Stephanie Bidon

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.

Bayesian sparse estimation of migrating targets for wideband radar

Wideband radar systems are highly resolved in range, which is a desirable feature for mitigating clutter. However, due to a smaller range resolution cell, moving targets are prone to migrate along the range during the coherent processing interval (CPI). This range walk, if ignored, can lead to huge performance degradation in detection. Even if compensated, conventional processing may lead to high sidelobes preventing from a proper detection in case of a multitarget scenario. Turning to a compressed sensing framework, we present a Bayesian algorithm that gives a sparse representation of migrating targets in case of a wideband waveform. Particularly, it is shown that the target signature is the sub-Nyquist version of a virtually well-sampled two-dimensional (2D)-cisoid. A sparse-promoting prior allows then this cisoid to be reconstructed and represented by a single peak without sidelobes. Performance of the proposed algorithm is finally assessed by numerical simulations on synthetic and semiexperimental data. Results obtained are very encouraging and show that a nonambiguous detection mode may be obtained with a single pulse repetition frequency (PRF).

Bounds for Estimation of Covariance Matrices From Heterogeneous Samples

This correspondence derives lower bounds on the mean-square error (MSE) for the estimation of a covariance matrix mbi Mp, using samples mbi Zk,k=1,...,K, whose covariance matrices mbi Mk are randomly distributed around mbi Mp. This framework can be encountered e.g., in a radar system operating in a nonhomogeneous environment, when it is desired to estimate the covariance matrix of a range cell under test, using training samples from adjacent cells, and the noise is nonhomogeneous between the cells. We consider two different assumptions for mbi Mp. First, we assume that mbi Mp is a deterministic and unknown matrix, and we derive the Cramer-Rao bound for its estimation. In a second step, we assume that mbi Mp is a random matrix, with some prior distribution, and we derive the Bayesian bound under this hypothesis.

Bayesian Estimation of Covariance Matrices in Non-Homogeneous Environments

In many applications, it is required to detect, from a primary vector, the presence of a signal of interest embedded in noise with unknown statistics. We consider a situation where the training samples used to infer the noise statistics do not share the same covariance matrix as the vector under test. A Bayesian model 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 reflect a rough knowledge about the environment. Within this framework, the minimum mean-square error (MMSE) estimator and the maximum a posteriori (MAP) estimator of the primary data covariance matrix are derived. A Gibbs sampling strategy is presented for the implementation of the MMSE estimator. Numerical simulations illustrate the performances of these estimators and compare them with those of the sample covariance matrix estimator.

Bayesian Covariance Matrix Estimation with Non-Homogeneous Snapshots

We address the problem of estimating the covariance matrix Mp of an observation vector, using K groups of training samples {Zk}Kk=1, of respective size Lk, whose covariance matrices Mk may differ from Mp. A Bayesian model is formulated where we assume that Mp and the matrices Mk are random, with some prior distribution. Within this framework, we derive the minimum mean-square error (MMSE) estimator of Mp which is implemented using a Gibbs-sampling strategy. Moreover, we consider simpler estimators based on a weighted sum of the sample covariance matrices of Zk. We derive an expression for the weights that result in minimum mean square error (MSE), within this class of estimators. Numerical simulations are presented to illustrate the performances of the different estimation schemes.

Using WCP-OFDM signals with time-frequency localized pulses for radar sensing

In this paper performance of a symbol-based WCP-OFDM radar estimation algorithm is studied. Particularly, benefits of using orthogonal time-frequency localized pulses rather than biorthogonal rectangular pulses (traditionally used in CP-OFDM receiver) is investigated in presence of white Gaussian noise. Numerical examples show that the former provide better dynamic range and tolerance to Doppler for short ranges.

Variational Bayes Phase Tracking for Correlated Dual-Frequency Measurements with Slow Dynamics

We consider the problem of estimating the absolute phase of a noisy signal when this latter consists of correlated dual-frequency measurements. This scenario may arise in many application areas such as global navigation satellite system (GNSS). In this paper, we assume a slow varying phase and propose accordingly a Bayesian filtering technique that makes use of the frequency diversity. More specifically, the method results from a variational Bayes approximation and belongs to the class of nonlinear filters. Numerical simulations are performed to assess the performance of the tracking technique especially in terms of mean square error and cycle-slip rate. Comparison with a more conventional approach, namely a Gaussian sum estimator, shows substantial improvements when the signal-to-noise ratio and/or the correlation of the measurements are low.