DOA estimation of incoherently distributed sources using importance sampling maximum likelihood

In this paper, an importance sampling maximum likelihood (ISML) estimator for direction-of-arrival (DOA) of incoherently distributed (ID) sources is proposed. Starting from the maximum likelihood estimation description of the uniform linear array (ULA), a decoupled concentrated likelihood function (CLF) is presented. A new objective function based on CLF which can obtain a closed-form solution of global maximum is constructed according to Pincus theorem. To obtain the optimal value of the objective function which is a complex high-dimensional integral, we propose an importance sampling approach based on Monte Carlo random calculation. Next, an importance function is derived, which can simplify the problem of generating random vector from a high-dimensional probability density function (PDF) to generate random variable from a one-dimensional PDF. Compared with the existing maximum likelihood (ML) algorithms for DOA estimation of ID sources, the proposed algorithm does not require initial estimates, and its performance is closer to Cramer-Rao lower bound (CRLB). The proposed algorithm performs better than the existing methods when the interval between sources to be estimated is small and in low signal to noise ratio (SNR) scenarios.