A Numerical Method for Constructing Geo-Location Isograms
Geo-location is often performed using measurements of scalar quantities such as range, Time Difference of Arrival, range rate, Frequency Difference of Arrival, and Angle of Arrival. Each of these can be represented geometrically as a line on the earth's surface along which the measured value is constant. In general, a line or path along which a specified parameter is constant is referred to as an isogram. The ability to generate points along a measurement isogram is necessary if the isogram is to be plotted for visualization of the geo-location scenario. Also, points along the isogram associated with one measurement may be treated as candidate target locations and used to determine the validity of successive measurements.
Points along an isogram are typically found by first defining a grid over the entire area of interest then evaluating a mathematical expression at each grid point. The computation performed at each grid point is used to determine whether that grid point lies on the isogram - most points do not. To accurately plot an isogram using this approach requires a very small grid spacing and is therefore computationally intensive. This algorithm constructs the isogram by numerically integrating the gradient of the isogram along the surface of a WGS84 earth model. This avoids grid point evaluations, is less demanding computationally, and constructs the isogram faster than the approach typically used.
A detailed paper on the technique is available upon request.
Mr. M. T. Hickman