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We study the time-dependent contributions from ice-dynamics and climatological forcing to mass changes of the Antarctic Ice Sheet using satellite gravimetry (GRACE) and satellite altimetry. By incorporating model products from regional climate modeling and firn modeling it is possible to resolve for the contributors to the mass balance. Deterministic least-squares methods have been commonly used to evaluate linear trends over discrete time periods. We have developed a coupled state space model to overcome limitations of those deterministic methods. We apply the state space model to drainage basin time series from GRACE, multi-mission altimetry, modeled surface mass balance (SMB), and modeled firn thickness change from April 2002 to August 2016. We separate long-term changes that we parameterize by a trend with a time-variable rate. Thereby we assume that the same long-term signal is present in GRACE and altimetry. In addition we determine short-term variations that can be cyclic, auto-correlated, or uncorrelated. Our approach has several advantages: (1) we can estimate the evolution of mass and volume changes without the restriction to predefined time-periods, (2) we do not enforce a single density to relate mass and volume changes, and (3) we allow for unmodeled SMB and firn thickness changes which are absorbed in the state space filtering framework. In West Antarctica our results show a time-variable rate of the trend that is presumably caused by a changing contribution of ice dynamics to the mass balance. In this region, we find a rate for the Pine Island Glacier drainage system that evolves from -11 ± 8 in April 2002 to -58 ± 8 Gt a⁻1 in August 2016. In East Antarctica the rate of the long-term signal is rather constant.