Homophase Signals Separation for Volterra Series Identification

Abstract

This article addresses the identification of nonlinear systems represented by Volterra series. To improve the robustness of state-of-the-art estimation methods, we introduce the notion of "homophase signals", for which a separation method is given. Those homophase signals are then used to derive a robust identification process. This prior step is similar to nonlinear homogeneous order separation, in which amplitude relations are used to separate the orders of a Volterra series, but offers a better conditioning by using phase deviations rather than amplitudes. First an academic phase-based method using complex-valued test signals is introduced for separating nonlinear orders. Second this notion of phase deviation is extended to real-valued signals, which leads to the design of the proposed homophase signals separation method. Finally, a new identification process is derived using the homophase signals. Simulations are used to highlight the benefits of the proposed identification process in comparison to the standard approach.

Phase-based order separation for Volterra series identification

“…It combines phase deviations (as in CPS) and amplitude gains (as in AS). In Bouvier et al (2018), a notion of homophase signals is introduced and used to derive an iterative identification method. To reject numerical difficulties due to Vandermonde matrices and reserve the amplitude of inputs as a free parameter, a better alternative for order separation is proposed below.…”

“…Recently, a separation method using phase deviations and amplitude gains has been proposed (Bouvier, Hélie, & Roze, 2017), for which previous remarks on conditioning of the Vandermonde matrices still apply. Those ideas have been further developed in Bouvier, Hélie, and Roze (2018) leading to another kind of separation into homophase signals, which has been used to develop new identification processes. The use of phase deviations can be related to the results of Gardner and Archer (1993), where, in a probabilistic framework, cyclostationary signals are used to obtain orthogonality between orders 1 (in a cross-correlation sense).…”

“…The use of phase deviations can be related to the results of Gardner and Archer (1993), where, in a probabilistic framework, cyclostationary signals are used to obtain orthogonality between orders 1 (in a cross-correlation sense). But even with those new developments, robust order separation can not yet been achieved: the method of Bouvier et al (2017) still uses a set of amplitude gains leading to conditioning problems, and the method proposed in Bouvier et al (2018) does not separate homogenous orders. This paper presents a new parameter-free order separation method exclusively based on phase deviation between excitation signals.…”