| The array processing problem is to estimate the parameters of a finite number of signals that have been corrupted by noise. This problem has many applications, including radar, sonar, telecommunications, and medical imaging. In each array processing application, a wavefield of superimposed signals impacts upon the sensors of the array. The array of sensors then samples the wavefield to produce a set of output data from which the parameters of the signals are estimated.; We use the maximum likelihood method to estimate the signal parameters. To do so requires minimizing a nonlinear function of a positive semidefinite matrix variable, a vector variable, and a scalar variable. Because of the positive semidefinite constraint on the matrix, and because the nonlinear function is nonconvex, this is a hard optimization problem to solve.; Current algorithms either relax the positive semidefinite constraint on the matrix or, in the case of Bresler's algorithm, separate the optimization algorithm into two parts. Of the current algorithms, only Bresler's is guaranteed to find the true ML estimates. The methods that do not require the matrix to be positive semidefinite may result in “pseudo” ML estimates. |
