目标Enumeration的欧拉示性数积分数值分析
Numerical Analysis of Target Enumeration via Euler Characteristic Integrals
摘要：
给定一个连续的传感器场，我们可以应用欧拉示性数积分方法来计算传感器场中目标的数量。如果传感器场是离散的，则欧拉积分方法将误差引入到目标计数中。在本文中，我们研究的欧拉积分时，应用到离散传感器领域的行为。在精确的假设下，我们计算了目标计数中一阶和二阶误差的数量，并发现了一个与更高阶误差成比例的公式。这使我们能够推导出一个点估计的离散传感器领域中的目标的数量。最后，我们推导出一个渐近结果，提供洞察如何离散欧拉积分的行为为大量的目标。
英文摘要：
Given a continuous sensor field, we can apply the Euler characteristic integral approach to count the number of targets in the sensor field. If the sensor field is discrete, the Euler integral approach introduces errors into our target count. In this paper, we study the behavior of the Euler integral when applied to discrete sensor fields. Under precise assumptions, we count the number of first- and second-order errors in target count, and discover a formula proportional to much higher order errors. This allows us to derive a point estimator for the number of targets in a discrete sensor field. Finally we derive an asymptotic result, providing insight into how the discrete Euler integral behaves for a large number of targets.
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