Low-Complexity Algorithms for Low Rank Clutter Parameters Estimation in Radar Systems

Sun, Ying; Breloy, Arnaud; Babu, Prabhu; Palomar, Daniel P.; Pascal, Frédéric; Ginolhac, Guillaume

doi:10.1109/tsp.2015.2512535

Cited by 43 publications

(50 citation statements)

References 46 publications

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“…• the Fixed-Point Estimator (FPE) [44], [45], [46] M FPE , that is obtained iteratively solving a fixed point equation; • the Low Rank clutter Estimator (LRE), [17], addressing a mixed Gaussian/compound Gaussian disturbance model. The covariance estimate can be computed as…”

Section: A Spatial Processingmentioning

confidence: 99%

“…where τ k is the estimated texture of the k-th clutter datum and Σ is the covariance estimate of the speckle obtained through the iterative algorithm proposed in [17].…”

Section: A Spatial Processingmentioning

confidence: 99%

“…Precisely, it is provided an iterative fixed point algorithm to compute the constrained estimate. Finally, in [17], an iterative algorithm to estimate, according to the ML approach, both the clutter subspace and the covariance is proposed, assuming the disturbance composed of a low rank compound Gaussian clutter plus a white Gaussian noise contribution. Further technically sound and effective covariance estimators can be found in [18], [19], [20], [21], [22], [23].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Geometric Approach to Covariance Matrix Estimation and its Applications to Radar Problems

Aubry

Maio

Pallotta

2018

IEEE Trans. Signal Process.

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Abstract-A new class of disturbance covariance matrix estimators for radar signal processing applications is introduced following a geometric paradigm. Each estimator is associated with a given unitary invariant norm and performs the sample covariance matrix projection into a specific set of structured covariance matrices. Regardless of the considered norm, an efficient solution technique to handle the resulting constrained optimization problem is developed. Specifically, it is shown that the new family of distribution-free estimators shares a shrinkagetype form; besides, the eigenvalues estimate just requires the solution of a one-dimensional convex problem whose objective function depends on the considered unitary norm. For the two most common norm instances, i.e., Frobenius and spectral, very efficient algorithms are developed to solve the aforementioned one-dimensional optimization leading to almost closed form covariance estimates. At the analysis stage, the performance of the new estimators is assessed in terms of achievable Signal to Interference plus Noise Ratio (SINR) both for a spatial and a Doppler processing assuming different data statistical characterizations. The results show that interesting SINR improvements with respect to some counterparts available in the open literature can be achieved especially in training starved regimes.

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Section: A Spatial Processingmentioning

confidence: 99%

“…where τ k is the estimated texture of the k-th clutter datum and Σ is the covariance estimate of the speckle obtained through the iterative algorithm proposed in [17].…”

Section: A Spatial Processingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Geometric Approach to Covariance Matrix Estimation and its Applications to Radar Problems

Aubry

Maio

Pallotta

2018

IEEE Trans. Signal Process.

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“…For instance, when number of samples K is less than the dimension of the data M , Tyler's M -estimator [4] is undefined. To solve this problem, the current approaches consider either regularize the M -estimator by shrinking it towards some given target, such as the identity matrix [6][7][8][9], or constraining the CM to have some structure known in a priori to reduce the numbers of parameters to be estimated [10][11][12].…”

Section: Introductionmentioning

confidence: 99%

“…The problem is hard to solve since both the objective function and the constraint set are nonconvex. Following the lines of [11,12], we derive iterative algorithms to compute these new CTE using the (block) Majorization-Minimization (MM) algorithmic framework [16]. The updates have closed-form expression, thus can be computed efficiently, and monotonically decrease the objective value.…”

Section: Introductionmentioning

confidence: 99%

Robust rank constrained kronecker covariance matrix estimation

Breloy¹,

Sun²,

Babu

et al. 2016

2016 50th Asilomar Conference on Signals, Systems and Computers

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International audienceIn this paper, we consider the problem of robustly estimating a structured covariance matrix (CM). Specifically, we focus on CM structures that involve Kronecker products of low rank matrices, which often arise in the context of array processing (e.g. in MIMO-Radar, COLD array, and STAP). To tackle this problem, we derive a new Constrained Tyler's Estimators (CTE), which is defined as the minimizer of the cost function associated to Tyler's estimator under Kronecker structural constraint. Algorithms to compute these new CTEs are derived based on the Majorization-Minimization algorithmic framework

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Bayesian signal subspace estimation with compound Gaussian sources

et al. 2020

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In this paper, we consider the problem of low dimensional signal subspace estimation in a Bayesian context. We focus on compound Gaussian signals embedded in white Gaussian noise, which is a realistic modeling for various array processing applications. Following the Bayesian framework, we derive two algorithms to compute the maximum a posteriori (MAP) estimator and the so-called minimum mean square distance (MMSD) estimator, which minimizes the average natural distance between the true range space of interest and its estimate. Such approaches have shown their interests for signal subspace estimation in the small sample support and/or low signal to noise ratio contexts. As a byproduct, we also introduce a generalized version of the complex Bingham Langevin distribution in order to model the prior on the subspace orthonormal basis. Finally, numerical simulations illustrate the performance of the proposed algorithms.

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Low-Complexity Algorithms for Low Rank Clutter Parameters Estimation in Radar Systems

Abstract: International audienc

Cited by 43 publications

References 46 publications

A Geometric Approach to Covariance Matrix Estimation and its Applications to Radar Problems

A Geometric Approach to Covariance Matrix Estimation and its Applications to Radar Problems

Robust rank constrained kronecker covariance matrix estimation

Bayesian signal subspace estimation with compound Gaussian sources

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