Calibrating Nested Sensor Arrays with Model Errors

We consider the problem of direction of arrival (DOA) estimation based on a nonuniform linear nested array, which is known to provide O(N²) degrees of freedom (DOFs) using only N sensors. Both subspace-based and sparsity-based algorithms require certain modeling assumptions, e.g., exactly known array geometry, including sensor gain and phase. In practice, however, the actual sensor gain and phase are often perturbed from their nominal values, which disrupts the existing DOA estimation algorithms. In this paper, we investigate the self-calibration problem for perturbed nested arrays, proposing corresponding robust algorithms to estimate both the model errors and the DOAs. The partial Toeplitz structure of the covariance matrix is employed to estimate the gain errors, and the sparse total least squares (STLS) is used to deal with the phase error issue. In addition, we provide the Cramér-Rao bound (CRB) to analyze the robustness of the estimation performance of the proposed approaches. Furthermore, we extend the calibration strategies to general nonuniform linear arrays. Numerical examples are provided to verify the effectiveness of the proposed strategies.