Robust Subspace Tracking by Soft-Projections and Signal Subspace Matching

We present a low-complexity solution to the problem of robust subspace tracking that does not assume knowledge of the dimension of the subspace, nor that it is fixed over time. The solution is based on a powerful characterization of the underlying subspace, referred to as soft projection (SP), wherein the subspace dimension is determined implicitly by the data, and on the signal subspace matching (SSM) metric. We derive a computationally simple and accurate rank-one time-update of the soft projection that enables very good tracking even in the challenging cases of fast-changing and abruptly-changing subspaces. To cope with outliers we present a “detect and skip” approach, wherein the outliers are detected by projecting the data vectors on the tracked subspace and comparing the squared norm of their projections to an adaptive threshold. Simulation results, demonstrating the clear superiority of the proposed solutions over existing solutions, are included.