一种新型磁跟踪模式及其L-M算法研究

Research on a new magnetic tracking pattern & L-M algorithm

为了提高磁跟踪系统的定位精度,设计了分时交流励磁跟踪方法,通过接收线圈检测目标的空间磁场,利用相关电磁场理论求解出目标方位.针对高次非线性定位方程组变量多、不单调、具有多个局部极值点的特点,将方程组求解问题转化成非线性无约束最小二乘问题,运用改进后的列文伯格(Levenberg-Mar-quardt)算法对其求解.仿真结果表明,改进后的定位算法具有不依赖于初值、精度高、收敛速度快的特点,成功解决了定位中多局部极值的高维优化问题,从而为跟踪方案的实现提供了理论依据.

To improve the positioning accuracy of electromagnetic position systems,a telemetric method based on alternating magnetic fields was designed.Coils of receiving were used to measure the magnetic field strength at the location of the objective.According to the relationship between the magnetic field strength and the relevant electromagnetic theory,the position and orientation of the objective could be obtained by solving a nonlinear system of equations.To simplify calculation,the system of equations for localization was transformed into an unconstrained nonlinear optimization problem of least squares.Then the improved Levenberg-Marquardt algorithm was employed to solve the problem.Simulation results show that the improved Levenberg-Marquardt algorithm is able to solve the high dimensional problem.Compared with conventional algorithms,the improved algorithm does not require a good initial guess to guarantee convergence.Furthermore,it has high precision and fast convergence speed.