Performance Estimation using the Fitness-Fatigue Model with Kalman Filter Feedback

Abstract Tracking and predicting the performance of athletes is of great interest, not only in training science but also, increasingly, for serious hobbyists. The increasing availability and use of smart watches and fitness trackers means that abundant data is becoming available, and the interest to optimally use this data for performance tracking and training optimization is great. One competitive model in this domain is the 3-time-constant fitness-fatigue model by Busso based on the model by Banister and colleagues. In the following, we will show that this model can be written equivalently as a linear, time-variant state-space model. With this understanding, it becomes clear that all methods for optimum tracking in statespace models are also directly applicable here. As an example, we show how a Kalman filter can be combined with the fitness-fatigue model in a mathematically consistent fashion. This gives us the opportunity to optimally consider measurements of performance to adapt the fitness and fatigue estimates in a datadriven manner. Results show that this approach is capable of clearly improving performance tracking and prediction over a range of different scenarios.