Array shape calibration using sources in unknown locations--Part II: Near-field sources and estimator implementation

Optimal source localization and tracking using arrays with uncertainties in sensor locations

“…The result in (69) is a generalization of the results developed in [1], [2], [4], [5]. This expression can be used to analyze the attainable m.s.e.…”

“…As demonstrated in [1] [2], uncertainties in the sensor positions may seriously degrade source localization accuracy. In such situations, it has been suggested to use auxiliary sources at known/unknown locations for the purpose of array calibration [2]- [5] . However, most of these studies have concentrated on analyzing the attainable mean square estimation errors without referring to the estimation algorithm that may achieve the indicated performance predictions.…”

“…Of course, we could decompose this complicated multidimensional optimization by processing each delay equation separately to obtain the estimate of the corresponding source location and track. However, by that we completely ignore the geometrical constraint imposed by the various sources to reduce the array uncertainties (the so-called callibration effect [2] [3] [5]) and thus to improve the localization accuracy of each signal source.…”

Array shape calibration using carry-on instrumental sensors

“…They are either active and need calibrating sources in known directions or passive and rely upon the sources present in the field to achieve self-calibration. To date, however most of these techniques do not work perfectly in the sense that they are unable to always acquire satisfactory array shape calibration due to convergence burden of multimodal nonlinear search [1]- [5], or if they can, they are either too costly to implement due to the need of auxiliary calibrating sources in known directions [6]- [8] or some certain pathological array-source geometries disable them at all [9]- [10]. Besides almost all these above array shape calibrating techniques assume that the position perturbations are relatively small deviations from the nominal positions and thus a first order approximation to the perturbed array response vector is often used to simplify the estimation procedures.…”

“…It relaxes the small error assumption and search convergence burden. The ambiguity problem of linear array identified in [9]- [10] can also be mitigated. The only price paid for above merits is that three carry-on instrumental sensors are needed to work as coordinate reference and at the same time introduce some more degrees of freedom to tackle the identifiability problem associated with the linear array.…”