Estimation of geopotential from satellite-to-satellite range rate data: Numerical results
A technique for high-resolution geopotential field estimation by recovering the harmonic coefficients from satellite-to-satellite range rate data is presented and tested against both a controlled analytical simulation of a one-day satellite mission (maximum degree and order 8) and then against a Cowell method simulation of a 32-day mission (maximum degree and order 180). Innovations include: (1) a new frequency-domain observation equation based on kinetic energy perturbations which avoids much of the complication of the usual Keplerian element perturbation approaches; (2) a new method for computing the normalized inclination functions which unlike previous methods is both efficient and numerically stable even for large harmonic degrees and orders; (3) the application of a mass storage FFT to the entire mission range rate history; (4) the exploitation of newly discovered symmetries in the block diagonal observation matrix which reduce each block to the product of (a) a real diagonal matrix factor, (b) a real trapezoidal factor with half the number of rows as before, and (c) a complex diagonal factor; (5) a block-by-block least-squares solution of the observation equation by means of a custom-designed Givens orthogonal rotation method which is both numerically stable and tailored to the trapezoidal matrix structure for fast execution.