Some robust estimators are suggested for two-dimensional (2D) noncausal autoregressive models. These estimators are based on the general theme that robust estimators are characterized by a mechanism that down-weights data which seem extreme relative to the aggregate data. Although there could be many schemes to accomplish this down-weighting, resulting estimates should be consistent and efficient, or nearly so. Two classes of robust estimators are presented. The first class uses robust covariance estimates in place of sample covariance estimates, while the second class embodies the idea that bounding the influence of outlying data produces robustness. Simulation results are included to demonstrate the usefulness of these estimators.>

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 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 can be used to evaluate the signal-plus-noise approach and compare its performance to those of 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. The approximate ML parameter estimate's asymptotic properties, such as consistency and normality, are established, and lower bounds for the estimate's errors are derived, assuming that the data are Gaussian.>

A noncausal autoregressive (NCAR) plus additive noise model is presented for model-based spectrum estimation of two-dimensional sinusoidal signals in noise. The maximum-likelihood (ML) procedure provides consistent and efficient parameter estimates for NCAR models with bilateral neighbor sets, and these properties carry over to the maximum-likelihood estimates of parameters for Gaussian-NCAR-plus-noise models. By assuming a toroidal lattice the complexity of the ML equation is significantly reduced with little impact on the observed accuracy of the estimated spectra. Initial conditions for starting the ML computation are proposed. Experimental results are presented for various signal-to-noise ratios.>

In this paper we investigate the use of parametric models and robustified maximum likelihood to estimate two-dimensional power spectra from imperfectly observed lattice data. The maximum likelihood (ML) estimates for the signal plus noise model are consistent and asymptotically efficient for noncausal autoregressive (NCAR) models, but the solution requires the use of computationally expensive non-linear optimization, such as Newton-Raphson. By approximating the ML equations through the use of a toroidal lattice the computational complexity is reduced without unduly destroying the asymptotic properties of the estimates. When outliers in the data occurs, ML might not perform well. In this case we make no strict assumption about the distribution of the observations but assume only that the data are nominally Gaussian but with heavier tails. Then we use a robust procedure to estimate the parameters for the model.