ON GLOBAL CONVERGENCE OF STEIGLITZ-MCBRIDE ADAPTIVE ALGORITHM

In this paper we investigate the ''global convergence'' phenomenon of the Steiglitz-McBridge adaptive identification/filtering method (SMM) observed previously under reduced order setting. Specifically, we rela te the closeness of SMM solutions to minimum mean square error (MSE) p oints through sharpness of the MSE surface at these minima. We first d efine 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 minimu m is, the closer the SMM solution will be to the minimum. This explain s the striking closeness of the two points observed earlier. Some addi tional first-order examples are also presented that all agree with the results of the analysis. These local results are then generalized to higher order cases. The global properties of the SMM solutions are fin ally proposed in the form of a conjecture which is based on numerous c alculated examples.