Geolocation of a known altitude object from TDOA and FDOA measurements
Geolocation of a known altitude object from TDOA and FDOA measurements
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DOI：
10.1109/7.599239
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发表时间：
1997-07
影响因子：
4.4
通讯作者：
K. C. Ho;Y. Chan
中科院分区：
文献类型：
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作者：
K. C. Ho;Y. Chan
大多数用于定位地球上物体的卫星系统仅使用到达时间差测量。当发射器与接收器之间存在相对运动时，也可使用到达频率差（FDOA）测量。通常，物体的高度是已知的（例如，它是零），或者可以用高度计测量。提出了两组利用高度约束提高定位精度的地理定位解决方案。一种是单独的TDOA，另一种是TDOA和FDOA测量的组合。通过施加约束的额外复杂性是一维牛顿搜索和多项式的求根。新的估计量的协方差矩阵推导出一个小的测量噪声的假设下，并达到约束Cramer-Rao下界（CRLB）。当假设的高度存在偏差误差时，使用高度约束将向解引入偏差。由于应用约束会降低方差，因此在均方误差（MSE）中的方差和偏差之间存在折衷。给出了使约束解保持上级优于无约束解的最大允许高度误差。仿真结果证实了理论的发展。
Most satellite systems for locating an object on Earth use only time difference of arrival (TDOA) measurements. When there are relative motions between an emitter and receivers, frequency difference of arrival (FDOA) measurements can be used as well. Often, the altitude of an object is known (it is zero, for example) or can be measured with an altimeter. Two sets of geolocation solutions are proposed which exploit the altitude constraint to improve the localization accuracy. One is for TDOAs alone and the other for the combination of TDOA and FDOA measurements. The additional complexity by imposing the constraint is a one-dimensional Newton's search and the rooting of a polynomial. The covariance matrices of the new estimators are derived under a small measurement noise assumption and shown to attain the constrained Cramer-Rao lower bound (CRLB). When there is a bias error in the assumed altitude, using the altitude constraint will introduce a bias to the solution. Since applying the constraint decreases the variance, there is a tradeoff between variance and bias in the mean square error (MSE). The maximum allowable altitude error such that the constraint solution will remain superior to the unconstraint is given. Simulation results are included to corroborate the theoretical development.