WGS-84模型下时差频差半定规划定位算法

Semidefinite programming algorithm with TDOA and FDOA measurements based on WGS-84 earth model

利用多颗卫星的时差频差对辐射源进行位置和速度的测量,其本质意义上是一个含有噪声项的高度非线性方程组求解问题,针对地面目标而言,可以采用基于WGS-84地球模型作为目标位置和速度约束,更进一步的增加了定位系统的复杂性。提出了一种基于半定规划(SDP)的定位解算法,将非线性方程求解问题通过适当的松弛,转化为半定优化(SDO)的问题,借助于业界较为成熟的CVX等优化软件进行定位求解,并研究了该模型条件下的克拉美罗下界(CRLB)。仿真结果表明,该算法能够较好地逼近克拉美罗下界。

In essence,detecting the location and velocity of a radiation source by utilizing time difference of arrival/frequency difference of arrival（TDOA/FDOA）for multiple satellites can be deemed as a highly nonlinear solution problem within noise.For a ground target,the WGS-84 earth model is the constraint condition,which makes the location system become more complicated.In this paper,a new algorithm for solving this location problem is proposed based on the semi-definite programming（SDP）.Based on the novel algorithm,the nonlinear location problem can turn into a semidefinite optimization（SDO）by an appropriate relaxation which can be solved by some mature software like CVX.According to this model,the Cramer-Rao Lower Bound（CRLB）of the location problem is then given.The computer simulation demonstrates that the proposed algorithm can approach the CRLB effectively.