In this brief paper, we present a simple approach to estimate the variance of measurement noise with time-varying 1-D signals. The proposed approach exploits the relationship between the noise variance and the variance of the prediction errors (or innovation sequence) of a linear estimator, the idea that was pioneered by [9] and [2]. Compared with the classic and more recent methods in the same category, the proposed method can render more robust estimates with the presence of unmodelled dynamics and outliers in the measurement.