SPHERICAL HARMONIC ANALYSIS. A NEW METHOD AND ITS VERIFICATION,
Abstract
A new method for performing a spherical harmonic analysis, using only observed components of the earth's magnetic field, is presented. Essential features of the method involve the use of (1) multidimensional vector spaces to exhibit clearllrand to make use of the coupling amound the X, Y, and Z expansions and to simplify the logic, (2) the Gram-SSHMIDT ORTHOGONALIZATION PROCESS TO SIMPLIFY THE SOLUTION OF THE NORMAL EQUATIONS OF LEAST SQUARES AND, MORE IMPORTANT, TO PROVIDE A SYSTEM OF ORTHOGONAL FUNCTIONS WITH THEIR MANY USEFUL PROPERTIES; AND (3) the variance ration test appaied to each orthogonal function in such a way that the significant functions are used in the final approximation and the insig cificant ones are used to estimate error. The method is verified by applying to to two indepen dent sets of data, both derived by evaluating a given set of Gaussian coefficients. That the method works in the error-free case is proved conclusively by the remarkable agreement between input and output coefficients for both sets of data. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1963
- Accession Number
- AD0412825
Entities
People
- Paul F. Fougere
Organizations
- Air Force Cambridge Research Laboratories