On the identifiability of a quadratic stochastic system

Quadratic systems are the simplest nonlinear time-invariant systems and correspond to the second term of the Volterra expansion. Such systems appear in various fields of signal processing, in particular in detection and estimation. The author studies the identifiability of a discrete and finite extent quadratic stochastic system, driven by a sequence of independent, identically distributed random variables. When the input is available, the system is identified using cross-cumulants between the input and the output. When the input is unobservable, only the output cumulants up to the third-order are considered.