Array element localization for horizontal arrays via Occam’s inversion

Accurate locations for the individual elements of an acoustic sensor array are required for the application of advanced array processing methods. This paper develops a general method of localizing horizontal line array (HLA) elements which overcomes bandwidth constraints of low-frequency arrays and uncertainty in the experimental configuration. Array elements are localized for two HLA’s associated with the Spinnaker Array, a three-dimensional sensor array located in the high Arctic. Recordings were made of imploding glass light bulbs deployed at a series of locations surrounding the array site. Implosion instants were not measured; hence, the data consist of relative travel times. In addition, the source locations were measured only approximately in the field, and are treated as unknown parameters. The inverse problem of determining hydrophone and source locations is nonunique and ill-conditioned. To determine the most physically meaningful solution, an iterative linearized inversion is developed which applies the method of regularization to include a priori information about the solution. Available a priori information includes source–location estimates from on-ice measurements, depth estimates for the array end points, and the expectation that each HLA is essentially linear. The inversion is formulated to jointly minimize the parameter-estimate residuals and the three-dimensional curvature of each HLA, subject to fitting the array element localization (AEL) data to a statistically appropriate level. Minimizing HLA curvature produces the simplest array shape that is consistent with the data: any deviations from a straight array are definitely required by the data, and are not artifacts of the inversion algorithm or starting model.