Trend and Bounds for Error Growth in Controlled Lagrangian Particle Tracking

Abstract

This paper establishes the method of controlled Lagrangian particle tracking (CLPT) to analyze the offsets between physical positions of marine robots in the ocean and simulated positions of controlled particles in an ocean model. The offset, which we term the CLPT error, demonstrates distinguished characteristics not previously seen in drifters and floats that cannot be actively controlled. The CLPT error growth over time is exponential until it reaches a turning point that only depends on the resolution of the ocean model. After this turning point, the error growth slows down significantly to polynomial functions of time. In the ideal case, a theoretical upper threshold on exponential growth of CLPT error can be derived. These characteristics are proved theoretically, verified via simulation, and justified with ocean experimental data. The method of CLPT may be applied to improve the accuracy of ocean circulation models and the performance of navigation algorithms for marine robots.