The use of the Barankin bound for determining the threshold SNR in estimating the bearing of a source in the presence of another

Abstract

In this paper we report results of a research in which we studied the problem of determining the threshold signal to noise ratio ( S N R ) between large and small errors estimation of the direction of arrival ( D O A ) of a radiating, farfield source in the presence of another. Using the Barankin lower bound ( B R ) we examine the conditions under which achievable mean square error ( m s e ) performance of any unbiased D O A estimator deviates substantially from the Carmer-Rao lower bound (CRB). We present expressions for the threshold S N R as a function of the source-array geometry and the sources S N R where one and two sources, of known/unknown spectral parameters and DOAs, are present.

Ambiguity in radar and sonar

“…We define ambiguity in the estimation of conditioned on the occurrence of , by (10) where is an upper bound of [defined by (9)] (11) Comments similar to the ones following Definition 1 apply here regarding the upper bound.…”

“…It would be desirable that a global measure of ambiguity depends only on the two values and . Mathematically, this corresponds to applying an operator to the conditioned ambiguity defined by (10) Obvious candidates for the operator are the mean value, the maximum, or the minimum taken over all possible values of . We will see, for a specific problem, the consequences of using one of these alternative operators.…”

“…Our definition applies to wideband signals, stochastic processes, and multipath problems. It has been used in [10] to determine the test points in the computation of the Barankin bounds in DOA estimation problems. When applied to the classical context, it recovers Woodward's definition.…”

Some results on the Weiss–Weinstein bound for conditional and unconditional signal models in array processing

“…In this paper, we have made the simpler assumption that the covariance matrix R s is known. These assumptions have already been used for the calculation of bounds more complex than the Cramér-Rao bound (see, e.g., [27], [33], [34]). …”

“…(44) and after an optimization over the test points. The optimization over the test points can be done over a search grid or by using the ambiguity diagram of the array in order to reduce significantly the computational cost (see [18], [27], [34], [45], [46]). …”