Modeling and Processing of Correlated Measurements in Satellite Gradiometry

In this paper, the issue of processing correlated measurements is considered. It is assumed that the true signal is distorted by a device, which, in fact, acts as a filter with a given frequency response. As a result, in the frequency domain, the signal spectrum is altered, and in the time domain, the value of the measured signal at time t₈ depends on previous values t₈-₁, t₈-₂,. This means that, in processing the measurements, it is necessary to know and be able to invert the covariance matrix, which is not diagonal and may be of large dimensions. In this case, direct inversion of the matrix turns out to be impossible. Therefore, an original method for computing the inverse covariance matrix and decorrelating the measurements is proposed for processing correlated measurements. The developed method is intended to be applied to the processing of gradiometric data obtained in the GOCE mission and to refine the the spherical harmonic coefficients coefficients of the classical series expansion of the Earth’s gravitational field.