Error analysis of MEMS gyroscope

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By analyzing the structure and working principle of the gyroscope, it can be seen that when it is working, various interference torques will be generated due to the friction of the inner and outer axes, electromagnetic interference, and the deviation of the center of mass of the gyroscope from the axis. These interference torques act on the gyroscope. Errors will occur. It can be seen that the error of the gyroscope is caused by the action of these interference torques, so the error of the gyroscope depends on the nature of the interference torque. The errors of gyroscopes generally include two categories: deterministic errors and random errors. Deterministic errors are regular and the numerical value can be determined through experimental methods. Random errors are caused by changes in the gyroscope’s use environment, bearing noise, and temperature. Irregular errors cannot be compensated by simple methods.



In order to use mathematical expressions to describe the drift error variation pattern of MEMS gyroscopes more accurately, the following models are usually used to describe:



1. Static drift error model:



Static drift errorωdis generated due to mass imbalance, various interference moments caused by unequal elasticity of the structure, and manufacturing processes. The expression is:



ωd=Kd+Kxax+Kyay+Kzaz+Kxyaxay+Kyzayaz+Kzxazax+Kxxax2+Kyyay2+Kzzaz2



In the formula:



Kd is the constant drift; Kx, Ky, Kz are the drift coefficients proportional to the specific force respectively; Kxx, Kyy, Kzz are the drift coefficients proportional to the square of the specific force respectively; Kxy, Kyz, Kzx are respectively The drift coefficient is proportional to the cross product of the specific force; ax, ay, and az are the specific forces along the corresponding axes of the gyroscope respectively.



2.Dynamic drift error model:



Dynamic drift error δωx is the error caused by angular velocity and angular acceleration under dynamic conditions. The expression is:



δωx=D’xώx+D’yώy+D’zώz+Dxωx+Dyωy+Dzωz+Dxyωxωy+Dyzωyωz+Dxzωxωz+Dxxωx2+Dyyωy2+Dzzωz2



In the formula:



D’x, D’y, D’z – angular acceleration error coefficient



Dx, Dy, Dz – calibration error coefficient



Dxx, Dyy, Dzz – angular velocity error coefficient



ώx, ώy, ώz – angular acceleration of each axis



ωx, ωy, ωz – angular velocity values of each axis



3.Random drift error model:



Random drift error has slow time variability and weak nonlinearity, which is difficult to describe with a specific mathematical model and can only be approximated by statistical characteristics. In the integrated navigation system, the random drift error is usually approximated as consisting of three parts: random constant drift, first-order Markov process and white noise. The expression is:



εi=εbi+εgi+ωgi




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