Quantitative comparison of time-varying system identification methods to describe human joint impedance

Accurate and swift tuning of joint impedance is crucial to perform movement and interaction with our environment. Time-varying system identification enables quantification of joint impedance during movement. Many methods have been developed over the years, each with their own mathematical approach and underlying assumptions. Yet, for the identification of joint impedance, a systematic comparison revealing each method's unique strengths and weaknesses, is lacking. Here, we propose a quantitative framework to compare these methods. The framework is used to review five time-varying system identification methods using both simulated data and experimental data. These methods included three time-domain methods: ensemble, short data segment, and basis impulse response function; and two frequency-domain methods: ensemble spectral, and kernel-based regression. In the simulation study, joint stiffness – the static component of impedance – was simulated as a square wave to mimic the most extreme case of time-varying behavior. The identification results were compared based on the (1) variance accounted for (VAF), (2) bias, (3) random, and (4) total estimation error with respect to the simulated joint stiffness; and (5) rise time between two stiffness levels. In the experimental study, human ankle joint impedance was identified. Identification performance was compared using the variability in estimating joint stiffness – representative of the random error – and VAF. The performance metrics revealed distinct identification properties for each method. Therefore, researchers must make a well-justified decision which method is most appropriate for their application. The combination of simulation and experimental work with extensive performance quantification creates a framework for quantitative assessment of newly developed time-varying system identification methods.