The time-variant frequency response function (TV-FRF) uniquely characterises the dynamic behaviour of a linear time-variant (LTV) system. This paper proposes a method for estimating nonparametrically the dynamic part of the TV-FRF from known input, noisy output observations. The arbitrary time-variation of the TV-FRF is modelled by Legendre polynomials. In opposition to existing solutions, the proposed method is applicable to arbitrary inputs. (C) 2014 Elsevier Ltd. All rights reserved.