An exact noniterative linear method for locating sources based on measuring receiver arrival times

In this paper an exact, linear solution to the source localization problem based on the time of arrival at the receivers is presented. The method is unique in that the source's position can be obtained by solving a system of linear equations, three for a plane and four for a volume. This simplification means adding an additional receiver to the minimum mathematically required (3+1 in two dimensions and 4+1 in three dimensions). The equations are easily worked out for any receiver configuration and their geometrical interpretation is straightforward. Unlike other methods, the system of reference used to-describe the receivers' positions is completely arbitrary. The relationship between this method and previously published ones is discussed, showing how the present, more general, method overcomes nonlinearity and unknown dependency issues. (c) 2007 Acoustical Society of America.