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.

Traditional and contemporary approaches to mathematical fitness-fatigue models in exercise science: A practical guide with resources. Part I.

“…In this way, each observation is used for both training and validation purposes, and k is typically an non-fixed parameter with recommendations ranging from k = 8 − 12 (folds). As a minimum standard, all future FFM research should include some form of cross-validation to assess predictive accuracy of the model (with additional attention paid to predictions for very different training load series) [4,15,67]. Practitioners can play an important role in improving the quality of validation research within the sphere of fitness-fatigue modelling due to the large amounts of data collected with the most relevant, but typically inaccessible populations (i.e.…”

“…The initial mathematical framework was devised by Banister and colleagues over four decades ago [2]. Study of the underlying mathematical structure reveals no single model, but instead a collection of related models with similar properties [2][3][4][5][6][7][8][9][10][11][12][13][14]. All FFMs take as input a series of quantified daily training doses and frequently measured performance values and attempt to model, and ultimately predict, performance across time [2].…”

Traditional and contemporary approaches to mathematical fitness-fatigue models in exercise science: A practical guide with resources. Part II.

“…It has been known for an extended period that the standard FFM and subsequent first-order filter extensions suffer from several limitations that are at odds with the conceptual understanding of training response (Banister et al, 1975;Busso et al, 1991Busso et al, , 1994Calvert et al, 1976;Morton et al, 1990;Rasche & Pfeiffer, 2019). Three key limitations include: 1) the linearity assumption, where performance can be arbitrarily increased by simply increasing the training dose and for example doubling the training dose leads to double the improvement (Hellard et al, 2006;Rasche & Pfeiffer, 2019); 2) the independence assumption, where there is no interaction between training sessions and therefore training performed on a given day does not influence the response generated from another session; and 3) the deterministic assumption, where uncertainty in model parameters and observed performance are not modelled directly and are not updated based on incoming information (Kolossa et al, 2017). Two general approaches have been proposed to address limitations inherent to basic FFMs: 1) altering the model input through constraining or saturating training loads (Hellard et al, 2005), and 2) altering the model formulation (Busso, 2003;Kolossa et al, 2017;Turner et al, 2017).…”

“…Three key limitations include: 1) the linearity assumption, where performance can be arbitrarily increased by simply increasing the training dose and for example doubling the training dose leads to double the improvement (Hellard et al, 2006;Rasche & Pfeiffer, 2019); 2) the independence assumption, where there is no interaction between training sessions and therefore training performed on a given day does not influence the response generated from another session; and 3) the deterministic assumption, where uncertainty in model parameters and observed performance are not modelled directly and are not updated based on incoming information (Kolossa et al, 2017). Two general approaches have been proposed to address limitations inherent to basic FFMs: 1) altering the model input through constraining or saturating training loads (Hellard et al, 2005), and 2) altering the model formulation (Busso, 2003;Kolossa et al, 2017;Turner et al, 2017). Under the first of these approaches, Hellard et al (2005) proposed the use of a threshold saturation function, termed the Hill function (Krzyzanski et al, 1999) to address the limitations of the linearity assumption and the result that indefinite increases in training loads result in continual increases in performance.…”

Training Load Responses Modelling in Elite Sports: How to Deal with Generalisation?

“…the training load) 11 and by introducing variations in the fatigue response to a single training bout 13 . Further adaptations to the Fitness -Fatigue model were also developed with the aim of improving both goodness-of-fit and prediction accuracy 14,15 . Nonetheless, because impulse-response models aiming to predict training effects in both endurance (running, cycling, skiing and swimming) 6,11,[16][17][18][19][20][21] and more complex (hammer throw, gymnastic and judo) 8,22,23 activities sought to mitigate the underpinning physiological processes involved by exercise into a small number of entities, accuracy of predictions might greatly suffer from 24 .…”