I. Krasbutter

GOCE Data Analysis: From Calibrated Measurements to the Global Earth Gravity Field

The goal of this chapter is to describe an in-situ approach to determine a global Earth gravity model and its variance/covariance information on the basis of calibrated measurements from the GOCE mission. As the main characteristics of this procedure, the GOCE data are processed sequentially on a parallel computer system, iteratively via application of the method of preconditioned conjugate gradient multiple adjustment (PCGMA), and in situ via development of the functionals at the actual location and orientation of the gradiometer. We will further explain the adaption of the unknown stochastic model, determined by estimating decorrelation filters and variance components with respect to the GOCE observation types (i.e. SST, SGG, and regularizing prior information).

Magic Square of Real Spectral and Time Series Analysis with an Application to Moving Average Processes

This paper is concerned with the spectral analysis of stochastic processes that are real-valued, one-dimensional, discrete-time, covariance-stationary, and which have a representation as a moving average (MA) process. In particular, we will review the meaning and interrelations of four fundamental quantities in the time and frequency domain, (1) the stochastic process itself (which includes filtered stochastic processes), (2) its autocovariance function, (3) the spectral representation of the stochastic process, and (4) the corresponding spectral distribution function, or if it exists, the spectral density function. These quantities will be viewed as forming the corners of a square (the “magic square of spectral and time series analysis”) with various connecting lines, which represent certain mathematical operations between them. To demonstrate the evaluation of these operations, we will discuss the example of a q-th order MA process.

Adjustment of Digital Filters for Decorrelation of GOCE SGG Data

GOCE satellite gravity gradiometry (SGG) data are strongly autocorrelated within the various tensor components. Consideration of these correlations in the least-squares adjustment for gravity field determination can be carried out by digital decorrelation filters. Due to the complexity of the correlation pattern the used decorrelation filters consist of a cascade of individual filters. In this contribution some of the properties of these filters and their application to GOCE SGG data decorrelation will be presented.

A Constrained Quadratic Programming Technique for Data-Adaptive Design of Decorrelation Filters

Signals from sensors with high sampling rates are often highly correlated. For the decorrelation of such data, which is often applied for the efficient estimation of parametric data models, discrete filters have proven to be both highly flexible and numerically efficient. Standard filter techniques are, however, often not suitable for eliminating strong local fluctuations or trends present in the noise spectral density. Therefore we propose a constrained least-squares filter design method. The spectral features to be filtered out are specified through inequality constraints regarding the noise spectral density. To solve for the optimal filter parameters under such inequality constraints, we review and apply the Active Set Method, a quadratic programming technique. Results are validated by statistical tests. The proposed filter design algorithm is applied to GOCE gradiometer signals to analyze its numerical behaviour and efficiency for a realistic and complex application.