Abstract: By adjusting the discrete coordinates of road circular curve collected by GNSS (Global Satellite Navigation System) dynamic positioning technology, the parameters of circular curve can be retrieved. The adjustment theory of barycentric coordinate method is not rigorous enough, the definition of minimum condition of least square method is not completely reasonable, and the conditional adjustment method with parameters is easily affected by the initial value of parameters. Aims to solve these problems, an iterative algorithm of nonlinear total least squares for retrieving road circular curve parameters was proposed. The model construction, solution algorithm and algorithm design of the proposed algorithm were discussed; and the proposed algorithm was tested with simulation data and measured data. Furthermore, the comparative analysis with other three methods was carried out. The research results show that: 1) comparing with other three methods, the result of the nonlinear total least squares method is more closer to the true value and the corresponding error is smaller, and the result is more stable; 2) comparing with the conditional adjustment method with parameters, the nonlinear total least squares method is less affected by the initial value, and can obtain the radius of circular curve which is more in line with the actual situation; 3) comparing with barycentric coordinate method and least squares, the nonlinear total least squares method holds more rigorous parameter estimation theory.

Key words: highway engineering, nonlinear total least squares, road circular curve, parameter estimation, iterative algorithm

摘要： 对GNSS（全球卫星导航系统）动态定位技术采集的道路圆曲线离散坐标进行平差计算，可反演出圆曲线参数。重心坐标法平差理论不 够严密，最小二乘法的极小值条件定义不完全合理，附有参数的条件平差法易受参数初值影响。针对这些问题提出一种基于非线性总体最小 二乘的道路圆曲线参数反演算法。主要对其模型构建、解算算法，以及算法设计等内容进行讨论，并采用仿真数据和实测数据对算法进行测 试，与其它3种方法做对比分析。研究表明：与其它3种方法相比，在统计上，非线性总体最小二乘法的结果更接近真值，真误差波动更小， 结果更稳定；与附有参数的条件平差法相比，非线性总体最小二乘法受初值的影响更小，能够获得更符合实际情况的圆曲线半径；与重心坐 标法和最小二乘法相比，非线性总体最小二乘法的参数估计理论更严密。

关键词: 道路工程, 非线性总体最小二乘, 道路圆曲线, 参数估计, 反演算法