Abstract
Miniature GPS devices now allow for measurement of the movement of animals in real time and provide high‐ quality and high‐resolution data. While these new data sets are a great improvement, one still encounters some measurement errors as well as device failures. Moreover, these devices only measure position and require further reconstruction techniques to extract the full dynamical state space with the velocity and acceleration. Direct differentiation of position is generally not adequate. We report on the successful implementation of a shadowing filter algorithm that (1) minimizes measurement errors and (2) reconstructs at the same time the full phase‐space from a position recording of a flying pigeon. This filter is based on a very simple assumption that the pigeon's dynamics are Newtonian. We explore not only how to choose the filter's parameters but also demonstrate its improvements over other techniques and give minimum data requirements. In contrast to competing filters, the shadowing filter's approach has not been widely implemented for practical problems. This article addresses these practicalities and provides a prototype for such application.
Highlights
One of the most conceptual and challenging problems in animal behavior is understanding how animals move within a group or flock
We have shown in (Zaitouny, 2012; Zaitouny et al, submitted, under review) that our tracking methodology (1) is able to minimize the error and can be optimized corresponding to the observational error and time resolution, (2) is easy to adjust for one dimension or higher dimensions, (3) is robust enough to consider or ignore the error correlation, (4) works successfully for regular or irregular time resolution, (5) is capable to be extended to track rigid bodies and (6) is able to reconstruct the full dynamical state space only from position observations
We have seen our shadowing filter tracking approach is able to track the dynamics of an individual pigeon very well and applying the filter improved the quality of the data
Summary
One of the most conceptual and challenging problems in animal behavior is understanding how animals move within a group or flock. In the last few years, because of new technology such as Global Positing System (GPS) devices and video recording systems, the interest in studying animal motion and collective behavior in vertebrates has increased—both from biology (Godley, Broderick, Glen & Hays, 2003; Ryan, Petersen, Peters & Gremillet, 2004) and from physics (Kattas, Xu & Small, 2012; Kattas, PerezBarberia, Small, Xu & Walker, 2013) This new technology allows researchers to record large spatial data sets of animal motion, which opens the door for better validated models and better understanding of collective and individual animal dynamics (Bonabeau, Dorigo & Theraulaz, 1999)
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