www.kit.edu ∑ ∑ = = - - + = - p i q j j t j t i t i t Z Z Y Y 1 1 θ φ AICC GIC CIC ARMA modelling of GNSS residuals using different model identification criteria Geodetic Institute X. Luo , M. Mayer, B. Heck KIT - The Cooperation of Forschungszentrum Karlsruhe GmbH and Universität Karlsruhe (TH) Geodetic Week 2009 September 22-24, Karlsruhe S6: Theoretical Geodesy Geodetic Institute: X. Luo, M. Mayer, B. Heck – [email protected] ARMA modelling of GNSS residuals using different model identification criteria 2 ARMA(p,q) model Introduction ARMA Applications generating prognostic models (e.g. in economic sciences) analysing physically correlated processes (e.g. in geosciences) modelling temporal correlations of GNSS observations (motivation) ARMA: AutoRegressive Moving Average ) 0 ( ) ( 2 1 1 1 1 ,σ WN Z Z Z Z Y Y Y t q t q t t p t p t t ~ , - - - - + + + = - - - θ θ φ φ L L : ) , ( q p order parameters : ) , , , , , ( 1 1 T q p θ θ φ φ K K = β model coefficients : 2 σ white noise (WN) variance Model identification criteria subjective methods (statistical tests, graphics, etc.) objective methods (specified decision criteria)