基于PWCS理论的单轴旋转惯导系统初始对准的可观测性分析

Observability analysis for initial alignment of single-axial rotating INS

针对旋转惯导系统的初始对准模型时变特点,基于单轴旋转惯导系统的误差方程分析了不同旋转方案中对准模型的区别主要表现为旋转变换矩阵不同,并进一步推导了绕3个不同轴向的单轴二位置转停方案的旋转变换矩阵,建立了不同旋转方案的卡尔曼滤波对准模型。而后,忽略转停方案中的旋转过程,基于PWCS理论对不同位置的对准模型进行研究,分析了不同时段内系统的总观测性矩阵和提取观测性矩阵,根据矩阵的秩确定了系统的可观测性。分析表明:IMU绕X轴二位置转停方案的可观测状态数由7增加为8;绕Y和Z轴二位置转停方案的可观测状态数由7增加为10,系统完全可观测。

Since the initial alignment model of rotating INS is time-varying, the piece-wise constant system（PWCS）theory was applied to analyze the observability of the rotating INS with different rotation schemes. Firstly, based on the analysis of error equations of rotating INS, it was found that the distinction of alignment models are difference of the rotation transform matrix between the body frame and the rotation frame. Thus the rotation transform matrixes of 3 different single-axial rotation schemes were deduced and the Kalman alignment filters for the different schemes were designed. Then, the PWCS theory was applied to analyze the total observability matrix （TOM） and stripped observahility matrix （SOM） of the each state in the rotation scheme. The observability of different rotation schemes was researched by calculating the rank of SOM. Analysis results show that the number of the observable state changes from 7 to 8 when IMU rotates with X axis, while it is up to 10 when IMU rotates with Y or Z axis.