Advances in tracking technologies for animal movement require new statistical tools to better exploit the increasing amount of data. Animal positions are usually calculated using the GPS or Argos satellite system and include potentially non-Gaussian and heavy-tailed measurement error patterns. Errors are usually handled through a Kalman filter algorithm, which can be sensitive to non-Gaussian error distributions. We introduce a latent movement model through an underdamped Langevin stochastic differential equation (SDE) that includes an additional drift term to ensure that the animal remains in a known spatial domain of interest. This can be applied to aquatic animals moving in water or terrestrial animals moving in a restricted zone delimited by fences or natural barriers. We demonstrate that the incorporation of these spatial constraints into the latent movement model can improve the accuracy of filtering for noisy observations of the positions. We implement an Extended Kalman Filter as well as a particle filter adapted to non-Gaussian error distributions. Our filters are based on solving the SDE through splitting schemes to approximate the latent dynamic. We illustrate the approach on a real Argos telemetry track of a bowhead whale in Foxe Basin, Canada.

翻译：动物追踪技术的进步需要新的统计工具来更好地利用日益增长的数据量。动物位置通常通过全球定位系统（GPS）或Argos卫星系统计算得出，其中包含潜在的非高斯重尾测量误差模式。这些误差通常通过卡尔曼滤波算法处理，但该算法对非高斯误差分布较为敏感。我们通过欠阻尼朗之万随机微分方程引入一种潜在运动模型，该模型包含额外的漂移项，以确保动物保持在已知的空间研究区域内。这适用于在水中移动的水生动物，或在由围栏或天然屏障界定的受限区域中的陆生动物。我们证明，将这些空间约束纳入潜在运动模型可以提高对含噪位置观测进行滤波的准确性。我们实现了扩展卡尔曼滤波以及适用于非高斯误差分布的自适应粒子滤波。我们的滤波方法基于通过分裂格式求解随机微分方程来近似潜在动力学。我们以加拿大福克斯盆地一头弓头鲸的真实Argos遥测轨迹为例说明了该方法。