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In this paper, we introduce a pilot-aided multipath channel estimator for multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems. Typical estimation algorithms assume the number of multipath components and delays to be known and constant, while their amplitudes may vary in time. In this work, we focus on the more realistic assumption that also the number of channel taps is unknown and time-varying. The estimation problem arising from this assumption is solved using random set theory (RST), which is a probability theory of finite sets. Due to the lack of a closed form of the optimal filter, a Rao-Blackwellized particle filter (RBPF) implementation of the channel estimator is derived. Simulation results demonstrate the estimator effectiveness.