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A generalized performance evaluation method is presented for extended Kalman filter based state estimation of first order nonlinear dynamic systems. The first order nonlinear dynamic systems are placed in three categorizes in terms of the upper bound of the absolute values of the derivatives of the nonlinear functions. According to the proposed theoretical analysis, it is shown that different state estimation performances are achieved by applying the extended Kalman filter to the first order nonlinear systems in these three categorizes. The steady state mean square error performance of the filter is presented explicitly in terms of the bounds on the nonlinearity and noise variance. The advantage of this performance evaluation method is that the convergence property of estimation error variance can be easily concluded from the system nonlinearity before its implementation. This provides insight into what is going to happen in applications, e.g. for dynamic systems used in chaotic synchronization. The simulation of several different nonlinear dynamic systems shows the effectiveness of the proposed performance evaluation criteria.