Observability Analysis for the INS Error Model with GPS/Uncalibrated Magnetometer Aiding
A commercial inertial navigation system (INS) yields time-diverging solutions due to errors in the inertial sensors, which can inhibit long term navigation. To circumvent this issue, a set of non-inertial sensors is used to limit these errors. The fusion between additional data and INS solution is often done by means of an extended Kalman filter using a state-error model. However, the Kalman filter estimates should be used when full observability produces small estimation uncertainty. This paper has analyzed conditions to achieve full observability using as non-inertial sensors a GPS receiver and an uncalibrated magnetometer combined with either a locally horizontal-stabilized IMU or with a strapdown IMU. The magnetometer bias was considered constant and augmented the error-state space. Observability analysis based on concepts of linear algebra provided a geometric insight on the requirements for attaining full observability when assuming piece-wise constant system dynamics. The novel analysis has been validated by covariance analysis of simulation results. Also, simulation results indicate that fusion with uncalibrated magnetometer data without proper processing gives rise to estimation divergence.
KeywordsObservability analysis INS error model GPS magnetometer
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