Fast, robust identification of nonlinear physiological systems using an implicit basis expansion.
Because the number of parameters required by a Volterra series grows rapidly with both the length of its memory and the order of its nonlinearity, methods for identifying these models from measurements of input/output data are 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 eliminate redundant storage and computations (e.g., the fast orthogonal algorithm), or apply a basis expansion, such as a Laguerre expansion, which seeks to reduce the number of model parameters, and hence, the size of the estimation problem. The use of an appropriate expansion basis can also decrease the noise sensitivity of the estimates. In this paper, we show how fast orthogonalization techniques can be combined with an expansion onto an arbitrary basis. We further demonstrate that the orthogonalization and expansion may be performed independently of each other. Thus, the results from a single application 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 using a direct basis expansion, and those computed using the fast, implicit basis expansion technique which we propose. Running times for this new algorithm are compared to those for existing techniques.