Diagonally Loaded Normalised Sample Matrix Inversion (LNSMI) for Outlier-Resistant Adaptive Filtering

Generalized Robust Shrinkage Estimator and Its Application to STAP Detection Problem

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Abstract-Recently, in the context of covariance matrix estimation, in order to improve as well as to regularize the performance of the Tyler's estimator [1] also called the FixedPoint Estimator (FPE) [2], a "shrinkage" fixed-point estimator has been originally introduced in [3]. First, this work extends the results of [4], [5] by giving the general solution of the "shrinkage" fixed-point algorithm.

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“…Moreover, the "optimal" 3 value of β has changed and is now closer to 0.8. Finally, previous comments concerning the robustness of the S-FPE to the contaminated data are still valid, as well as the similar results between S-FPE and S-FPE-W. Now, to highlight the improvement brought by the shrinkage 3 optimal in the sense that there is a good clutter cancellation …”

“…Let us consider now the shrinkage (diagonally loaded) fixed point originally introduced in [3], fully analyzed in [4] and defined as the solution of the following fixed point equation, for β ∈ [0, 1]…”

“…More recently, a shrinkage has been proposed in [29] but also applied to the SCM. To deal with non-Gaussian models and to have a robust approach, this shrinkage has been applied to the Tyler's estimator [1] to obtain a "shrinkage" fixed-point estimator (FPE), originally introduced by [3] for the case where the number of samples is less than the dimension. A rigorous proof of existence, uniqueness and convergence of the associated recursive algorithm has been given by [4] in the case where a trace normalization has been added.…”

A subspace approach for shrinkage parameter selection in undersampled configuration for Regularised Tyler Estimators

“…In order to solve this issue, the estimator is regularised, an operation also known as "shrinkage towards identity." A first algorithm for the regularised Tyler estimator (RTE) has been proposed in [17] …”