A bayesian approach to adaptive detection in nonhomogeneous environments

We consider the adaptive detection of a signal of interest embedded in colored noise, when the environment is nonhomogeneous, i.e., when the training samples used for adaptation do not share the same covariance matrix as the vector under test. A Bayesian framework is proposed where the covariance matrices of the primary and the secondary data are assumed to be random, with some appropriate joint distribution. The prior distributions of these matrices require a rough knowledge about the environment. This provides a flexible, yet simple, knowledge-aided model where the degree of nonhomogeneity can be tuned through some scalar variables. Within this framework, an approximate generalized likelihood ratio test is formulated. Accordingly, two Bayesian versions of the adaptive matched filter are presented, where the conventional maximum likelihood estimate of the primary data covariance matrix is replaced either by its minimum mean-square error estimate or by its maximum a posteriori estimate. Two detectors require generating samples distributed according to the joint posterior distribution of primary and secondary data covariance matrices. This is achieved through the use of a Gibbs sampling strategy. Numerical simulations illustrate the performances of these detectors, and compare them with those of the conventional adaptive matched filter

A Normalized Fractionally Lower-Order Moment Algorithm for Space-Time Adaptive Processing

A new space-time adaptive processing algorithm is proposed for clutter suppression in phased array radar systems. In contrast to the commonly used normalized least mean square (NLMS) algorithm which uses the second order moments of the data for adaptation, the proposed method uses the lower order moments of the data to adapt the weight coefficients. The normalization is also performed based on the data sample dispersion rather than the variance. Processing results using simulated and measured data show that the proposed algorithm converges faster than the NLMS algorithms in Gaussian and non-Gaussian clutter environments. It also provides better clutter suppression than the NLMS algorithm under heavy-tailed, impulsive, non-Gaussian environments. It in turn improves the target detection performance

Adaptive processing with signal contaminated training samples

We consider the adaptive beamforming or adaptive detection problem in the case of signal contaminated training samples, i.e., when the latter may contain a signal-like component. Since this results in a significant degradation of the signal to interference and noise ratio at the output of the adaptive filter, we investigate a scheme to jointly detect the contaminated samples and subsequently take this information into account for estimation of the disturbance covariance matrix. Towards this end, a Bayesian model is proposed, parameterized by binary variables indicating the presence/absence of signal-like components in the training samples. These variables, together with the signal amplitudes and the disturbance covariance matrix are jointly estimated using a minimum mean-square error (MMSE) approach. Two strategies are proposed to implement the MMSE estimator. First, a stochastic Markov Chain Monte Carlo method is presented based on Gibbs sampling. Then a computationally more efficient scheme based on variational Bayesian analysis is proposed. Numerical simulations attest to the improvement achieved by this method compared to conventional methods such as diagonal loading. A successful application to real radar data is also presented

Robust adaptive filtering algorithms for system identification and array signal processing in non-Gaussian environment

This dissertation proposes four new algorithms based on fractionally lower order statistics for adaptive filtering in a non-Gaussian interference environment. One is the affine projection sign algorithm (APSA) based on L₁ norm minimization, which combines the ability of decorrelating colored input and suppressing divergence when an outlier occurs. The second one is the variable-step-size normalized sign algorithm (VSS-NSA), which adjusts its step size automatically by matching the L₁ norm of the a posteriori error to that of noise. The third one adopts the same variable-step-size scheme but extends L₁ minimization to Lp minimization and the variable step-size normalized fractionally lower-order moment (VSS-NFLOM) algorithms are generalized. Instead of variable step size, the variable order is another trial to facilitate adaptive algorithms where no a priori statistics are available, which leads to the variable-order least mean pth norm (VO-LMP) algorithm, as the fourth one. These algorithms are applied to system identification for impulsive interference suppression, echo cancelation, and noise reduction. They are also applied to a phased array radar system with space-time adaptive processing (beamforming) to combat heavy-tailed non-Gaussian clutters. The proposed algorithms are tested by extensive computer simulations. The results demonstrate significant performance improvements in terms of convergence rate, steady-state error, computational simplicity, and robustness against impulsive noise and interference --Abstract, page iv

Adaptive radar detection in the presence of textured and discrete interference

Under a number of practical operating scenarios, traditional moving target indicator (MTI) systems inadequately suppress ground clutter in airborne radar systems. Due to the moving platform, the clutter gains a nonzero relative velocity and spreads the power across Doppler frequencies. This obfuscates slow-moving targets of interest near the "direct current" component of the spectrum. In response, space-time adaptive processing (STAP) techniques have been developed that simultaneously operate in the space and time dimensions for effective clutter cancellation. STAP algorithms commonly operate under the assumption of homogeneous clutter, where the returns are described by complex, white Gaussian distributions. Empirical evidence shows that this assumption is invalid for many radar systems of interest, including high-resolution radar and radars operating at low grazing angles. We are interested in these heterogeneous cases, i.e., cases when the Gaussian model no longer suffices. Hence, the development of reliable STAP algorithms for real systems depends on the accuracy of the heterogeneous clutter models. The clutter of interest in this work includes heterogeneous texture clutter and point clutter. We have developed a cell-based clutter model (CCM) that provides simple, yet faithful means to simulate clutter scenarios for algorithm testing. The scene generated by the CMM can be tuned with two parameters, essentially describing the spikiness of the clutter scene. In one extreme, the texture resembles point clutter, generating strong returns from localized range-azimuth bins. On the other hand, our model can also simulate a flat, homogeneous environment. We prove the importance of model-based STAP techniques, namely knowledge-aided parametric covariance estimation (KAPE), in filtering a gamut of heterogeneous texture scenes. We demonstrate that the efficacy of KAPE does not diminish in the presence of typical spiky clutter. Computational complexities and susceptibility to modeling errors prohibit the use of KAPE in real systems. The computational complexity is a major concern, as the standard KAPE algorithm requires the inversion of an MNxMN matrix for each range bin, where M and N are the number of array elements and the number of pulses of the radar system, respectively. We developed a Gram Schmidt (GS) KAPE method that circumvents the need of a direct inversion and reduces the number of required power estimates. Another unavoidable concern is the performance degradations arising from uncalibrated array errors. This problem is exacerbated in KAPE, as it is a model-based technique; mismatched element amplitudes and phase errors amount to a modeling mismatch. We have developed the power-ridge aligning (PRA) calibration technique, a novel iterative gradient descent algorithm that outperforms current methods. We demonstrate the vast improvements attained using a combination of GS KAPE and PRA over the standard KAPE algorithm under various clutter scenarios in the presence of array errors.Ph.D