Cross-Burg algorithm for single-input two-outputs autoregressive modeling

This work addresses the Auto-Regressive modeling in Single-Input Two-Outputs (SITO) scenarios, where the lack of input signal diversity prevents application of state-of-the-art multichannel methods. Firstly, we derive a system of Yule-Walker-like equations involving only the cross-correlation of the observations. Then, we leverage the Toeplitz, not Hermitian, structure of the system coefficient matrix to derive an Asymmetric Levinson recursion. Finally, we present a novel lattice based computation of the recursion, named Cross-Burg algorithm. The Cross-Burg lattice is built by two sub-lattices, mutually connected by the reflection coefficients. The Cross-Burg algorithm is inherently robust to uncorrelated additive noise on the two observed channels. Numerical simulations show that the Cross-Burg algorithm outperforms traditional methods in accuracy and noise robustness for SITO-AR modeling and spectral estimation.