Simple robust bearing-range source's localization with curved wavefronts

Abstract

In array processing, the far-field assumption of planar wavefronts is widely used by direction of arrival (DOA) estimators but not always satisfied. In this letter, we introduce a new method for bearing-range estimation, which extends classical subspace-based bearing estimators to a curved wavefront context. The bearing estimation is provided by a one-dimensional procedure, and ranges are simply analytically deduced from the bearing estimates. The proposed approach is illustrated by the introduction of the music curved wavefront (MCW) algorithm.Index Terms-Curved wavefronts, direct of arrival (DOA) estimation, range estimation, subspace-based methods.

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

“…The estimation accuracy of the proposed algorithm is compared with that of previous algorithms. The cumulant algorithm in [19 ], the subarray algorithm in [6 ] and the two‐dimensional‐MUSIC (2D‐MUSIC) algorithm in [4 ] are considered for comparison. Note that the algorithms in [6, 19 ] are derived based on the approximation model (c).…”

“…The solution is the same as given in (36 ) and (37 ). Note that, when this model is assumed, more accurate parameter estimation is likely achievable if previous algorithms in [3–32 ] are applied. Nonetheless, the estimation presented here remains useful for evaluating the impact of model mismatch on the algorithm.…”

“…Bearing and range estimates are then derived from the sensor array response's magnitude, or the phase, or joint from both. Note that the algorithm in [4 ] is also based on the exact model. However, this algorithm is computationally expensive since open‐form searching steps are involved. For the presented algorithm, the array sensor‐spacing is no longer restricted within a half or a quarter wavelength.…”

Mismatch of Near-Field Bearing-Range Spatial Geometry in Source-Localization by a Uniform Linear Array

“…For example, the "Fresnel approximation" [4] represents a second-order Taylor-series expansion of the phase-delay among identical isotropic sensors in a uniformly spaced linear array (ULA), to produce a second-order polynomial with respect to the sensor-index [3], [5], [7]- [13], [15]- [23], [25]- [40]. Similarly, [6], [24] discard the exact ULA array-manifold for an approximation consisting of a sum of approximate array-manifolds, each corresponding to a different order of a Taylor-series expansion of the exact array-manifold. A systemic model-mismatch is thus intentionally introduced by the above references into their bearing-range measurementmodel, in order to facilitate their algorithms' signal processing.…”