To maximise the energy converted from a Wave Energy Converter (WEC), a real-time control law is required, which, due to its non-causal nature, necessitates the knowledge of the wave excitation force in future time. This future excitation force time series is usually obtained using forecasting strategies, which are essentially based on present and past values of the wave excitation force. Unfortunately, the excitation force is virtually always a non-measurable quantity, which leads to the necessity of a suitable estimation technique. There have been several methods developed for this unknown-input estimation problem, though some drawbacks can be readily identified. One fundamental issue comes from the convolution term accounting for the effect of radiation forces acting on the WEC. The usual approach is to approximate this convolution operation by a suitable parametric representation. However, in general, a more accurate parametric approximation directly implies a higher dimension of the model representing the WEC dynamics. This can potentially constitute a problem for real-time capabilities as it naturally increases the underlying computational complexity. In this paper, a newly developed moment-based estimator is presented, which does not require of an approximation of the radiation force dynamics. The presented moment-based estimator has been compared to an input-unknown Kalman filter, which represents a benchmark method for excitation force estimation within the wave energy community.