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.

翻译：我们认为一个信号是由一个定期函数的若干时期组成的信号,我们观察到一个噪音的重新校正。阶段估计问题包括发现重新校正,特别是观察期的数目。现有的方法非常适合已知定期函数或至少简单的地方。当它未知时,我们考虑这个情况,我们根据信号的形状提出一个估计方法。我们使用信号子级数据集的持久性同质性来捕捉其局部外体的时间结构。我们用持久性图中的点数及其多功能来推断信号中的期数。我们用估计的时数来计算重新校正。我们用估计的时数来计算重新校正的估计数。我们是根据信号中足够突出的当地微型数字来计算的。这项工作的动机是车辆定位问题,我们据此评估了拟议方法。