多点定位是民航飞机导航系统的新技术,精确的目标位置解算方法是多点定位的关键。通过设定参考站和变换,将非线性到达时间(TOA)方程组转化为线性到在时间差(TDOA)方程组,提出了一种两步求解目标位置的闭式算法。首先忽略TDOA测量误差,获得了目标位置的粗解,在粗解的基础上做泰勒级数展开,克服了未知量不独立对精度的影响,再采用最优线性无偏估计(BLUE)估计算法,得到了精确的目标位置,几何稀释精度(GDOP)分布特性显著提高。对估计算法的克莱美-罗界分析和仿真结果表明,所提出的基于部分泰勒级数展开的BLUE算法的精度逼近克莱美-罗界。
Multilateration is a novel and popular technology in civil aircraft navigation. The precise algorithm to calculate target location is the key of multilateration. By setting the reference station and using corresponding transform, the nonlinear TOA equations are transferred into linear TDOA equations. After that a two-steps closed-form algorithm to calculate target position is proposed in this paper. Ignoring the TDOA measurement errors, we can obtain the initial results first. Then Taylor expansion is exploited based on initial results to overcome the dependent relationship between unknown variables. Finally, accurate target location is estimated by BLUE method. The GDOP performance of the new algorithm is apparently improved. Cramer-Rao bound of this algorithm is derived and the simulation results show that accuracy of the BLUE method based on partly Taylor expansion is approximately equal to Cramer-Rao bound.
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