to have same power level as noise in the test data. Having previously shown that ACE is a maximal invariant statistic, we complete a proof that a threshold test on ACE is uniformly-most-powerful (UMP) invariant. This requires a second result, that the statistic possesses a monotone likelihood ratio (MLR). We establish the MLR property by relating it to the property of the density being a totally positive kernel. By repeatedly applying a basic composition formula for such kernels, we show that the density for ACE is totally positive. Thus the density has MLR, and a simple threshold test on ACE has the strict optimality property of being UMP-invariant.

High-resolution direction finding and scan-free spectrum estimation with rotational-shear interferometric sensor arrays

In this paper we investigate the application of a rotational-shear interferometer, toward the problem of simultaneously estimating the directions of well-localized sources, and their spectral profiles. Rotational shear makes possible the acquisition of a spectrum estimate, without the mechanical scan required in using a Michelson interferometer in Fourier-transform spectroscopy. The spectrum and angle estimates are obtained computationally. The interferometric data enables the application of super-resolution direction-finding techniques commonly used in radar and sonar array processing.