Improved source number detection and direction estimation with nested arrays and ULAs using jackknifing

We consider the problem of source number detection and direction-of-arrival (DOA) estimation, based on uniform linear arrays (ULAs) and the newly proposed nested arrays. A ULA with N sensors can detect at most N-1 sources, whereas a nested array provides O(N^{2}) degrees of freedom with O(N) sensors, enabling us to detect K sources with N<K sensors. In order to make full use of the available limited valuable data, we propose a novel strategy, which is inspired by the jackknifing resampling method. Exploiting numerous iterations of subsets of the whole data set, this strategy greatly improves the results of the existing source number detection and DOA estimation methods. With the assumption that the subsets of the data set contain enough information, we theoretically prove that the improvement of detection or estimation performance, compared with the original performance without jackknifing, is guaranteed when the detection or estimation accuracy is greater than or equal to 50%. Numerical simulations demonstrate the superiority of our strategy when applied to source number detection and DOA estimation, both for ULAs and nested arrays.