On ´global convergence´ of Steiglitz-McBride adaptive algorithm

The authors investigate the global convergence phenomenon of the Steiglitz-McBride adaptive identification/filtering method (SMM) observed previously under reduced order setting. Specifically, they relate the closeness of SMM solutions to minimum mean square error (MSE) points through sharpness of the MSE surface at these minima. They first define the sharpness, and then propose that generally global minima are sharper than local minima. A local analysis based on the first-order case then reveals that the smaller the MSE is and the sharper a minimum is, the closer the SMM solution will be to the minimum. This explains the striking closeness of the two points observed earlier. Some additional first-order examples that all agree with the results of the analysis are presented. These local results are then generalized to higher order cases. The global properties of the SMM solutions are finally proposed in the form of a conjecture which is based on numerous calculated examples.