Two-step self-calibration for circular acoustic vector sensor array under axis-angle bias

In this work, we consider the problem of joint calibration and direction-of-arrival (DOA) estimation for a non-ideal circular acoustic vector sensor array (CAVSA), where the particle velocity sensors of the acoustic vector sensors (AVSs) are either orthogonal or non-orthogonal and suffer from axis-angle bias. For these two types of non-ideal array configurations, a two-step self-calibration method based on the Capon cost function and the subspace criterion is proposed. The proposed method decouples the axis-angle bias vector from the CAVSA steering vector. An optimization problem is formulated by integrating this vector as a constraint into the Capon cost function. The target DOA is estimated by minimizing the cost function across all spatial search angles. Next, the axis-angle bias parameters are estimated by enforcing the orthogonality between the reparametrized steering vector for the estimated DOAs and the noise subspace. Numerical simulations show the superior performance of the proposed method, enabling robust DOA estimation and accurate calibration of axis-angle bias parameters, and experimental results using a five-element CAVSA further demonstrate its practical effectiveness.