Source direction estimation based on separable parameterization
Bamrung Tausieskul, Somchai Jitapankul · 2004
This thesis deals with the problem of estimating the nominal direction and its underlying angular spread in the presence of local scattering around the vicinity of source. Contents presented herein can be classified into two portions. The first part presents a large-sample approximation of the ML estimator in spatially distributed source localization. And the another proposes an incorporation of the Toeplitz-Hermitian structure in array covariance matrix into two previous estimators. The AML estimator in the first part is proposed to jointly estimate nominal directions and angular spreads. Rather than (3N[subscript s] + l)-dimensional optimization as the ML, the AML needs only 2N[subscript s] -dimensional search, where N[subscript s] signifies the number of sources. Since the proposed approach is an asymptotic approximation of the ML, its standard deviation of estimate error attains the CRB in large sample. Numerical simulation is shown, however, that by means of improved speed with respect to the ML, the computational advantage of AML is less than that of WLS, approximately one times. In the second portion, five contributions are affordable. First of all, we indicate that without any assumption on angle deviation model, the array covariance matrix is itself not only Hermitian but also Toeplitz when employing the ULA. Secondly, we provide a relationship between two well-known methods-RA and WCM—for estimating a Toeplitz-Hermitian covariance matrix. The analysis presented therein enables us to their connection by mean of optimal weight performed. We propose a large-sample approximation of ML criterion for estimating a covariance matrix with linearly affine structure. Later, a connection of the proposed estimator to an existed criterion is provided. It is conceivable that the presented criterion yields the same solution as derived from the WCM method. To decrease the estimate error, the last contribution is to incorporate the imposed Toeplitz-Hermitian matrix into both WLS and AML. With respect to the ML, computational complexity increased by including the Toeplit constraint is approximately at most one times.