Modeling and Analytic Error Assessment of Gyro-Free INS

摘要

A conventional inertial measurement unit contains three orthogonalrnaccelerometers and three orthogonal gyroscopes to measure acceleration andrnangular rate of the vehicle. A different possibility is to use a set of distributedrnaccelerometers to measure both acceleration and angular rate. This concept,rnknown as gyro-free navigation, was proposed over 45 years ago and recentlyrnarousing a growing interest because of the emergence of low cost MEMS basedrnaccelerometers with rapidly increasing performance. Most research in the gyrofreernfield had focused on seeking optimal accelerometer locations and it appearsrnthat less attention was given for deriving appropriate state-space models andrnanalytical error assessment as in a conventional INS. In this paper, we aim tornfill this gap. We derive gyro-free kinematic equations expressed in the navigationrnframe fitting for any set of accelerometer configurations. Such a set may bernarbitrary in terms of the number of accelerometers in the configuration, theirrnrelative location and orientation. We further derive gyro-free INS error staterndynamic equations in a state space model and augment them with dynamicrnequations representing the accelerometers residuals. In addition, simplified errorrnmodels and their corresponding closed form solutions, suitable for any gyro-freernconfigurations are derived and their characteristics are analyzed. A case study ofrnsix accelerometers configuration is used to illustrate the gyro-free concept and tornanalyze its performance throughout all the models derived in the paper.