# The effect of sampling methods on the validity and reliability of the estimation of the orbital stability of human gait

## TL;DR

This study examines how sampling methods affect the accuracy of measuring gait stability in humans using Floquet multipliers.

## Contribution

The study introduces a framework to quantify how sampling conditions influence the reliability of gait stability estimates.

## Key findings

- Bias and variance in Floquet multiplier estimates decrease with longer time series.
- Partitioning long time series into segments improves FM estimation reliability.
- A strong correlation with true FM values is achieved after 140 strides for a 14-dimensional state vector.

## Abstract

Floquet multiplier (FM) is a commonly used metric for evaluating gait orbital stability in biomechanics. However, variability of human gait and noise from various sources can induce significant bias and variance in the estimation of FM. Furthermore, FM is employed in gait analysis without standardized protocols, leading to highly case-dependent outcomes. To address these challenges, we quantify the effects of sampling conditions on the accuracy and consistency of FM estimations. We recruited 20 healthy participants and conducted five trials of 10 minutes of walking per participant. Using individualized Jacobian matrices calculated from the walking experiments, we synthesized multiple sets of virtual time series with varying lengths and trial counts. Using stochastic linear models, we simulated the error dynamics depending on the sampling methods. The bias and variance of FM estimates decreased as the time series lengthened, achieving a strong correlation with the true value after 140 strides for 14-dimensional state vector. Our results further suggest that partitioning a long time series into appropriately sized segments can yield more reliable FM estimates, reducing both bias and variance in FM estimations.