Modeling and calibration of pointing errors using a semi-parametric regression method with applications in inertially stabilized platforms

Abstract

This article investigates modeling and calibration issues that are associated with inertially stabilized platforms to achieve accurate pointing. In modeling part, the Denavit-Hartenberg notation is used to perform an error analysis of the kinematics of inertially stabilized platforms. A physical model is then established to illustrate the effects of geometric errors that are caused by imprecision in the manufacturing and assembly processes on the pointing accuracy of inertially stabilized platforms. In the calibration part, an improved hybrid model denoted as the semi-parametric regression model is developed to compensate for remaining nonlinear errors. With applications to a two-degree-of-freedom miniature inertially stabilized platform, semi-parametric regression model is shown to outperform physical model substantially in all cases. The experimental results also indicate that the proposed semi-parametric regression model eliminates both the geometric and nonlinear errors, and that the pointing accuracy of miniature inertially stabilized platform significantly improves after compensation.

Calibration error analysis of inertially stabilized platforms using quaternions and octonions in rotation decomposition

“…However, in order to improve its pointing accuracy further, it is necessary to analyze errors that result from the platform's misalignment error, nonperpendicularity, initialization error and so on, and then relevant compensation models can be adopted. The detailed information has been presented and reported in Hong et al 9 and Tang et al 17…”

Static pointing error analysis of electro-optical detection systems

“…Rate gyroscopes are utilized to measure the rotation speed and sense the platform vibration to attenuate the disturbance to the line of sight (LOS). [2][3][4][5] Proper control algorithm will increase dynamic pointing accuracy in inertial space and hold LOS stationary to obtain clear target images. Position sensors such as opticalelectricity encoders or rotary transformers are utilized to obtain the rotation angle, and the spatial pointing direction of LOS can hence be calculated.…”

“…There are still nonlinear errors that are not considered, such as the environment factors including temperature, atmosphere, gravity, wind and vibration. 4,5 To improve the pointing accuracy, it is necessary to compensate for these nonlinear errors. Since a semi-parametric model contains both parametric and nonparametric components, it provides a convenient way to analyse nonlinearities and has been widely used.…”

“…To identify the optimal estimate of equation (12), a commonly used solution is adding a penalty term to standard least squares as shown in equation (13), and relevant derivation is also presented in Hong et al, 4 Sun and Wu 18 and Pan and Sun 21…”

“…Therefore, it is necessary to model and calibrate these errors to improve the pointing accuracy. 8 At present, there are various approaches to establish the error model, such as Debye-Hu¨ckel (D-H) equation 4,9 and coordinate transformation (rotation matrix). 10 Since quaternions can visually represent a rotation, 11 this article employs quaternions to analyse integrant errors of EODS for the first time.…”