Trial-to-trial variability during visuomotor adaptation is usually explained as the result of two different sources, planning noise and execution noise. The estimation of the underlying variance parameters from observations involving varying feedback conditions cannot be achieved by standard techniques (Kalman filter) because they do not account for recursive noise propagation in a closed-loop system. We therefore developed a method to compute the exact likelihood of the output of a time-discrete and linear adaptation system as has been used to model visuomotor adaptation (Smith et al. in PLoS Biol 4(6):e179, 2006), observed under closed-loop and error-clamp conditions. We identified the variance parameters by maximizing this likelihood and compared the model prediction of the time course of variance and autocovariance with empiric data. The observed increase in variability during the early training phase could not be explained by planning noise and execution noise with constant variances. Extending the model by signal-dependent components of either execution noise or planning noise showed that the observed temporal changes of the trial-to-trial variability can be modeled by signal-dependent planning noise rather than signal-dependent execution noise. Comparing the variance time course between different training schedules showed that the signal-dependent increase of planning variance was specific for the fast adapting mechanism, whereas the assumption of constant planning variance was sufficient for the slow adapting mechanisms.

视觉运动适应期间的试验变异性通常被解释为两个不同来源的结果：计划噪声和执行噪声。标准技术（卡尔曼滤波器）无法通过涉及不同反馈条件的观测来估计基础方差参数，因为它们没有考虑闭环系统中的递归噪声传播。因此，我们开发了一种方法来计算时间离散和线性适应系统的输出的确切可能性，该系统已用于模拟视觉运动适应（Smith 等人，PLoS Biol 4(6):e179, 2006），在闭环和误差钳条件。我们通过最大化这种可能性来识别方差参数，并将方差和自协方差的时间过程的模型预测与经验数据进行比较。在早期训练阶段观察到的变异性增加无法用具有恒定方差的计划噪声和执行噪声来解释。通过执行噪声或计划噪声的信号相关分量来扩展模型表明，观察到的试验间变异性的时间变化可以通过信号相关的计划噪声而不是信号相关的执行噪声来建模。比较不同训练计划之间的方差时间过程表明，计划方差的信号依赖性增加对于快速适应机制是特定的，而恒定计划方差的假设对于慢速适应机制来说是足够的。