车载惯性定位标定的理论推导及误差分析

Theoretical Derivation and Error Analysis of Onboard Inertial Positioning Calibration

为了解决车载惯性定位系统误差常用的起点纬度标定计算法在安装偏差角90°附近时误差较大已不适用的问题,以及充实车载惯性定位系统标定计算的理论,首先进行了车载惯性定位系统误差标定计算的推导,证明了误差的可标定性。借鉴等角航线反解理论,得到车载惯性定位系统标定理论依据。参考中分纬度理论,推导出使用平均纬度进行简化计算的航程及航向角误差公式,将其引入惯性定位系统标定计算,提出了一种使用平均纬度代替起点纬度进行标定计算的方法,并对两种标定计算方法的误差进行了公式推导及仿真分析。仿真结果表明,使用平均纬度进行标定计算的误差明显小于使用起点纬度,在安装偏差角较大时,使用平均纬度进行标定计算可使标定计算误差降低90%。证明了提出的标定计算方法在南北纬55°、行程不超过90km时可用,高纬度、更长行程下可参照文中公式进行误差估计。

The commonly used calibration method,which uses the starting latitude to calculate the vehicle inertial location errors is not applicable when the installation deviation angle is near 90°.In order to solve this problem and enrich the theory of calibration for onboard inertial positioning system,the theoretical calibration formula of location errors for the onboard inertial positioning system is deduced,and it is proved that the errors can be calibrated.Using the rhumb line theory,the theoretical basis of onboard inertial positioning system is proposed.The simplified formulas of the voyage and course angle are deduced with the theory of the mid-latitude.And then,a calibration method that uses the mean latitude to calculate the inertial positioning system errors is proposed using the simplified formulas,and the calibration calculation method which uses the starting latitude is comparatively analyzed and simulated.The simulation analysis results show that the calibration calculation errors using the mean latitude are less than the calculation errors that use the starting latitude,when the installation deviation angle is large,calibration calculation errors can be decreased by 90%using the mean latitude.The calibration calculation method in this paper is applicable at 55°north-south latitude and with voyage not more than 90 kilometers.For higher latitude and longer voyages,errors can be estimated refering to the formula in this paper.