Decoupled Delay-Doppler and Angle Estimation in BD-RIS Sensing via Nested Tucker Decomposition

We study single-target localization in a group-connected beyond-diagonal reconfigurable intelligent surface (BD-RIS)-assisted monostatic network with K element groups. We propose a Nested Tensor Factorization and Estimation (NTFE) algorithm that models the received signal as a 3rd-order nested Tucker tensor, decoupling the delay-Doppler and angle domains. The resulting two-stage procedure estimates the target-bearing tensor factors and then extracts the other physical parameters using subspace and closed-form steps. We also analyze identifiability and uniqueness conditions. Simulations show that NTFE exploits the group-connected BD-RIS structure and outperforms state-of-the-art sensing benchmarks.