Carrier phase signals form the basis of various interferometric measurement models and estimation techniques that have parameters of which some are integer. In this paper, integer least-squares estimation theory is extended and applied to bias-bounded mixed-integer models. This extension accommodates the presence of bounded real-valued parameters in mixed-integer models through incorporating prior knowledge of a set, in which the parameters reside, into the estimation process. This enables one to jointly estimate the ambiguous phase cycles and the parameters of interest. To compute such mixed-integer estimates, a fast search strategy is developed that makes use of a dual-ellipsoid encompassing region. The volume of the stated region is quantified and its links to existing ellipsoidal search spaces are highlighted. Simulated and real-world data are employed to illustrate the theory. It is then, for the first time, shown that the proposed method makes single-epoch, phase-only positioning feasible with Global Navigation Satellite Systems (GNSS).

中文翻译：

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模糊度的有界估计：一种无线电干涉定位方法

载波相位信号构成了各种干涉测量模型和估计技术的基础，这些模型的参数有些是整数。在本文中，整数最小二乘估计理论被扩展并应用于有偏差的混合整数模型。此扩展通过将参数所在的集合的先验知识合并到估计过程中来适应混合整数模型中有界实值参数的存在。这使得人们能够联合估计模糊的相位周期和感兴趣的参数。为了计算这种混合整数估计，开发了一种使用双椭球包围区域的快速搜索策略。对所述区域的体积进行量化，并突出显示其与现有椭球搜索空间的链接。模拟和真实世界的数据用于说明该理论。然后，第一次表明，所提出的方法使使用全球导航卫星系统 (GNSS) 可行的单历元、仅相位定位。