Closed-form solution of hyperbolic geolocation equations

Ezzat G. Bakhoum

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Closed-form solution of hyperbolic geolocation equations

机译：双曲地理位置方程的封闭形式解

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A 3-dimensional (3D), closed-form solution for the time difference of arrival (TDOA) problem that does not depend on range data is given. Such a solution did not exist previously in the literature. For aerospace and military applications, the solution is precise. For civilian cellular phone applications, however, the solution is susceptible to unrelated errors from the phenomenon of multipath delays in the channels. This phenomenon is factored in mathematically in the solution and a simulation that characterizes its error bounds is presented

机译：给出了不依赖于范围数据的到达时间差（TDOA）问题的3维（3D）闭式解。这种解决方案以前在文献中不存在。对于航空航天和军事应用，解决方案非常精确。然而，对于民用蜂窝电话应用，该解决方案容易受到信道中多径延迟现象引起的无关错误的影响。在解决方案中以数学方式考虑了此现象，并给出了表征其误差范围的仿真

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来源
《IEEE Transactions on Aerospace and Electronic Systems》 |2006年第2006期|p.1396-1404|共9页
作者
Ezzat G. Bakhoum;
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正文语种 eng
中图分类航空;
关键词
multipath channels; time-of-arrival estimation; closed-form solution; error bound; hyperbolic geolocation equations; multipath delays; time difference of arrival;

机译：多径通道;到达时间估计;闭式解;误差限制;双曲地理位置方程;多径时滞;到达时间差;

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专利

1. Closed-form solution of hyperbolic geolocation equations [J] . Ezzat G. Bakhoum IEEE Transactions on Aerospace and Electronic Systems . 2006,第4期

机译：双曲地理位置方程的封闭形式解
2. Discussion on ????????Numerical solution of 2nd-order hyperbolic partial differential equations by the method of continuous characteristics????????, ????????Analogue solution of 2nd-order hyperbolic partial differential equations by the method of continuous characteristics???????? and ????????Analogue solution of elliptic differential equations by conformal transformations???????? [J] . Electrical Engineers, Proceedings of the Institution of . 1971,第6期

机译：用连续特性方法讨论二阶双曲型偏微分方程的数值解??????，二阶双曲型的模拟解偏微分方程的连续特性方法和利用共形变换的椭圆型微分方程的模拟解
3. Exact closed-form solution of the hyperbolic equation of string vibrations with material relaxation properties taken into account [J] . Kudinov I. V., Kudinov V. A. Mechanics of solids . 2014,第5期

机译：考虑材料松弛特性的弦振动双曲方程的精确闭式解
4. An Extended Closed-Form Least-Squares Solution for Three-Dimensional Hyperbolic Geolocation [C] . Mohamed Khalaf-Allah IEEE Symposium on Industrial Electronics and Applications . 2014

机译：三维双曲地理地理位置的延长闭合形式最小二乘解
5. Finding closed-form solutions of difference equations by symbolic methods. [D] . Petkovsek, Marko. 1991

机译：用符号法寻找差分方程的闭式解。
6. Method for Remote Determination of Object Coordinates in Space Based on Exact Analytical Solution of Hyperbolic Equations [O] . Vladimir Kuptsov, Vladimir Badenko, Sergei Ivanov, 2020

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7. Response and residual curvature of bent-stretched circular rods with applications to metal forming: closed-form solutions for elastic-perfectly plastic and hyperbolic hardening materials [O] . Bonfanti, Alessandra, Syngellakis, Stavros, Bhaskar, Atul 2017

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8. Using Lie Transformation Groups to Find Closed-Form Solutions to First-Order Ordinary Differential Equations (Extended Abstract) [R] . Char, B. 1981

机译：利用李变换群寻找一阶常微分方程的闭式解（扩展摘要）

Closed-form solution of hyperbolic geolocation equations

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