A Study of Anomalies in GPS Time Series via Polynomial Filtering

For the purpose of analyzing discrete time series, in particular originating from GPS or GLONASS coordinate measurements, we discuss an approach based on linear polynomial filtering. By expanding the given data set in terms of a (discrete) orthogonal polynomial basis it is possible to detect and analyze outliers from an expected smooth progression. Several aspects of this approach are discussed and illustrated via numerical experiments based on available measurements. We also consider a potential alternative approach based on (non-orthogonal) discrete Chebyshev polynomials.