When a person makes a movement, a motor error is typically observed that then drives motor planning corrections on subsequent movements. This error correction, quantified as a trial-by-trial adaptation rate, provides insight into how the nervous system is operating, particularly regarding how much confidence a person places in different sources of information such as sensory feedback or motor command reproducibility. Traditional analysis has required carefully controlled laboratory conditions such as the application of perturbations or error clamping, limiting the usefulness of motor analysis in clinical and everyday environments. Here we focus on error adaptation during unperturbed and naturalistic movements. With increasing motor noise, we show that the conventional estimation of trial-by-trial adaptation increases, a counterintuitive finding that is the consequence of systematic bias in the estimate due to noise masking the learner's intention. We present an analytic solution relying on stochastic signal processing to reduce this effect of noise, producing an estimate of motor adaptation with reduced bias. The result is an improved estimate of trial-by-trial adaptation in a human learner compared to conventional methods. We demonstrate the effectiveness of the new method in analyzing simulated and empirical movement data under different noise conditions.