A new expression of the asymptotic performances of Maximum Likelihood DOA estimation method with modeling errors

This paper provides a new analytic expression of the RMS (Root Mean Square) error and bias of the Maximum Likelihood (ML) Direction Of Arrival (DOA) estimator in the presence of steering vectors modeling errors. The reference [4] proposes a first order approximation of these performances which is adapted to small modeling errors. In order to take into account larger modeling errors and provide tools for designing experimental set-up, a more accurate and easily usable derivation of these performances is necessary For such an investigation, the DOA estimation errors are written as an hermitean form with a stochastic vector composed by the modeling errors. Finally, a closed form expression between the performances (bias and RMS error) and statistical moments of the model error are deduced from the statistics of the hermitean form. Simulations confirm the theoretical results.