Adaptive unknown input reconstruction scheme for Hammerstein-Wiener systems

In this paper an adaptive time-varying filter for unknown/unmeasurable input reconstruction is proposed. The algorithm is based on parity-equations and is applicable to Hammerstein-Wiener systems, i.e. systems composed of a linear dynamic part followed and preceded by a memoryless nonlinearity. An error-in-variables case is considered, i.e. known input and output signals are both subjected to measurement uncertainties. The scheme forms an extension to a filter previously proposed by the authors. As the input reconstruction involves transformation of noisy signals through memoryless static functions, measurement noise is either amplified or reduced, depending on the gradient of the nonlinear function. Thus, in the proposed scheme the bandwidth of the filter is adjusted depending on the operating point allowing for a trade-off between noise attenuation and a phase lag.