Using the 20 questions estimation framework with query-dependent noise, we study non-adaptive search strategies for a moving target over the unit cube with unknown initial location and velocities under a piecewise constant velocity model. In this search problem, there is an oracle who knows the instantaneous location of the target at any time. Our task is to query the oracle as few times as possible to accurately estimate the location of the target at any specified time. We first study the case where the oracle's answer to each query is corrupted by discrete noise and then generalize our results to the case of additive white Gaussian noise. In our formulation, the performance criterion is the resolution, which is defined as the maximal $L_\infty$ distance between the true locations and estimated locations. We characterize the minimal resolution of an optimal non-adaptive query procedure with a finite number of queries by deriving non-asymptotic and asymptotic bounds. Our bounds are tight in the first-order asymptotic sense when the number of queries satisfies a certain condition and our bounds are tight in the stronger second-order asymptotic sense when the target moves with a constant velocity. To prove our results, we relate the current problem to channel coding, borrow ideas from finite blocklength information theory and construct bounds on the number of possible quantized target trajectories.

翻译：摘要：采用带有查询依赖噪声的二十问估计框架，本文研究了在分段恒定速度模型下，针对单位立方体中初始位置和速度未知的移动目标的非自适应搜索策略。在该搜索问题中，存在一个知晓目标任意时刻瞬时位置的先知。我们的任务是尽可能少地查询该先知，以准确估计目标在任意指定时刻的位置。我们首先研究了先知对每个查询的响应受到离散噪声干扰的情况，随后将结果推广至加性高斯白噪声的情形。在本文的表述中，性能准则为分辨率，定义为真实位置与估计位置之间的最大$L_\infty$距离。通过推导非渐近和渐近界，我们刻画了有限查询次数下最优非自适应查询过程的最小分辨率。当查询次数满足特定条件时，我们的界在一阶渐近意义下是紧的；当目标以恒定速度运动时，我们的界在更强的二阶渐近意义下是紧的。为证明结果，我们将当前问题与信道编码相关联，借鉴有限块长信息论的思想，并构建了可能量化目标轨迹数量的界。