When attempting to estimate the state of a dynamic system, one of the common assumptions is that the uncertainty information for the inputs (measurements and dynamics) is known a-priori. Unfortunately, this is not a valid assumption in many cases, leading to the development of multiple covariance estimation techniques for both the Kalman filter and smoothing techniques. This paper presents a novel method to estimate the covariances of the inputs in a factor-graph formulation of the Bayesian estimation problem. A general solution, based on covariance estimation in linear regression problems, is presented that gives unbiased estimators of multiple variances from measured data. An iteratively re-weighted least squares (IRLS) algorithm is then used to estimate the input variances of a non-linear system using factor graph optimization. Simulation studies using a robot localization problem demonstrate the efficacy of our proposed techniques.