Rank Properties for Matrices Constructed From Time Differences of Arrival - 2018


Time Difference of Arrival (TDOA) positioning has been a lively analysis over the years due to its made amounts of applications. Improving the quality of the TDOA measurements, especially beneath harsh scenarios, is crucial to attain better localization accuracy and better noise tolerance. Increasing the TDOA quality has been historically primarily based on the statistical estimation point of view. Nevertheless, TDOA exhibits attention-grabbing algebraic properties, that when exploited can more enhance the measurements. This Project develops two algebraic properties of TDOA in things where multiple sources and sensors are present, like sensor network and joint source-sensor localizations. The algebraic properties are new and have not appeared within the literature. They are in terms of the rank behaviors of two matrices that are formed by the TDOA themselves and their squared values. The development starts from a longtime property of your time of Arrival and applies determinant and vector space manipulations to get the concrete results. An example is included to illustrate the use of the algebraic properties for reducing the noise in TDOAs.

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