Bias correction and uncertainty characterization of Dead-Reckoned paths of marine mammals

Biologgers incorporating triaxial magnetometers and accelerometers can record animal movements at infra-second frequencies. Such data allow the Dead-Reckoned (DR) path of an animal to be reconstructed at high resolution. However, poor measures of speed, undocumented movements caused by ocean currents, confounding between movement and gravitational acceleration and measurement error in the sensors, limits the accuracy and precision of DR paths. The conventional method for calculating DR paths attempts to reduce random errors and systematic biases using GPS observations without rigorous statistical justification or quantification of uncertainty in the derived swimming paths. We developed a Bayesian Melding (BM) approach to characterize uncertainty and correct for bias of DR paths. Our method used a Brownian Bridge process to combine the fine-resolution (but seriously biased) DR path and the sparse (but precise and accurate) GPS measurements in a statistically rigorous way. We also exploited the properties of underlying processes and some approximations to the likelihood to dramatically reduce the computational burden of handling large, high-resolution data sets. We implemented this approach in an R package “BayesianAnimalTracker”, and applied it to bio-logging data obtained from northern fur seals ( Callorhinus ursinus ) foraging in the Bering Sea. We also tested the accuracy of our method using cross-validation analysis and compared it to the conventional bias correction of DR and linear interpolation between GPS observations (connecting two consecutive GPS observations by a straight line). Our BM approach yielded accurate, high-resolution estimated paths with uncertainty quantified as credible intervals. Cross-validation analysis demonstrated the greater prediction accuracy of the BM method to reconstruct movements versus the conventional and linear interpolation methods. Moreover, the credible intervals covered the true path points albeit with probabilities somewhat higher than 95 %. The GPS corrected high-resolution path also revealed that the total distance traveled by the northern fur seals we tracked was 40–50 % further than that calculated by linear interpolation of the GPS observations.

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