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Quantitative analysis of observability in linear time-varying systems

The general observability theory of linear time-varying systems was introduced. Definitions of local observability and local observability matrix were further made, accordingly. In order to test the observability of a system, a local observability criterion for linear time-varying systems was derived. Moreover, the degree of observability was formulated based on Kalman observability theory in order to know how state-variables are observed. The application of proposed observability analysis methods to integrated navigation systems showed that the degree of observability of velocity errors is better than that of misalignment angles and even better than that of drift rates; the normalized degree of observability may serve as a quantitative criterion for information fusion of navigation sensors.