基于重要性采样的纯方位定位算法

An importance sampling method for bearing-only localization

应用纯方位角解决固定目标无源定位问题时,极大似然估计算法可以转换为非线性优化问题,但该算法需要迭代求解且对初始条件敏感。为此,提出一种新的纯方位定位算法,使用蒙特卡洛重要性采样算法计算该问题的近似全局解。首先,通过观测方程得到关于方位角的极大似然函数,应用Pincus定理得到全局解的形式,从而获得目标位置的概率密度函数;然后,使用伪线性估计算法对目标位置进行初步估计;最后,使用重要性采样算法进行近似计算。仿真实例表明,在不同场景中,重要性采样算法与极大似然估计算法性能相当,非常接近Cramer-Rao下界。

The bearing-only is used to consider the passive localization problem of fixed targets.The maximum likelihood estimation algorithm can be converted into a nonlinear or non-convex optimization problem,requiring gradient descent methods for iterative calculations,sensitive to initial conditions and easy to diverge,making it difficult to obtain the approximate global solution.A new bearing-only localization algorithm is proposed,which uses Monte Carlo importance sampling algorithm to calculate the approximate global solution of the problem.Firstly,write the maximum likelihood function about the bearing angle;secondly,use the Pincus theorem to write the global solution form and obtain the probability density function of the target position;and then,use the pseudo-linear estimation algorithm to make a preliminary estimate of the target position;finally,use the importance sampling algorithm to approximate it.The simulation example shows that the importance sampling algorithm has the same performance as that of the maximum likelihood estimation algorithm,which is close to the Cramer-Rao lower bound.