Estimation of Directions-Of-Arrival (DOA) is an important problem in various applications and a priori knowledge on the source location is sometimes available. To exploit this information, standard methods are based on the orthogonal projection of the steering manifold onto the noise subspace associated with the a priori known DOA. In this work, we derive and analyze the Cramér-Rao Bound associated with this model and in particular we point out the limitations of this approach when the known and unknown DOA are closely spaced and the associated sources are uncorrelated (block-diagonal source covariance). To fill this need, we propose to integrate a priori known locations of several sources into the MUSIC algorithm based on oblique projection of the steering manifold. Finally, we show that the proposed approach is able to almost completely cancel the influence of the known DOA on the unknown ones for block-diagonal source covariance and for sufficient Signal to Noise Ratio. Index TermsPrior-knowledge of DOA, orthogonal and oblique projectors, MUSIC algorithm, Cramér-Rao Bound.

In certain frequency estimation applications one or more of the underlying frequencies are known. For example, in rotary machines the known frequency may be a strong network frequency masking important closely spaced frequencies. Being able to include this information in the design of the estimator can be expected to improve the performance when estimating such closely spaced frequencies. We present a framework to include such prior information in a class of subspace-based estimators. Through Monte Carlo simulations and real-data applications we show the usefulness of our approach.

Abstract-In certain applications involving direction of arrival (DOA) estimation we may have a priori information on some of the DOAs. This information could refer to a target known to be present at a certain position, or to a reflection. In this paper we investigate a methodology for array processing that exploits the information on the known DOAs for estimating the unknown DOAs as accurately as possible. We present algorithms that can efficiently handle the case of both correlated and uncorrelated sources when the receiver is a uniform linear array. We find a major improvement in estimator accuracy in feasible scenarios, and we compare the estimator performance to the corresponding theoretical stochastic Cramér-Rao Bounds (CRBs) as well as to the performance of other methods capable of exploiting such prior knowledge. In addition, we apply the investigated estimators to real data from an ultra-sound array.