Closed-Form Hybrid Cramer-Rao Bound for DOA Estimation by an Acoustic Vector Sensor Under Orientation Deviation

Acousticvector sensors have been widely used for direction-of-arrival (DOA) estimation in hydroacoustics and aeroacoustics. The orientation of the acoustic vector sensor must be measured, e.g., by an attitude sensor, before its application to DOA estimation. However, the measured orientation generally deviates slightly from its actual orientation because of imperfect attitude measurements. This letter investigates how random deviations in the orientation degrade the performance of DOA estimation. We derive a closed-form approximation of the hybrid Cramer-Rao bound for DOA estimation by modeling the deviations as zero-mean Gaussian variables with small variances. A relationship based on a determinant-differential formula is introduced to avoid a complicated brute-force solution, yielding a sufficiently simple expression with quantitative observations. Numerical results illustrate the high accuracy and effectiveness of the closed-form approximation.