Nonlinear model identification I need to build nonlinear model having recorded input/output data. The object is not simple and linear model will fail for sure.  What other options exist besides Least Mean Squares?

I need to identify dynamic system with one input. I’m provided recorded sequences of input and output data. I built linear regression model, which is called finite impulse response, but it is very inaccurate. I need more accurate model.
Volterra Series modeling and its adaptive implementations can be used to perform some simple nonlinear system identification tasks... See if it fits to your problem.