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The near-field array manifold of the acoustic vector sensor was recently derived by Wu et al [see `the acoustic vector sensor`s near-field array manifold` in IEEE Trans. Signal Process.]. The CraméŕRao bounds (CRBs) of direction-of-arrival and distance estimation with a single pure tone were also derived therein. This study aims to investigate the estimation accuracy of the acoustic vector sensor in the near-field, through the CRBs analysis, by modelling the incident source as: (i) a Gaussian distributed random sequence, and (ii) a polynomial-phase signal. All the four different compositions of the acoustic vector sensor in the near-field are considered, and their ́closed-forḿ CRBs are derived.