A negative group delay model for feedback-delayed manual tracking

TL;DR

This paper introduces a linear negative group delay model to explain feedback delay effects in manual tracking, capturing reactive and predictive behaviors and their transition as feedback delay increases.

Contribution

It presents a simple, parameterized linear model that explains key experimental observations of feedback delay effects in manual tracking tasks.

Findings

Prediction time increases linearly with feedback delay.

Transition from reactive to predictive behavior occurs with increased delay.

Model accurately predicts experimental observations with a single free parameter.

Abstract

We propose that feedback-delayed manual tracking performance is limited by fundamental constraints imposed by the physics of negative group delay. To test this hypothesis, the results of an experiment in which subjects demonstrate both reactive and predictive dynamics are modeled by a linear system with delay-induced negative group delay. Although one of the simplest real-time predictors conceivable, this model explains key components of experimental observations. Most notably, it explains the observation that prediction time linearly increases with feedback delay, up to a certain point when tracking performance deteriorates. It also explains the transition from reactive to predictive behavior with increasing feedback delay. The model contains only one free parameter, the feedback gain, which has been fixed by comparison with one set of experimental observations for the reactive case. Our model provides quantitative predictions that can be tested in further experiments.