arXiv:2610.29059v1 Announce Type: new Abstract: Dense-grid spectrum search is computationally costly for multiple signal classification (MUSIC) direction-of-arrival (DOA) estimation, and low-precision evaluation can introduce numerical errors that distort candidate selection. This paper proposes precision-aware hierarchical MUSIC (PAH-MUSIC), a multistage framework that coordinates arithmetic precision, angular grids, and candidate windows in spectrum evaluation, while covariance estimation and eigendecomposition remain in FP64. Stage-dependent precision is assigned from coarse candidate discovery to final DOA estimation. Under bounded perturbations and local spectral growth, a conditional displacement bound gives a sufficient window-width condition for retained, correctly associated candidates. For a two-stage continuous cost model with fixed precision weights and window coefficients, a closed-form optimal coarse step and a cost-gain condition are derived. Simulations with two separated sources and 500 frames at each tested signal-to-noise ratio (SNR) from -10 to 15 dB show that FP8, FP16, and FP32 coarse searches followed by FP64 refinement achieve DOA root-mean-square errors close to a baseline using FP64 at both search stages. Relative to that baseline, the selected configurations reduce weighted spectrum-evaluation cost by 28.36\%--44.66\% under the adopted precision weights.