陀螺定向的三角多项式拟合法

TRIGONOMETRIC POLYNOMIAL FITTING METHOD FOR GYROORIENTATION

提出了陀螺定向数据处理的一种新方法———三角多项式拟合法。首先从高等数学、陀螺力学和平差理论出发，论述了该方法的数学模型和数据处理方法，即用三角多项式对陀螺轴运动进行最小二乘拟合，确定陀螺轴的摆动中心；导出了新旧两种数学模型之间的关系：新模型是普遍形式，而旧模型只是新模型的一种特例，当三角多项式的阶数为１时，新模型就变成了旧模型，它包含有模型误差；随着三角多项式阶数的增加，新模型中模型误差减小了。然后用新旧方法对各种观测条件下的观测值进行数据处理，结果表明：新方法数据处理成果精度比旧方法的高，曲线拟合效果良好，不仅验证了新方法的可行性，而且确定了适合于陀螺定向的三角多项式的阶数为３或４的情况。

A new dataprocessing method for gyroorientation——the trigonometric polynomial fitting method has been put forward. First, the mathematical model and dataprocessing method of fitting was dealt, according to higher mathematics, gyromechanics and adjustment theory. In order to determine the swing centre of gyroaxis the real method is leastsquares fitting with trigonometric polynomial. The relation between the new model and the old one was established. The new model is the universal form and the old one is a special form of the new one. When the index of trigonometric polynomial equals 1 the new model becomes the old one and it contains model error. With the increase of the index the model error is weakened. Then, the new method was applied to practical dataprocessing of different environmental observation conditions. The results show that the accuracy of new method is higher than that of old one and curve fitting is very good. The index of trigonometric polynomial that is suitable to gyroorientation equals 3 or 4.