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The observability and observable degree of attitude errors in tightly coupled global navigation satellite system/inertial navigation system attitude determination system are studied in this paper. The mathematical relationship between the observable degree and the attitude dilution of precision (ATDOP) is determined by the singular value decomposition of the observability Gramian. The influence of the ATDOP on the observable degree is analyzed. The observability analysis of the attitude errors under different numbers of visible satellites is performed via a rank test of the observability Gramian. The results of a field test demonstrate that, a higher observable degree of attitude error will be obtained for the pitch, roll and yaw at a given time under a lower ATDOP. When the number of visible satellites is equivalent, a lower ATDOP leads to a higher observable degree of error for any one of the three attitudes at different times. Moreover, the results show that the three attitude errors are all externally observable under the condition of at least three visible satellites with three antennas.

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The Influence of Attitude Dilution of Precision on the Observable Degree and Observability Analysis With Different Numbers of Visible Satellites in a Multi-Antenna GNSS/INS Attitude Determination System