A performance analysis of multi-satellite joint geolocation

Determining the position of an emitter on Earth by using a satellite cluster has many important applications, such as in navigation, surveillance, and remote sensing. However, in realistic situations, a number of factors, such as errors in the measurement of signal parameters, uncertainties regarding the position of satellites, and errors in the location of calibration sources, are known to degrade the accuracy of target localization in satellite geolocation systems. We systematically analyze the performance of multi-satellite joint geolocation based on time difference of arrival （TDOA） measurements. The theoretical analysis starts with Cramer Rao bound （CRB） derivations for four localization scenarios under an altitude constraint and Gaussian noise assumption. In scenario 1, only the TDOA measurement errors of the emitting source are considered and the satellite positions are assumed to be perfectly estimated. In scenario 2, both the TDOA measurement errors and satellite position uncertainties are taken into account. Scenario 3 assumes that some calibration sources with accurate position information are used to mitigate the influence of satellite position perturbations. In scenario 4, several calibration sources at inaccurate locations are used to alleviate satellite position errors in target localization. Through comparing the CRBs of the four localization scenarios, some valuable＇s insights are gained into the effects of various error sources on the estimation performance. Two kinds of location mean-square errors （MSE） expressions under the altitude constraint are derived through first-order perturbation analysis and the Lagrange method. The first location MSE provides the theoretical prediction when an estimator assumes that the satellite locations are accurate but in fact have errors. The second location MSE provides the localization accuracy if an estimator assumes that the known calibration source locations are precise while in fact erroneous. Simulation results are included to verify the theoretical analysis.

为利用卫星束确定地球表面目标的位置信息具有很多重要应用,例如导航,监控,遥感等。然而,在实际条件下,会有很多因素影响卫星定位系统的精度,比如说信号参数的测量误差,卫星位置误差以及校正源的位置误差。本文基于时差观测量系统分析了多星联合定位的理论性能。首先在基于目标高程约束和高斯误差的假设下,推导四种定位场景下目标位置估计方差的克拉美罗界。第一种场景仅考虑时差观测量误差,并且假设卫星位置精确已知;第二种场景同时考虑时差观测量误差和卫星位置误差;第三种场景假设存在若干位置信息精确已知的校正源,其用于消除卫星位置的影响;第四种场景则假设校正源位置也存在测量误差。此外,文中基于一阶扰动分析和拉格朗日方法推导了两种情形下的定位均方根误差的表达式。第一种情形是假设卫星位置精确已知但实际上却含有误差;第二种情形则是假设校正源位置精确已知但实际上却含有误差。仿真结果验证了文中理论分析的有效性。