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.
Abstract-A number of signal processing applications require the estimation of covariance matrices. Sometimes, the particular scenario or system imparts a certain theoretical structure on the matrices that are to be estimated. Using this knowledge allows the design of algorithms exploiting such structure, resulting in more robust and accurate estimators, especially for small samples. We study a scenario with a measured covariance matrix known to be the Kronecker product of two other, possibly structured, covariance matrices that are to be estimated. Examples of scenarios in which such a problem occurs are MIMO-communications and EEG measurements. When the matrices that are to be estimated are Toeplitz structured, we show our algorithms to be able to achieve the Cramér-Rao Lower Bound already at very small sample sizes.
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