Online calibration of sensor arrays using higher order statistics

Aktaş, Metin
Higher Order Statistics (HOS) and Second Order Statistics (SOS) approaches have certain advantages and disadvantages in signal processing applications. HOS approach provides more statistical information for non-Gaussian signals. On the other hand, SOS approach is more robust to the estimation errors than the HOS approach, especially when the number of observations is small. In this thesis, HOS and SOS approaches are jointly used in order to take advantage of both methods. In this respect, the joint use of HOS and SOS approaches are introduced for online calibration of sensor arrays with arbitrary geometries. Three different problems in online array calibration are considered and new algorithms for each of these problems are proposed. In the first problem, the positions of the randomly deployed sensors are completely unknown except the two reference sensors and HOS and SOS approaches are used iteratively for the joint Direction of Arrival (DOA) and sensor position estimation. Iterative HOS-SOS algorithm (IHOSS) solves the ambiguity problem in sensor position estimation by observing the source signals at least in two different frequencies and hence it is applicable for wideband signals. The conditions on these frequencies are presented. IHOSS is the first algorithm in the literature which finds the DOA and sensor position estimations in case of randomly deployed sensors with unknown coordinates. In the second problem, narrowband signals are considered and it is assumed that the nominal sensor positions are known. Modified IHOSS (MIHOSS) algorithm uses the nominal sensor positions to solve the ambiguity problem in sensor position estimation. This algorithm can handle both small and large errors in sensor positions. The upper bound of perturbations for unambiguous sensor position estimation is presented. In the last problem, an online array calibration method is proposed for sensor arrays where the sensors have unknown gain/phase mismatches and mutual coupling coefficients. In this case, sensor positions are assumed to be known. The mutual coupling matrix is unstructured. The two reference sensors are assumed to be perfectly calibrated. IHOSS algorithm is adapted for online calibration and parameter estimation, and hence CIHOSS algorithm is obtained. While CIHOSS originates from IHOSS, it is fundamentally different in many aspects. CIHOSS uses multiple virtual ESPRIT structures and employs an alignment technique to order the elements of rows of the actual array steering matrix. In this thesis, a new cumulant matrix estimation technique is proposed for the HOS approach by converting the multi-source problem into a single source one. The proposed algorithms perform well even in the case of correlated source signals due to the effectiveness of the proposed cumulant matrix estimate. The iterative procedure in all the proposed algorithms is guaranteed to converge. Closed form expressions are derived for the deterministic Craḿer-Rao bound (CRB) for DOA and unknown calibration parameters for non-circular complex Gaussian noise with unknown covariance matrix. Simulation results show that the performances of the proposed methods approach to the CRB for both DOA and unknown calibration parameter estimations for high SNR.


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Citation Formats
M. Aktaş, “Online calibration of sensor arrays using higher order statistics,” Ph.D. - Doctoral Program, Middle East Technical University, 2012.