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Creators/Authors contains: "Bates, Daniel"

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  1. ; ; ; (, PLOS ONE)
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  2. ; ; ; ; ; (, PLOS Computational Biology)
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  3. ; (, 2018 IEEE Radar Conference (RadarConf18))
    The problem of geolocation of a radiofrequency transmitter via time difference of arrival (TDOA) and frequency difference of arrival (FDOA) is given as a system of polynomial equations. This allows for the use of homotopy continuation-based methods from numerical algebraic geometry. A novel geolocation algorithm employs numerical algebraic geometry techniques in conjunction with the random sample consensus (RANSAC) method. This is all developed and demonstrated in the setting of only FDOA measurements, without loss of generality. Additionally, the problem formulation as polynomial systems immediately provides lower bounds on the number of receivers or measurements required for the solution set to consist of only isolated points. 
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  4. ; ; ; ; (, MACIS 2017: Mathematical Aspects of Computer and Information Sciences)
    Given a polynomial system f, this article provides a general construction for homotopies that yield at least one point of each con- nected component on the set of solutions of f = 0. This algorithmic approach is then used to compute a superset of the isolated points in the image of an algebraic set which arises in many applications, such as com- puting critical sets used in the decomposition of real algebraic sets. An example is presented which demonstrates the efficiency of this approach. 
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