Iterative HOS-SOS (IHOSS) Algorithm for Direction-of-Arrival Estimation and Sensor Localization

A new method for joint direction-of-arrival (DOA) and sensor position estimation is introduced. The sensors are assumed to be randomly deployed except two reference sensors. The proposed method exploits the advantages of both higher-order-statistics (HOS) and second-order-statistics (SOS) with an iterative algorithm, namely Iterative Higher-Order Second-Order Statistics (IHOSS). A new cumulant matrix estimation technique is proposed for the HOS approach by converting the multisource problem into a single source one. IHOSS performs well even in case of correlated source signals due to the effectiveness of the proposed cumulant matrix estimate. A cost function is defined for the joint DOA and position estimation. The iterative procedure is guaranteed to converge. The ambiguity problem in sensor position estimation is solved by observing the source signals at least in two different frequencies. The conditions on these frequencies are presented. Closed-form expressions are derived for the deterministic Cramér-Rao bound (CRB) for DOA and unknown sensor positions for noncircular complex Gaussian noise with unknown covariance matrix. Simulation results show that the performance of IHOSS is significantly better than the HOS approaches for DOA estimation and closely follows the CRB for both DOA and sensor position estimations.