Bearing and range estimation with an exact source-sensor spatial model

: In sensor array processing literature, near-field bearing and range estimation algorithms generally use spherical wavefront to model only array sensors’ phase response (sometimes with Fresnel approximation) and assume equality in amplitude response. Ignoring the range dependent amplitudes, though facilitating the algorithmic development, will cause systematic estimation errors due to model mismatch. By taking the spherical wavefront amplitude into account, a new bearing and range estimation algorithm for locating multiple near-field sinusoid sources is presented. With the estimation of the near- field sensor array's response vector, closed-form formulas for bearing and range estimates are derived from its magnitude, or phase, or both. The problem of estimation ambiguity is discussed as well. Cramér-Rao bound is also derived to serve as a benchmark for performance study.