论文标题
重新参与周期功能的拓扑相估计方法
Topological phase estimation method for reparameterized periodic functions
论文作者
论文摘要
我们考虑一个由周期性功能的几个时期组成的信号，我们观察到嘈杂的重新构度。相位估计问题包括发现该重新测量，尤其是观察到的时期数量。现有方法非常适合于已知或至少简单的周期函数的设置。我们考虑未知的情况，并根据信号形状提出了一种估计方法。我们使用信号的持续同源性来捕获其局部极值的时间结构。我们通过计数持久图及其多重性中的计数点来推断信号中的周期数。使用估计的周期数，我们构建了一个修复的估计量。它基于计算信号中足够突出的局部最小值的数量。这项工作是由车辆定位问题激发的，我们在其上评估了所提出的方法。
We consider a signal composed of several periods of a periodic function, of which we observe a noisy reparametrisation. The phase estimation problem consists of finding that reparametrisation, and, in particular, the number of observed periods. Existing methods are well-suited to the setting where the periodic function is known, or at least, simple. We consider the case when it is unknown and we propose an estimation method based on the shape of the signal. We use the persistent homology of sublevel sets of the signal to capture the temporal structure of its local extrema. We infer the number of periods in the signal by counting points in the persistence diagram and their multiplicities. Using the estimated number of periods, we construct an estimator of the reparametrisation. It is based on counting the number of sufficiently prominent local minima in the signal. This work is motivated by a vehicle positioning problem, on which we evaluated the proposed method.
