Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
Identification of linear systems: a practical guideline to accurate modeling
Identification of linear systems: a practical guideline to accurate modeling
Fundamentals of statistical signal processing: estimation theory
Fundamentals of statistical signal processing: estimation theory
System identification (2nd ed.): theory for the user
System identification (2nd ed.): theory for the user
Matrix analysis and applied linear algebra
Matrix analysis and applied linear algebra
sdpsol: a parse/solver for semidefinite programs with matrix structure
Advances in linear matrix inequality methods in control
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In linear system identification, optimal excitation signals can be determined using the Cramer-Rao bound. This problem has not been thoroughly studied for the nonlinear case. In this work, the Cramer-Rao bound for a factorisable Volterra model is derived. The analytical result is supported with simulation examples. The bound is then used to find the optimal excitation signal out of the class of discrete multitone signals. As the model is nonlinear in the parameters, the bound depends on the model parameters themselves. On this basis, a three-step identification procedure is proposed. To illustrate the procedure, signal optimisation is explicitly performed for a third-order nonlinear model. Methods of nonlinear optimisation are applied for the parameter estimation of the model. As a baseline, the problem of optimal discrete multitone signals for linear FIR filter estimation is reviewed.