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The recursive posterior Cramer-Rao bound (PCRB) has recently been shown to be the information-theoretic mean square error (MSE) bound for an unbiased sequential Bayesian estimator. The expectation integrals for the Fisher information components, which arise out of the recursive PCRB formulation, are intractable in general and must be approximated numerically. We introduce a sequential Monte Carlo method for computing the PCRB in a nonlinear nonstationary dynamic system. To validate the bound accuracy, we run a particle filter on a nonstationary logistic function and see how the MSE compares to the PCRB.