Positioning Pelagic Fish from Sunrise and Sunset Times: Complex Observation Errors Call for Constrained, Robust Modeling

Abstract

Current lightbased geolocation techniques used to identify migration routes of highly mobile species have inherent limitations, depending on the type of tag technologies used. Recovered data storage tags provide detailed time series of light-levels suited for extensive post-processing, while pop-up satellite tags (PSATs) are bandwidth-limited and generally provide samples only at critical times of the day. An alternative approach is to detect a sunrise or sunset event and transmit only this information, thus freeing bandwidth for depth or temperature data. We show here that this geolocation technique retains the essential information to correct for known problems such as errors at the equinoxes. We describe the suitable model for such data, as well as the behavior of resulting location error and bias in simulated cases. Illustrations from PSAT tags at the ocean’s surface and on a freely-swimming fish reveal a highly non-Gaussian error distribution. To solve for this, we present a more generalized estimation framework than linear Gaussian models, based on an extension of the Kalman filter. We apply iterative nonlinear Least squares to address non-Gaussian errors, non-linear dynamics and missing data. The proposed optimization method may include coastlines or bathymetric limits as hard constraints. Our results indicate that sunrise/sunset-based geolocation is a viable technique technique to surmount tag design or engineering limitations when tracking pelagic fish