Performance characteristics of a three-dimensional array shape estimator

Sonar line arrays have become increasingly important for seismic exploration, underwater communication, tactical systems, and oceanographic studies. A fundamental requirement for optimal array performance is locating the hydrophone positions with respect to one another. This paper presents the performance characteristics of a newly developed, three-dimensional polynomial algorithm for computing the spatial coordinates of the hydrophones as a function of array arc length based on heading and depth sensor inputs. Since the array shape algorithm is not limited to any special configuration, the performance expressions are valid for floor, moored, drifting, or suspended arrays. The error bounds developed are a function of both the sensor error characteristics and the attitude of the array.