A novel variable-length sliding window blockwise least-squares algorithm for on-line estimation of time-varying parameters

2004 ◽  
Vol 18 (6) ◽  
pp. 505-521 ◽  
Author(s):  
Jin Jiang ◽  
Youmin Zhang
Keyword(s):  
Least Squares ◽  
Sliding Window ◽  
Variable Length ◽  
Time Varying ◽  
Varying Parameters ◽  
Time Varying Parameters ◽  
On Line ◽  
Least Squares Algorithm ◽  
Estimation Of Time

Modeling of adaptations to physical training by using a recursive least squares algorithm

1997 ◽  
Vol 82 (5) ◽  
pp. 1685-1693 ◽  
Author(s):  
Thierry Busso ◽  
Christian Denis ◽  
Régis Bonnefoy ◽  
André Geyssant ◽  
Jean-René Lacour
Keyword(s):  
Least Squares ◽  
Physical Training ◽  
Recursive Least Squares ◽  
Model Parameters ◽  
Time Varying ◽  
Varying Parameters ◽  
Recursive Least Squares Algorithm ◽  
Time Varying Parameters ◽  
Least Squares Algorithm ◽  
Time Invariant

Busso, Thierry, Christian Denis, Régis Bonnefoy, André Geyssant, and Jean-René Lacour. Modeling of adaptations to physical training by using a recursive least squares algorithm. J. Appl. Physiol. 82(5): 1685–1693, 1997.—The present study assesses the usefulness of a systems model with time-varying parameters for describing the responses of physical performance to training. Data for two subjects who undertook a 14-wk training on a cycle ergometer were used to test the proposed model, and the results were compared with a model with time-invariant parameters. Two 4-wk periods of intensive training were separated by a 2-wk period of reduced training and followed by a 4-wk period of reduced training. The systems input ascribed to the training doses was made up of interval exercises and computed in arbitrary units. The systems output was evaluated one to five times per week by using the endurance time at a constant workload. The time-invariant parameters were fitted from actual performances by using the least squares method. The time-varying parameters were fitted by using a recursive least squares algorithm. The coefficients of determination r 2 were 0.875 and 0.879 for the two subjects using the time-varying model, higher than the values of 0.682 and 0.666, respectively, obtained with the time-invariant model. The variations over time in the model parameters resulting from the expected reduction in the residuals appeared generally to account for changes in responses to training. Such a model would be useful for investigating the underlying mechanisms of adaptation and fatigue.

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