有限声速的纯方位算法

Bearing-Only Arithmetic with Finite Sound Velocity

针对纯方位条件下对等速直航目标观测的算法问题,将目标运动要素及平均声速作为待估计参数,给出了计算非线性最小二乘法目标函数梯度与Hessian矩阵的解析公式,基于这些公式,可以构造估计目标运动要素的一些算法及编程实现。部分数值实验表明,信赖域算法、Levenberg-Marquardt算法与Matlab用于解非线性最小二乘问题的函数lsqnonlin的计算精度基本一致。

Aiming at the arithmetic of observing target which has uniform course and velocity, using target motion factor and average sound velocity to be the parameters for estimated, the analytic formulas to compute gradient vector and Hessian ma- trix for the nonlinear least square objective function are given. Based on these formulas, it can construct the arithmetic and program realization for estimating target motion factor. Some numerical experiments indicate that the trust region arithmetic and Levenberg-Marquardt arithmetic have almost the same computational accuracy to lsqnonlin which is a Matlab function used specially for solving nonlinear least square problem.