Time-Varying Human Operator Identification With Box-Jenkins Models

The identification of time-varying, adaptive behavior of a human operator in basic manual control tasks is currently still a focus area, since most methodologies only account for time-invariant system dynamics. Previous authors have proven that estimation techniques based on ARX model structures can be used to identify time-varying HO model parameters. However, ARX methods do present several problems, such as a persistent bias in the obtained estimates of the HO model poles (neuromuscular parameters) that increases due to coupled noise and system models. Therefore, in this paper a novel identification technique based on Box-Jenkins (BJ) models is proposed, to achieve a better match between the BJ estimator's inherently uncoupled system and noise models and measured HO control dynamics. The identification process was tested offline (batch-fitting) using Ordinary Least Squares and the Prediction Error Method for both ARX and BJ models, respectively, or online when Recursive Least Squares and Recursive PEM are employed. The BJ estimator has excellent potential as an identification tool due to its bias reduction capabilities, as clearly shown in batch-fitting, although the non-linear optimization processes decrease its convergence speed by 500%. An RPEM algorithm with a forgetting factor of λ = 0.99609 and a first-order remnant model incorporated in the BJ structure was tested on Monte Carlo simulation and experimental data. While the recursive BJ estimator showed the same bias-diminishing advantages also seen in batch-fitting, the non-linear RPEM estimator's results showed much slower convergence after HO behavior adaptations and frequent instabilities of the obtained parameter estimates. Hence, further research is needed for implementing a practical bias-free HO model estimator based on the BJ model structure.