(中山市測量鉆探隊(duì)，中山 528403)
摘 要: 提出了陀螺定向數(shù)據(jù)處理的一種新方法——三 角多項(xiàng)式擬合法。首先從高等數(shù)學(xué)、 陀螺力學(xué)和平差理論出發(fā)， 論述了該方法的數(shù)學(xué)模型和數(shù)據(jù)處理方法, 即用三角多項(xiàng)式對陀螺軸運(yùn)動進(jìn)行最小二乘擬合， 確定陀螺軸的擺動中心；導(dǎo)出了新舊兩種數(shù)學(xué)模型之間的關(guān)系： 新模型是普遍形式， 而舊模型只是新模型的一種特例，當(dāng)三角多項(xiàng)式的階數(shù)為1時(shí)， 新模型就變成了舊模型，它包含有模型誤差； 隨著三角多項(xiàng)式階數(shù)的增加，新模型中模型誤差減小了。 然后用新舊方法對各種觀測條件下的觀測值進(jìn)行數(shù)據(jù)處理，結(jié)果表明： 新方法數(shù)據(jù)處理成果精度比舊方法的高，曲線擬合效果良好，不僅驗(yàn)證了新方法的可行性，而且確定了適合于陀螺定向的三角多項(xiàng)式的階數(shù)為3或4的情況。
關(guān)鍵字: 陀螺定向 數(shù)學(xué)模型 數(shù)據(jù)處理
（Zhongshan Survey Company, Zhongshan 528403, P. R. China）
Abstract: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.
Key words: gyro-orientation mathematical model data-processing
