Optimal prior knowledge-based direction of arrival estimation

Abstract

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.

Prior-exploiting direction-of-arrival algorithm for partially uncorrelated source signals

“…Hence there is no need to estimate such directions. Actually, in many cases the presence of such known emitters has an adverse effect on the estimation of the unknown sources [1]. Thus there is a need to remove or at least mitigate this negative effect.…”

“…This assumption was implemented in a Root-MUSIC-type algorithm in [1], but it was seen that the thus defined estimator had highly undesirable properties in some scenarios. In this work we exploit the same assumption, but in a more structured way, and we derive a weighted-subspace type [3] algorithm POWDER (Prior-exploiting Orthogonally Weighted Direction EstimatoR), which treats the resulting problem in a statistically optimal manner.…”

“…A different approach is taken in [1], where asymptotically efficient (in the number of samples) methods are investigated. It was shown that very large performance gains were possible when coupling the prior bearing knowledge with the information that the sources are uncorrelated.…”

“…1 we vary the SNR, and compare POWDER to PLEDGE [4], which is optimal for the case when some of the signal bearings are known (but when no assumptions on the signal covariance matrix can be made). We also show CRB P [1] (which is the theoretical performance bound when some signal bearings are known, attainable by PLEDGE) and CRB BD (which is the bound exploiting the block-diagonal structure of P in conjunction with the knowledge of some signal bearings; this bound will be explicitly derived in the journal version of this article). For comparison, we also show the bound CRB θ for which the known sources are absent.…”

“…• T ; to start with we let the respective signals be coherent since this is typically a difficult scenario in which many (e.g., MUSIC-type [1], [9]) estimators fail. Thus,…”