Fast, robust identification of nonlinear physiological systems using an implicit basis expansion

Because the number of parameters required by a Volterra series grows rapidl y with both the length of its memory and the order of its nonlinearity, met hods for identifying these models from measurements of input/output data ar e limited to low-order systems with relatively short memories. To deal with these computational and storage requirements one can either make extensive use of the structure of the Volterra series estimation problem to eliminat e redundant storage and computations (e.g., the fast orthogonal algorithm), or apply a basis expansion, such as a Laguerre expansion, which seeks to r educe the number of model parameters, and hence, the size of the estimation problem. The use of an appropriate expansion basis can also decrease the n oise sensitivity of the estimates. In this paper, we show how fast orthogon alization techniques can be combined with an expansion onto an arbitrary ba sis. We further demonstrate that the orthogonalization and expansion may be performed independently of each other. Thus, the results from a single app lication of the fast orthogonal algorithm can be used to generate multiple basis expansions. Simulations, using a simple nonlinear model of peripheral auditory processing, show the equivalence between the kernels estimated us ing a direct basis expansion, and those computed using the fast, implicit b asis expansion technique which we propose. Running times for this new algor ithm are compared to those for existing techniques. (C) 2000 Biomedical Eng ineering Society. [S0090-6964(00)00109-0].