NONCAUSAL 2-D SPECTRUM ESTIMATION FOR DIRECTION FINDING

A two-dimensional noncausal autoregressive (NCAR) plus additive noise model-based spectrum estimation method is presented for planar array data typical of signals encountered in radar, sonar, seismology, radio astronomy, and other similar array processing applications. Since the likelihood function for NCAR plus noise data is nonlinear in the model parameters and is further complicated by the unknown variance of the additive noise, computationally intensive gradient search algorithms are required for computing the estimates. If a doubly periodic lattice is assumed, the complexity of the approximate maximum likelihood (ML) equation is significantly reduced without destroying the theoretical asymptotic properties of the estimates and degrading the observed accuracy of the estimated spectra. Initial conditions for starting the approximate ML computation are suggested. Experimental results that evaluate the signal-plus-noise approach and compare its performance to signal-only methods are presented for Gaussian and simulated planar array data. Statistics of estimated spectrum parameters are given, and estimated spectra for signals with close spatial frequencies are shown. Finally, we establish the approximate ML parameter estimate's asymptotic properties such as consistency and normality and derive lower bounds for the estimate's errors assuming that the data are Gaussian. © 1990 IEEE