Optimization approaches for the identification of FIR models using cumulants

Several methods for the identification of FIR systems using cumulants have been proposed in the literature. These methods can be classified into three categories of solutions: linear algebra, closed form and optimization. Only linear algebra solutions are considered in this paper. For the sake of simplicity, these methods use the least squares approach to solve a system of equations characterized by a redundant vector of unknown parameters and assumed to be linear, but it not. Mathematically, this approach is not suitable, since the obtained system is nonlinear and must be treated as an optimization problem. To overcome this problem, we define three optimization problems and based on that the best algorithm to solve it will be selected. Simulations are performed to demonstrate the performance of the proposed methods.