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This paper is concerned with the finite-horizon recursive filtering problem for a class of nonlinear time-varying systems with missing measurements. The missing measurements are modeled by a series of mutually independent random variables obeying Bernoulli distributions with possibly different occurrence probabilities. Attention is focused on the design of a recursive filter such that, for the missing measurements, an upper bound for the filtering error covariance is guaranteed and such an upper bound is subsequently minimized by properly designing the filter parameters at each sampling instant. The desired filter parameters are obtained by solving two Riccati-like difference equations that are of a recursive form suitable for online applications. A simulation example is exploited to demonstrate the effectiveness of the proposed filter design scheme.