We present a probabilistic interpretation of inverse kinematics and extend it to sequential data. The resulting model is used to estimate articulated human motion in visual data. The approach allows us to express the prior temporal models in spatial limb coordinates, which is in contrast to most recent work where prior models are derived in terms of joint angles. This approach has several advantages. First of all, it allows us to construct motion models in low dimensional spaces, which makes motion estimation more robust. Secondly, as many types of motion are easily expressed in spatial coordinates, the approach allows us to construct high quality application specific motion models with little effort. Thirdly, the state space is a real vector space, which allows us to use off-the-shelf stochastic processes as motion models, which is rarely possible when working with joint angles. Fourthly, we avoid the problem of accumulated variance, where noise in one joint affects all joints further down the kinematic chains. All this combined allows us to more easily construct high quality motion models. In the evaluation, we show that an activity independent version of our model is superior to the corresponding state-of-the-art model. We also give examples of activity dependent models that would be hard to phrase directly in terms of joint angles.