Implementation of Nuttall’s vector-sensing target motion analysis algorithm

Abstract

Direction cosine measurements, obtained from an array of vector sensors, are processed and used to estimate the location and motion of a moving source. Nuttall derived this unpublished TMA algorithm in 2006, which recently was reviewed, implemented, and evaluated using newly collected experimental data. Both stationary and moving sources are examined. It is assumed that the array element positions are known; however, at any given time instant, the measured direction cosines are presumed noisy. Originally, Nuttall’s formulation only utilized the three orthogonal components of acoustic particle velocity at each array location, however adding acoustic pressure is straight-forward and resolves bearing ambiguity. For a non-moving source, the TMA processor (linear in source position variables) generates a 3-by-3 set of simultaneous equations, with solution vector for the source position (xs, ys, zs). Range from any array element to the source can then be estimated. For a moving source, a 6-by-6 set of simultaneous equations is obtained; the solution vector is now the initial source position (xs, ys, zs) and the source velocity components (a, b, c). It is presumed that the source velocity is constant over the observation interval.