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A particle filter approach is proposed for adaptive narrowband beamforming in the presence of strong interference and uncertain steering vector of interest signal. From the viewpoint of subspace decomposition, we first describe the known subspace projection beamformer as an orthogonal component of the steering vector that is perpendicular to the interference space. Then a Rao-Blackwellized particle filter algorithm is designed to estimate the subspace projection beamforming weights. All steps including the important sampling, weight updating, resampling and analytical computation have been discussed in detail. Finally, the overall adaptive beamforming algorithm is summarized and the computational complexity analysis is presented. The main contribution of this paper is to apply and formulate Rao-Blackwellized particle filtering to estimate the distribution over the subspace projection beamforming weights. Different from other two particle-filter-based beamformers proposed by Li and Chandrasekar, it is a STI-based method with unknown source steering vector. The sampled state variables are the signal power, noise power and a model parameter for beamformer weights transition; the marginalized analytical state variables are the subspace projection beamforming weights; and the measurements are a series of constructed signal samples by using the estimated projection operator and random noise loading. Numerical simulations show that the proposed beamformer outperforms linearly constrained minimum variance, subspace projection, Bayesian and other two particle-filter-based beamformers. After convergence, it has similar performance to the optimal max-SINR beamformer which uses the true steering vector and ideal interference-plus-noise covariance matrix.