Investigating the Propagation Mechanism of Unmodelled Systematic Errors on Coordinate Time Series Estimated Using Least Squares

The propagation of unmodelled systematic errors into coordinate time series computed using least squares is addressed, to improve the understanding of unexplained signals and apparent noise in geodetic (especially GPS) coordinate time series. Such coordinate time series are invariably based on a functional model linearised using only zero and first order terms of a (Taylor) series expansion about the approximate coordinates of the unknown point. The effect of such truncation errors is investigated through the derivation of a generalised systematic error model for the simple case of range observations from a single known reference point to a point which is assumed to be at rest by the least squares model but is in fact in motion