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“Maximum Likelihood Method for 2-D Non-Causal Model Based Spectrum Estimation”
by Richard Hansen, Jr. and Rama Chellappa
March 1988
This report presents noncausal autoagressive (NCAR) plus additive noise model based spectrum estimation for planar array data typical of signals encountered in radar, sonar, seismology, radio astronomy, and other similar array processing applications. Previous research has shown that the maximum likelihood )ML) procedure provides consistent and efficient spectrum parameter estimates for NCAR models with noncausal neighbor sets. Here we show that these properties carry over to the approximate maximum likelihood estimates of parameters for Gaussian NCAR plus noise models. Since the likelihood function is nonlinear in the model parameters and is further complicated by the unknown variance parameter of the additive noise, computationally intensive gradient search algorithms are required for computing the estimates. By assuming a toroidal lattice the complexity of the approximate ML equation is significantly reduced without destroying the theoretical asymptotic properties of the estimates and with little impact on the observed accuracy of the estimated spectra. initial conditions for starting the toroidal ML computation are proposed. Experimental results which evaluate the signal plus noise approach and compare its performance to signal only methods are presented for Gaussian and simulated planar array data. Spectrum parameter estimate statistics are given and estimated spectra for signals with close spatial frequencies are shown.