The Processing of Band-Limited Measurements; Filtering Techniques in the Least Squares Context and in the Presence of Data Gaps

Abstract

This paper discusses the treatment of correlated measurements in the least squares context. We focus on the processing of band-limited measurements and on long time series with a constant sampling interval. Time domain as well as frequency domain approaches were discussed to offer different ways to integrate the filtering process into the optimization scheme as good as possible. The focus was on long equispaced data sets. The application of discrete filters in the space domain makes it possible to decorrelate the observations during data acquisition. This opens the way to a sequential adjustment procedure, where the design matrix is treated row-by-row. Huge systems with millions of observations can be solved by direct or iterative strategies, and both approaches benefit from well-tailored filter techniques. Because of the sequential access the computational effort of this giant task can be easily distributed to a cluster of parallel processors and offers, in addition, the possibility to treat data gaps in a straightforward way.