A Koopman operator-based approach to position sensing and estimation in unsteady flow

Position estimation using a time-series of pressure data from distributed sensors on a moving body in an unsteady flow field is a challenging problem that biological swimmers, such as fish, adeptly solve to enable effective station keeping, navigation, and swarming. Similar proprioceptive sensing is desired for bio-inspired artificial swimmers to enable similar behaviors. In flows with high Reynolds number and fluid-body interaction, the lack of a reduced model invalidates model-based estimation approaches, so data-driven time-series classification approaches must be used. In this work, we introduce a hybrid data-driven and model-driven approach, whereby pressure data is used to generate an approximation of the Koopman operator, which is the linear flow map that maps the observations (pressure data) one step forward in time with minimal error. The eigenvalues of that operator, sometimes known as the DMD modes, represent physical flow structures. We consider those modes as 'features' of the flow and use machine learning to perform estimation of the position based on these features, which results in higher estimation accuracy compared to applying machine learning directly to the time-series data.