This paper describes the derivation and implementation of a new method to overbound Kalman filter (KF) based estimate error distributions in the presence of time-correlated measurement and process noise. The method is specific to problems where each input noise component is first-order Gauss-Markov with a distinct variance σ2 ∈ [σmin2 , σmax2 ] and time constant τ ∈ [τmin, τmax]. The bounds on σ2 and τ are known. Reference  derives an overbound for the continuous-time KF, and we extend the result to the more common case of sampled-data systems with discrete-time measurements. We prove that the KF covariance matrix overbounds the estimate error distribution when Gauss-Markov processes are defined using a time constant τmax and a process noise variance inflated by (τmax/τmin). We also show that the overbound is tightest by initializing the variance of the Gauss-Markov process with σ02 = 2σmax2 /[1 + (τmin/τmax)]. The new method is evaluated using covariance analysis for an example application in advanced receiver autonomous integrity monitoring (ARAIM) .