Identification of discrete Volterra series using maximum length sequences

Abstract

An efficient method is described for the determination of the Volterra kernels of a discrete nonlinear system. It makes use of the Wiener general model for a nonlinear system to achieve a change of basis. The orthonormal basis required by the model is constructed from a modified binary maximum sequence (MLS). A multilevel test sequence is generated by time reversing the MLS used to form the model and suitably summing delayed forms of the sequence. This allows a sparse matrix solution of the Wiener model coefficients to be performed. The Volterra kernels are then obtained from the Wiener model by a change of basis.

Identification of cascade of Hammerstein models for the description of nonlinearities in vibrating devices

“…the output of the system is a linear combination of the Kernels {h n (t)} n∈{1...N } . A naive approach is to identify the model using a classical least square method, as proposed for general Volterra systems in [36]. Thus the mean squared error between the actual output of the system y(t) and the output of the estimated model s(t) given in Eq.…”

Compensation of biased excitation effects for MLS-based nonlinear systems׳ identification

“…Dynamic range adjustments in MLS-based nonlinear systems' identification had already been addressed in [11 ] where an adjustable gain parameter a was introduced to the input matrix X. On the contrary, no prior contribution has evaluated the impact of DC-level.…”

“…(2) in a compact matrix form, and a least-squares (LS) algorithm is then applied, yielding estimates on the values of the Volterra kernels. Combining Schetzen's method [1] with this matrix form, Reed and Hawksford [11 ] derived an identification method that employs linear combinations of MLS. Such signals had already been used in characterizing the distortion generated by nonlinearities inside a system [12], In Reed and Hawksford's approach, MLS are used to build a convenient orthogonal filter bank.…”

“…The individual sequences m¡ are generated from one single MLS sequence m 0 as we did before for matrix M. The resulting matrix X is built row-wise from sequences m in the way the following equation states. The probe sequence that is finally used to excite the system is extracted from matrix X as proposed in [11]. Authors described there how to shorten the excitation length attending to repeated patterns arising in X, and reconstruct from the respective system output the output that corresponds to X:…”

“…According to the construction of the filter bank proposed in [18] and used in [11], based on successive one-sample circular shifts, M displays Toeplitz structure. Starting from one single MLS sequence m 0 , we then apply circular shifts to generate all other rows; the elements of which are m¡[n] = m 0 \(n+i)\.…”