Calibration Method Of Error Model Coefficients Of Pendulous Integrating Gyroscopic Accelerometer

With the increasing requirements for accuracy and stability of Pendulous Integrating Gyroscopic Accelerometer（PIGA）,it is much more difficult to enhance the performance by improving the material,design and manufacturing technology of accelerometer.Therefore,the key to the development of accuracy potential of PIGA is the advanced test methods which can accurately calibrate the error model coefficients.This paper focuses on the calibration methods of error model coefficients of PIGA.The mechanism of formation,excitation,and transfer of the error sources of the PIGA is analyzed in detail.The optimum methods for testing the PIGA on the indexing table,precision centrifuge,and linear vibration table are designed.The techniques of error compensation and error suppression are used to accurately calibrate the error terms of the PIGA,so that the calibration accuracy of PIGA can be effectively improved.In addition,the research results can provide reference for testing other high precision inertial instruments.According to the summaries of the PIGA development situation and calibration techniques,the defects of the existing calibration methods and the development trend of PIGA are discussed firstly.Then,the corresponding coordinate systems of outer gimbal,inner gimbal,and gyro rotor are established by analyzing the structure of PIGA.Based on the Euler dynamic equations,the dynamics analysis of PIGA is carried out and the integrated error model of PIGA is established.The error terms are simplified by calculating and organizing;thus,the engineering error model of PIGA is proposed.In order to provide the theoretical and engineering basis for testing the PIGA,the simulations are constructed to illustrate the influence of the major error terms on the accuracy of PIGA.Calibration method of PIGA in the gravity field through using the indexing table is studied.The propagation of the levelness of horizontal rotation axis line,the angular position errors,and the installation errors of PIGA is analyzed.Then,the precision specific force and angular velocity components along the three input reference axes of PIGA due to gravity acceleration and the earth’s rotation are obtained.According to the established error model of PIGA,the error calibration model of PIGA is established including bias,scale factor,second-order term,and the error term due to the gravity.Based on the Least Square（LS）method,the calibration method of equal-spaced angle and the calibration method of equal-spaced specific force method are designed.The characteristics of the two calibration methods are analyzed through the use of the determinants of information matrix and the designed sensitivity coefficients.Focusing on different parameters in the error calibration model,the optimum calibration methods are proposed.The simulation results verify the effectiveness of the proposed calibration methods.Calibration method of PIGA on the disk precision centrifuge is studied.Firstly,the coordinate systems are established by considering the pose errors of the centrifuge calibration system.Then,the homogeneous transformation matrix of the PIGA coordinate system with respect to the geographic coordinate system is obtained by transferring the pose errors.The precision inputs of the specific force and angular velocity of PIGA are deduced by calculating the second derivative of displacement with respect to time,considering the gravity and earth rate,and other series of transformations.Thus,the error calibration model including bias,scale factor,second-order term,cross-quadratic term,odd-quadratic term,third-order term,angular velocity quadratic term,and mixed quadratic term is established.Aiming at the established model,the symmetrical position combination calibration method of PIGA for precession within integer periods are proposed and the closure errors are restrained by the reasonable design of the test time.Moreover,the misalignments are restrained and the installation displacement errors are compensated automatically by this calibration method;thus,the impacts of the centrifuge errors on measurement accuracy are suppressed effectively and the output uncertainty of PIGA can be decreased to 10^-6rad/s.The simulation results show that the order of calibration uncertainty of PIGA’s second-order term coefficient are decreased from10^-6 to 10^-7,and the order of calibration uncertainty of the other nonlinear error term coefficients are also less than 10^-6.Finally,the calibration accuracy of PIGA reaches 1×10^-7g/g.Calibration method of PIGA on the precision centrifuge with a counter-rotating platform is studied.This kind of precision centrifuge can not only provide constant centripetal acceleration in the position mode of counter-rotating platform,but also can provide harmonic specific force input in the synchronous counter-rotating mode of the platform.The precision inputs along the three referrence input axes of PIGA are calculated and the error calibration models are established respectively in these two different running modes of the platform.By combining the advantages of the two running modes,the sequential calibration method of PIGA is proposed.All the nonlinear error term coefficients are identified just by installing PIGA only once.Experimental results show that the order of the calibration uncertainty of PIGA’s nonlinear error coefficients is less than 10^-6;furthermore,the calibration accuracy of counter-rotating test is decreased to 10^-7.In order to solve the problem of long test time for calibrating the PIGA precession within the integer number of periods during the synchronous counter-rotating test,a new calibration method with inclined fixture installing the PIGA is proposed,so that both the components of harmonic specific force and gravity acceleration are decomposed along the input axis of PIGA.The simulation results show that the test time is reduced greatly and the calibration accuracy can be ensured.Calibration method of PIGA on the precision linear vibration table is studied.The linear vibration table can also excite the harmonic specific force input,but the structure is simpler and the input angular velocity is less than that of the precision centrifuge with a counter-rotating platform.According to the calculated inputs of PIGA and the measured error sources of linear vibration table,the error calibration models of PIGA on the linear vibration table are established.By comparing with the calibration methods of linear vibration within the integer number of periods and the calibration methods of PIGA precession within the integer number of periods,the4-state method is proposed for testing PIGA precession within the integer number of periods.After compensating for the errors generated by the vibration without integer periods,the second-order term and third-order term are accurately and easily calibrated by the 4-state calibration method.In order to solve the problem that the cross-quadratic term cannot be identified by the 4-state calibration method,the multi-position calibration method for PIGA precession within integer periods is proposed by using the indexing device;thus,the second-order term,cross-quadratic term,and third-order term can be calibrated.The simulation results show that the calibration methods for PIGA precession within integer periods can accurately calibrate the nonlinear error terms,and the order of the calibration uncertainty is decreased from 10^-7 to 10^-8.