In this paper, the active calibration method for multiplicative modelling errors using phase-modulated (also called constant modulus) auxiliary sources is presented. Compared with some existing calibration methods, the proposed approach can exploit the constant modulus characteristic of the sources and has significantly better performance. For the purpose of incorporating the constant modulus information into the procedure for finding array error parameters, the maximum likelihood criterion is chosen as the optimisation function and a concentrated alternating iteration algorithm is developed, which has rapid convergence rate. In addition, to reduce the effects of azimuth deviations of the auxiliary sources, the study proceeds to extend the novel algorithm to the scenario where the true azimuths of the sources deviate slightly from the nominal values with a prior known Gaussian distribution. The Cramér–Rao bound (CRB) expressions for the unknowns are derived for the case when it is known that the sources are phase-modulated. Simulation results show that the performance of the proposed algorithms are considerably better than that of subspace-based calibration methods and closely follows the CRB for array error estimation.

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Calibration algorithm for multiplicative modelling errors using constant modulus auxiliary signals

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