Method and apparatus for wave field estimation

1. A method for estimating wave field characteristics in three dimensions (3D) comprising the following steps:

using a 3D ray trace model to estimate radio frequency (RF) wave front paths as the RF wave fronts propagate through Earth's atmosphere from a transmitter to a plurality of given points within a geographical area of interest, wherein the 3D ray trace model also estimates each point's phase path, group path, apogee, and hop count;

constructing a ray bundle for each point, wherein each ray bundle has a center axis, a polarization that varies along the bundle's axis, and a field amplitude that varies as a two-dimensional Gaussian curve with distance from the bundle's center axis;

sorting the points into mode constellations according to the points' hop count and apogee characteristics;

constructing a Delaunay triangulation of each mode constellation;

computing a covariance estimation for each triangle in each mode constellation, wherein nearest neighbor points in the Delaunay triangulation are included in the covariance estimation, and the semi-major and semi-minor axes of each ellipse respectively define characteristic scales of the ray bundles' Gaussian cross-section and orientation in space;

estimating the wave field characteristics over the entire geographical area of interest based on a summation of constituent ray bundles' characteristics within each mode constellation; and

adjusting an RF transmitter to compensate for atmospheric conditions based on the estimated wave field characteristics.

2. The method of claim 1 , wherein the summation is coherent.

3. The method of claim 1 , wherein the summation is incoherent.

4. The method of claim 1 , wherein the RF wave fronts are high frequency (HF) (3 to 30 megahertz) wave fronts and the HF wave fronts propagate through the Earth's ionosphere.

5. The method of claim 4 , wherein for each point, the 3D ray trace model also estimates the intersection location, initial and final elation and azimuthal angles, frequency and Doppler shift, and transverse and longitudinal complex polarizations.

6. The method of claim 4 , wherein each point's apogee is used to decipher from which ionosphere layer a corresponding ray reflected, and wherein a percent difference in reflection height is used to define a threshold between modes.

7. The method of claim 6 , wherein the wave field characteristics include phase, vector intensity, and polarization of HF skywave signals.

8. The method of claim 1 , further comprising the following steps:

calculating, for each mode constellation, a median edge length of the triangles in the Delaunay triangulation; and

eliminating triangles in a given mode constellation having a circumcircle radius that is greater than two times the median edge length of the given mode constellation.

9. The method of claim 1 , further comprising the step of displaying the estimated wave field characteristics on a map of the geographical area of interest.

10. The method of claim 9 , further comprising the step of identifying on the map areas of limited RF wave front propagation.

11. A method for estimating wave field characteristics in three dimensions (3D) comprising the following steps:

inputting radio frequency (RF) transmitter characteristics into a processor;

inputting propagation medium characteristics into the processor;

identifying a geographical area of interest;

tracing in 3D a plurality of ray paths from the transmitter to corresponding intersection points on the area of interest;

generating a separate constellation of points for intersection points having the same mode of transmission;

using Delaunay triangulation to create a triangulation mesh for each constellation of points;

constructing a Gaussian ray bundle from each ray path, wherein each Gaussian ray bundle comprises a plurality of Gaussian functions centered on a corresponding ray wherein differences in depth between neighboring rays is represented by a 2×2 matrix that represents the variance of rays distributed around the corresponding ray;

for each constellation of points, coherently summing the constituent ray bundles at a given intersection point;

determining a phase-coherent channel response of the propagation medium to RF transmissions from the transmitter over the entire area of interest based on the coherent sum of constellation points for each mode; and

adjusting the RF transmitter characteristics to account for propagation medium conditions based on the determined phase-coherent channel response of the propagation medium.

12. The method of claim 11 , further comprising the step of filtering the triangulation by eliminating triangles in a given mode constellation that have a dimension that is greater than a threshold.

13. The method of claim 12 , wherein the RF wave fronts are high frequency (HF) (3 to 30 megahertz) wave fronts and the HF wave fronts propagate through the Earth's ionosphere.

14. The method of claim 13 , wherein for each point, the 3D ray trace model also estimates the intersection location, initial and final elation and azimuthal angles, frequency and Doppler shift, and transverse and longitudinal complex polarizations.

15. The method of claim 14 , wherein each point's apogee is used to decipher from which ionosphere layer a corresponding ray reflected, and wherein a percent difference in reflection height is used to define a threshold between modes.

16. The method of claim 13 , wherein the wave field characteristics include phase, vector intensity, and polarization of HF skywave signals.

17. The method of claim 11 , further comprising the step of displaying the estimated wave field characteristics on a map of the geographical area of interest.

18. The method of claim 17 , further comprising the step of identifying on the map areas of limited RF wave front propagation.