Low-Complexity Adaptive Algorithms for Robust Subspace Tracking

Robust Subspace Tracking With Missing Data and Outliers: Novel Algorithm With Convergence Guarantee

“…Specifically, PETRELS is a recursive least squares-type algorithm applying the second order stochastic gradient descent to the cost function. Inspired by PETRELS, several variants have been proposed to deal with missing data in the same line such as [9], [18], [19]. The subspace tracking algorithm in [9] is derived from minimizing the sum of squared residuals, but adding a regularization of the nuclear norm of subspace U.…”

“…Robust online subspace estimation and tracking (ROSETA) in [18] applies an adaptive step size at the stage of subspace estimation to enhance the convergence rate. Meanwhile the main idea of PETRELS-CFAR algorithm [19] is to handle "outliers-removed" data (i.e., outliers are first removed before performing subspace tracking) using a constant false alarm rate (CFAR) detector. However, the convergence of these PETRELS-based algorithms has not been mathematically proved yet.…”

“…Among the subspace tracking algorithms reviewed above, only a few of them are robust in the presence of both outliers and missing observations, including GRASTA [15], pROST [22], ROSETA [18], ReProCS-based algorithms [20], [21] and PETRELS-CFAR [19].…”

“…Adopting the approach of PETRELS-CFAR [19] but aiming to improve RST performance, we are interested in looking for a method that can remove outliers more effectively. Following our preliminary study presented in [26], the main contributions of the paper are as follows.…”

“…By contrast, our ADMM solver exploits only a new incoming data vector, hence requiring a lower storage complexity. Moreover, the performance of CFAR depends on predefined parameters such as the probability of false alarm and the size of the reference window [19]. Our ADMM solver does not involve such parameters and hence it is more efficient.…”