Source-parameter estimation by approximate maximum likelihood and nonlinear regression

Statistical properties of certain parametric methods for array processing in wave fields are investigated. Potential applications are the classic location problem in underwater acoustics and wavenumber-spectrum analysis in geophysical work. Asymptotic normality of Fourier-transformed outputs of an array of sensors is applied to define approximate likelihood functions to be maximized for source-parameter estimation. Usually, the parameters are those of the spectral-density matrix. Liggett's estimates are approximations of maximum likelihood estimates in this sense. Another possibility is to use conditional likelihood functions. As a consequence, the source parameters can be found by solving nonlinear-regression problems. Approximate solutions of the latter, which enhance certain simple estimates by some iterations related to Fisher's scoring method, compare favorably with Liggett's estimates. Key Words-Array processing, beam forming, applications in passive sonar, radar and geophysical work; parametric methods: maximum likelihood and nonlinear regression; theoretical study and numerical experiments.