The auxiliary model identification idea is presented for the systems with unmeasurable variables.It is an important method for studying the system identification with unknown variables.Introducing the auxiliary model identification idea and taking the input nonlinear finite impulse response system with white noise as an example,this paper studies the auxiliary model (AM) based gradient identification algorithms,the AM multi-innovation gradient identification algorithms,the interval-varying AM multi-innovation gradient identification algorithms;the interval-equating AM gradient identification algorithms and the interval-equating AM multi-innovation gradient identification algorithms.