基于非线性最小二乘法的无人机机载光电平台目标定位

陈丹琪, 金国栋, 谭力宁, 等. 基于非线性最小二乘法的无人机机载光电平台目标定位[J]. 光电工程, 2019, 46(9): 190056. doi: 10.12086/oee.2019.190056
引用本文: 陈丹琪, 金国栋, 谭力宁, 等. 基于非线性最小二乘法的无人机机载光电平台目标定位[J]. 光电工程, 2019, 46(9): 190056. doi: 10.12086/oee.2019.190056
Chen Danqi, Jin Guodong, Tan Lining, et al. Target positioning of UAV airborne optoelectronic platform based on nonlinear least squares[J]. Opto-Electronic Engineering, 2019, 46(9): 190056. doi: 10.12086/oee.2019.190056
Citation: Chen Danqi, Jin Guodong, Tan Lining, et al. Target positioning of UAV airborne optoelectronic platform based on nonlinear least squares[J]. Opto-Electronic Engineering, 2019, 46(9): 190056. doi: 10.12086/oee.2019.190056

基于非线性最小二乘法的无人机机载光电平台目标定位

  • 基金项目:
    国家自然科学基金资助项目(61673017, 61403398)
详细信息
    作者简介:
    通讯作者: 金国栋(1979-),男,博士,副教授,主要从事无人机测绘、目标定位方面的研究。E-mail:18578031@qq.com
  • 中图分类号: TP391.4

Target positioning of UAV airborne optoelectronic platform based on nonlinear least squares

  • Fund Project: Supported by National Natural Science Foundation of China (61673017, 61403398)
More Information
  • 传统无人机机载光电平台目标定位算法由于引入大量测角误差,导致目标定位精度不高。本文从非线性角度出发,提出了一种最小二乘和高斯牛顿的混合非线性算法。首先推导了基于激光测距值的高斯牛顿迭代非线性目标定位算法,然后利用线性最小二乘的粗解作为非线性牛顿迭代法的初值进行目标定位估计。该算法结合了最小二乘法简单易实现的优点和高斯牛顿法收敛速度快精度高的优点,并满足了高斯牛顿法对初值精度的要求。实测数据实验结果显示,该方法对实测固定目标定位结果的经度误差小于(1.37×10-5)°,纬度误差小于(6.31×10-5)°,高度误差小于1.78 m,并且单次定位处理时间在6 ms以内,符合实时定位的要求。

  • Overview: In the past few decades, unmanned aerial vehicles (UAV) have developed rapidly, and they have been widely used in actual intelligence reconnaissance and target surveillance with their unique advantages such as zero casualties, long-term endurance, and high flexibility. Accurate positioning and tracking of battlefield targets is one of the most important military applications for UAV. At present, the traditional UAV airborne photoelectric platform target positioning algorithm is based on the single UAV photoelectric platform for angle information measurement and distance information measurement. However, the UAV attitude angle error and the photoelectric platform attitude angle error are introduced into the algorithm, which leads to the low target positioning accuracy. The target positioning method based on laser ranging value avoids the attitude angle of the UAV and the attitude angle error of the photoelectric platform in the calculation process, and has the advantages of less error source and high positioning accuracy, which is a common method for high-precision target positioning algorithm. The algorithm commonly used in target location estimation based on laser ranging values is a pseudo-linearized linear least squares method, but the pseudo-linearization process in the algorithm results in a large loss of observation accuracy, especially the target height localization precision. In this paper, a hybrid nonlinear algorithm of least squares and Gauss-Newton is proposed. The Gauss-Newton iteration method is a nonlinear algorithm with fast convergence speed and high precision, but it has certain requirements for the initial value of iteration. Therefore, this paper firstly deduces the pseudo-linearized least squares target localization algorithm, and based on this algorithm, roughly estimates the target position and obtains the coarse positioning result. Secondly, the Gauss-Newton iterative nonlinear target localization algorithm based on laser ranging value is derived. Then the linear least squares rough result is used as the initial value of the nonlinear Newton iteration method for target location estimation. The algorithm combines the advantages of the simple and easy implementation of the least squares method and the high convergence accuracy of the Gauss-Newton method, and satisfies the certain requirements of the Gauss-Newton method for the initial value accuracy. Experimental results of measured data show that the longitude error of fixed target positioning results of this method is less than 1.37×10-5 degrees, the latitude error is less than 6.31×10-5 degrees, and the height error is less than 1.78 meters. And the processing time of each positioning is within 8 ms, which meets the requirements of real-time positioning. The experimental results show that this algorithm has high engineering application value.

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  • 图 1  大地直角坐标系ECEF

    Figure 1.  Earth rectangular coordinate system ECEF

    图 2  测距定位模型示意

    Figure 2.  Ranging positioning model

    图 3  仿真飞行航迹示意图

    Figure 3.  Schematic diagram of simulated flight track

    图 4  仿真目标定位误差

    Figure 4.  The positioning error of the simulation target

    图 5  不同仿真轨迹下目标定位结果。(a)不同仿真飞行航迹;(b)目标定位误差

    Figure 5.  Target positioning results under different simulation trajectories. (a) Different simulated flight paths; (b) Target positioning error

    图 6  不同误差条件下目标定位结果。(a)不同无人机位置误差;(b)不同激光测距误差

    Figure 6.  Target positioning results under different error conditions. (a) Different UAV position errors; (b) Different laser ranging errors

    图 7  实测飞行轨迹示意图。(a)飞行航迹平面示意图;(b)飞行航迹高度变换示意图

    Figure 7.  Schematic diagram of flight trajectory measured. (a) Schematic diagram of flight path; (b) Flight path height transformation diagram

    图 8  激光测距值

    Figure 8.  Laser ranging value

    图 9  目标定位结果-经度

    Figure 9.  Target positioning results - longitude

    图 10  目标定位结果-纬度

    Figure 10.  Target positioning results - latitude

    图 11  目标定位结果-高度

    Figure 11.  Target positioning results - height

    图 12  目标定位误差

    Figure 12.  Target positioning error

    图 13  混合算法单次定位迭代次数

    Figure 13.  Hybrid algorithm iterations for each positioning

    图 14  混合算法单次定位耗时

    Figure 14.  Hybrid algorithm time-consuming for each positioning

    表 1  三种定位方法性能比较

    Table 1.  Performance comparison of three positioning methods

    NLS RLS EKF
    Longitude error/(°) 1.37×10-5 5.92×10-5 2.49×10-5
    Longitude plane error/m 1.45 6.27 26.42
    Latitude error /(°) 6.31×10-5 9.79×10-5 4.93×10-4
    Latitude plane error/m 7.00 10.86 54.76
    Height error/m 1.78 3387.49 4.75
    Plane error/m2 7.15 12.54 60.79
    Spatial error/m3 7.37 3387.51 60.98
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出版历程
收稿日期:  2019-02-02
修回日期:  2019-04-04
刊出日期:  2019-09-30

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