Iterative constrained least squares array shape estimation using sources in unknown locations under a planewave assumption

Array shape estimation is an important problem in array signal processing. We present an iterative algorithm that estimates two dimensional array element positions via an algebraic solution to a least squares problem, under the assumption that the sources are in the far-field with unknown positions. Under some assumptions, we calculate the dependence of performance on the distribution of the localizing sources. We give examples of algorithm performance from both simulations and real data. We also illustrate algorithm performance for horizontal arrays as a function of time delay estimation variance and the variance of vertical arrival angle estimates.