Joint TOA and 2D-DOA Estimation Based on Space-Frequency Nested Array Motion

In this paper, the problem of joint time-of-arrival and two-dimensional direction-of-arrival (TOA/2D-DOA) estimation is solved using space-frequency nested array (SFNA) motion. SFNA is developed by incorporating the linear nested array structure and the frequency offset set generated by nested sampling, aiming to save on physical costs and computational resources. Additionally, a SFNA-based vertical movement strategy is proposed, which transforms the TOA/2D-DOA joint estimation into TOA/1D angle joint estimation and the other 1D angle estimation, significantly alleviating the enormous computational burden brought by 3D parameters joint estimation. Meanwhile, this strategy further reduces the number of sensors required, as it only needs a linear array to achieve 2D-DOA estimation. Based on the cross-covariance matrix of the novel signal model, the sparse iterative covariance-based estimation (SPICE) algorithm is applied to the TOA/1D angle joint estimation. However, the SPICE algorithm necessitates grid search, and its estimation accuracy degrades when the parameter values are not on the grids. Therefore, an improved SPICE (ISPICE) algorithm is proposed for off-grid TOA/1D angle joint estimation. Simultaneously, Euclidean distance-based grid estimation algorithm (EDGE) is developed to achieve accurate estimation of the other 1D angle. Multiple simulations are conducted to verify the effectiveness of the proposed strategy and algorithms.