A Method of Deflection of the Vertical Measurement Based on Phase Correction

The combination of the strapdown inertial navigation system (SINS) and the global navigation satellite system (GNSS) is an ingenious means to measure the deflection of the vertical (DOV). The error characteristics of the traditional direct difference model show that the DOV cannot be recovered by the traditional method because of the ignorance of the frequency characteristics of DOV. The error propagation relationship considering frequency domain characteristics between the horizontal attitude angles error and DOV is established. The Bode diagrams of the transfer functions between the horizontal attitude angles error and DOV show that there is a phase lag in the transfer functions, which is shown as a time delay in time domain, when the frequency of DOV in time domain is in the range of $7\times 10^{-4}{rad} \mathord {\left /{ {\vphantom {rad s}} }\right. } s . Then the improved direct difference model considering the time delay is established, and is simplified according to the spherical harmonic characteristics of gravity field. The simulation results show that the improved model with phase correction can recover the high-frequency component of DOV with the error standard deviations of $\delta \xi =1.0{5}^{\prime \prime }$ and $\delta \eta =0.9{9}^{\prime \prime }$ . Finally, the model is also verified by a section of ship test data, and the error standard deviations of the DOV recovered are $\delta \xi =1.4{6}^{\prime \prime }$ and $\delta \eta =1.2{4}^{\prime \prime }$ .