Mean-square error surfaces of 2-D recursive adaptive filters

Recursive adaptive filters which utilize a stochastic gradient search algorithm in order to optimize their coefficients are apt to converge to local minima if the mean-square error surface is not unimodal. Such conditions are known to result since the IIR mean-square error surfaces is not quadratic. Two-dimensional adaptive filter error surfaces are examined in this paper, and their properties are seen to be very similar to those of 1-D IIR adaptive filter error surfaces.