An quantitative method for observability analysis and its application in SINS calibration

In the strapdown inertial navigation system (SINS) calibration, the observability of SINS error states has significant impacts on calibration results. In order to analyze the observability of SINS error states quantitatively, this paper proposes the observability degree for the states of linear time-varying systems. It is shown that the proposed observability degree illustrates the sensitivity of state estimations to disturbances and determines the upper bound of estimation accuracy. Based on the proposed observability degree, the sufficient and necessary conditions for the states to be observable are presented. In addition, an experiment of ship-mounted SINS calibration is given to validate the proposed observability degree. According to the experiment results, the proposed observability degree can make accurate evaluations on the observability of SINS error states, thus providing direct understandings on the accuracy of calibration results.