An Algebraic Solution for Single-Observer Passive Coherent Location Using DOA-TDOA-FDOA Measurements
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摘要: 针对利用单站接收多个外辐射源信号实现目标定位的问题，该文提出一种基于两步加权最小二乘的到达角度(DOA)、时差(TDOA)和频差(FDOA)联合定位代数解算法。首先，在第1步加权最小二乘估计中，通过引入辅助参数，将非线性的角度、时差和频差方程转化为伪线性形式，并利用加权最小二乘得到目标位置和速度的粗估计；而后在第2步加权最小二乘估计中利用辅助参数和目标位置参数之间的约束关系来构造另外一组线性方程，并再次利用加权最小二乘得到目标位置和速度的精确估计。推导了联合角度、时差和频差定位的克拉美罗界。理论分析和仿真结果表明，算法在观测误差较小时的定位误差可以达到克拉美罗界。Abstract: To achieve the target localization using single-observer receiving multiple external illuminators, an algebraic solution based on two-step Weighted Least Squares (2WLS) is proposed to find the target position and velocity from Direction Of Arrival (DOA), Time Difference Of Arrival (TDOA), and Frequency Difference Of Arrival (FDOA) measurements. In the first WLS step, the DOA, TDOA, and FDOA measurements are pseudo-linearized by introducing additional parameters and a WLS minimization is used to obtain an rough estimate of target position and velocity; Then in the second WLS step, the relationship between the additional parameters and the target location parameters is utilized to form another set of linear equations, from which the final accurate estimate of target position and velocity are obtained by using WLS minimization again. The Cramer-Row Lower Bound (CRLB) for DOA-TDOA-FDOA-based target position and velocity estimation are derived. Theoretical accuracy analysis and simulation results indicate that the proposed solution can achieve the CRLB at sufficiently small measurement noise levels.
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