An adaptive algorithm of linear computational complexity for both rank and subspace tracking

Rank and subspace estimation is important in a variety of modern signal processing applications. In this paper we present a new approach for tracking both the rank and the signal subspace recursively. At arrival of each new sample, we update the eigenvectors spanning the signal subspace plus one or a fixed number of auxiliary eigenvectors, their corresponding eigenvalues, and an averaged noise eigenvalue. Then we apply information theoretic criteria to estimate the number of signals. The resulting adaptive algorithm has a computational complexity which is linearly proportional to the sample vector size n. In comparison to the URV based subspace tracking requiring O(n²) operations, our approach is computationally simpler, easier to implement, and does not need user supplied tolerances. Simulation results show similar tracking performance of our algorithm to the URV updating and the exact eigenvalue decomposition