The effect of an unknown data bias in least-squares adjustment: some concerns for the estimation of geodetic parameters C. Kotsakis Department of Geodesy and Surveying, Aristotle University of Thessaloniki University Box 440, Thessaloniki, GR-54124, Greece, Email: kotsaki@topo.auth.gr Abstract Least-squares (LS) estimation is a standard tool for the optimal processing of geodetic data. In the framework of global gravity field modelling, for example, such methods are extensively applied for the determination of geoid solutions from CHAMP and GRACE data via the estimation of a large set of spherical harmonic coefficients. Frequently, in geodetic applications additional nuisance parameters need to be included in the least-squares adjustment procedure to account for external biases and disturbances that have affected the available measurements. The objective of this paper is to expose a trade-off which exists in the LS inversion of linear models that are augmented by additional parameters in the presence of unknown systematic errors in the input data. Specifically, it is shown that if a linear model of full rank is extended by a scalar parameter to account for a common bias in the data, the LS estimation accuracy of all the other model parameters automatically worsens. Some simple numerical examples are also given to demonstrate the significance of this accuracy degradation in the geodetic practice. 1. Introduction Least-squares (LS) estimation is a standard tool for the optimal processing of geodetic data. Its use is commonly associated with a linear(-ized) model of observation equations v x A y + = (1) 0 v} { = E , (2) C v v } { T = E where y is a vector of observations, v is a vector of zero-mean random errors with a covariance (CV) matrix C, A is a matrix of known coefficients, and x is a parameter vector that needs to be estimated from the given data. Despite its simplistic linear character and its inherent restriction for additive noise, the above model is frequently employed in every field of geodetic research (e.g., Dermanis and Rummel 2000). A problem that is often encountered in geodetic data analysis with the aforementioned general model is the presence of external disturbances (biases) in the available measurements. In cases where the effect of such disturbances can be determined a-priori with sufficiently high accuracy (i.e. with an uncertainty that is significantly lower than the data noise level), the original measurements y should be replaced with a ‘corrected’ set that is compatible with the theoretical