1. Statistical modeling of animal movement is of critical importance. The continuous trajectory of an animal’s movements is only observed at discrete, often irregularly spaced time points. Most existing models do not allow inactivity periods such as resting or sleeping.
2. The recently proposed moving-resting (MR) model is a Brownian motion governed by a telegraph process, which allows periods of inactivity in one state of the telegraph process. The MR model, like any other continuous-time model, naturally handles unequal sampling intervals.
3. The MR model shows promise in modeling the movements of predators with long inactive periods, such as many felids, but the lack of accommodation of measurement errors seriously prohibits its application in practice. Here we incorporate measurement errors in the MR model and derive basic properties of the model. Inferences are based on a composite likelihood using the Markov property of the chain composed by every other observed increments.
4. The performance of the method is validated in finite sample simulation studies. Application to the movement data of a mountain lion in Wyoming illustrates the utility of the method.

中文翻译：

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动物运动建模中带有测量误差的动静过程

1. 动物运动的统计建模至关重要。动物运动的连续轨迹只能在离散的、通常不规则间隔的时间点观察到。大多数现有模型不允许休息或睡眠等不活动期。
2. 最近提出的动静 (MR) 模型是一种由电报过程控制的布朗运动，它允许在电报过程的一种状态下有一段时间不活动。MR 模型与任何其他连续时间模型一样，自然会处理不相等的采样间隔。
3. MR 模型在模拟长时间不活动的捕食者（例如许多猫科动物）的运动方面显示出前景，但缺乏对测量误差的适应严重阻碍了其在实践中的应用。在这里，我们将测量误差纳入 MR 模型并推导出模型的基本属性。推论基于使用由每隔一个观察到的增量组成的链的马尔可夫特性的复合似然。
4. 该方法的性能在有限样本模拟研究中得到验证。对怀俄明州美洲狮运动数据的应用说明了该方法的实用性。