The Kalman filter is applied to the analysis of trace gas concentrations in ice core air bubbles. A simple model for atmospheric methane is investigated to infer information about source variability from the concentration measurements. A random walk model for source evolution is tested in the role of nonprescriptive prior. Key inputs to the model are the covariance of stochastic forcing, Q, and measurement error, R. We look at both the physics and the statistics to determine the most appropriate values for Q and R in this application. We explore the sensitivity of the calculation to the input statistics in preparation for use of the method for analyzing ice core CO2 and δ13CO2 measurements in a companion paper. The method allows a rigorous analysis of the variability of concentrations and sources from ice core measurements.