A robust bearing estimator based on Jacobi-Anger expansion for large angular spread source

In the estimation of the bearing of an angularly spread source, the Taylor-expansion is commonly used, which may lead to a distinct model approximation error, especially for the large spread case. In order to overcome this problem as much as possible, we employ the JA-expansion model. On one hand, the model accuracy mainly depends on the order of the JA expansion but has no direct relation with angular spread; on the other hand, as the coefficients of the JA expansion for array response are just the harmonics of the incident angle, and hence of the array, a covariance matrix can be computed exactly by the Fourier transform of the angular power density. For a symmetric angular spread, utilizing the structural knowledge of the array covariance matrix and the decoupling property of the JA-expansion model, a nonlinear least squares estimator is proposed. Numerical results demonstrate its robustness for large angular spread and extension of the array size. Its asymptotic performance is also examined for the large sample case.