用正交函数求解光纤陀螺误差的数学模型分析

Mathematical model analysis of solving fiber optic gyroscope error by orthogonal function

为了准确计算光纤陀螺误差,提出基于正交函数求解的光纤陀螺误差估计数学模型。构建光纤陀螺误差求解的约束参量模型,采用二元微分方程组进行光纤陀螺误差求解和线性规划模型设计,建立光纤陀螺误差分析的正交函数,结合线性拟合方法进行光纤陀螺误差的分布式拟合控制,建立积分函数进行光纤陀螺误差的正交误差特征分解,结合小波函数多尺度分解方法进行光纤陀螺误差特征量的多维分解,构建光纤陀螺误差分量的特征重组模型,结合正交函数的自动寻优方法进行光纤陀螺误差的自适应求解,提高光纤陀螺误差求解的精度,实现光纤陀螺误差求解的数学模型。仿真结果表明,所设计的模型在误差测量精度中误差更小,惯性转矩相对文献[2]和文献[3]更小,且控制准确率能够达到95%以上,采用该方法进行光纤陀螺误差求解的收敛性较好,误差求解的精度较高。

In order to accurately calculate the error of optical fib gyro,a mathematical model of the estimation of the error of the optical fiber gyroscope based on the orthogonal function is proposed.A constraint parameter model for solving the error of optical fiber gyroscope is constructed,a two-dimensional differential equation group is used for carrying out the optical fiber gyro error solving and the linear programming model design,the orthogonal function of the error analysis of optical fiber gyroscope is established,and the distributed fitting control of the error of optical fiber gyroscope is carried out in combination with a linear fitting method,the method comprises the following steps of:establishing an integral function to perform the orthogonal error characteristic decomposition of optical fiber gyroscope error,carrying out multi-dimensional decomposition of the error characteristic amount of optical fiber gyroscope in combination with the wavelet function multi-scale decomposition method,and constructing a characteristic recombination model of the error component of optical fiber gyroscope.The self-adaptive solution of the error of optical fiber gyroscope is carried out in combination with automatic optimization method of the orthogonal function,the precision of the error solution of optical fiber gyroscope is improved,and the mathematical model of the error solution of optical fiber gyroscope is realized.The simulation results show that the model designed in this paper has smaller error in error measurement accuracy,smaller inertia torque than literature[2]and literature[3],the control accuracy can reach more than95%,the convergence of the error solution of fiber optic gyroscope is good,and the accuracy of error solution is high.