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This paper presents modifications to the stochastic stability lemma which is then used to estimate the convergence rate and persistent error of the linear Kalman filter online without using knowledge of the true state. Unlike previous uses of the stochastic stability lemma for stability proof, this new convergence analysis technique considers time-varying parameters, which can be calculated online in real-time to monitor the performance of the filter. Through simulation of an example problem,doi:10.1155/2013/240295 fatcat:n27k45smzjdp7hl7luajc4iyre