Infrared and Laser Engineering, Volume. 51, Issue 7, 20210784(2022)

Full parameter rapid field calibration method for regular tetrahedral redundant inertial navigation

Xuerui Zhai, Yuan Ren, Lifen Wang, Ting Zhu, and Chen Wang
Author Affiliations
  • Space Engineering University, Department of Aerospace Science and Technology, Beijing 101416, China
  • show less
    Figures & Tables(17)
    Tetrahedron redundant configuration diagram
    Six-position transposition diagram
    Three-position rotation scheme
    Structure diagram of tetrahedral redundant inertial navigation system
    Experiment equipment and environment
    Attitude error of navigation solution
    Velocity error of navigation solution
    Position error of navigation solution
    • Table 1. IMU axial biases for each position estimation

      View table
      View in Article

      Table 1. IMU axial biases for each position estimation

      BiasPos1Pos2Pos3Pos4Pos5Pos6
      $\delta {\hat \omega _U}$$\delta \hat \omega _{x1}^b$$ - \delta \hat \omega _{x2}^b$$\delta \hat \omega _{y1}^b$$ - \delta \hat \omega _{y2}^b$$\delta \hat \omega _{z1}^b$$ - \delta \hat \omega _{z2}^b$
      $\delta {\hat f_U}$$\delta \hat f_{x1}^b$$ - \delta \hat f_{x2}^b$$\delta \hat f_{y1}^b$$ - \delta \hat f_{y2}^b$$\delta \hat f_{z1}^b$$ - \delta \hat f_{z2}^b$
    • Table 2. Setting values of gyroscope error parameters

      View table
      View in Article

      Table 2. Setting values of gyroscope error parameters

      ParameterGyro scope 1 Gyro scope 2 Gyro scope 3 Gyro scope 4
      Bias/(°)·h−10.60.5−0.30.4
      Scale factor/bits·((°)/s)−1170000170000170000170000
      Installation error $\delta {u_{gi}}$/(″) 40404040
      Installation error $\delta {v_{gi}}$/(″) 40404040
      Noise/(°)·h−1/20.010.010.010.01
    • Table 3. Setting values of accelerometer error parameters

      View table
      View in Article

      Table 3. Setting values of accelerometer error parameters

      ParameterAccelerometer 1Accelerometer 2Accelerometer 3Accelerometer 4
      Bias/mg0.30.2−0.40.5
      Scale factor /bits·((°)/s)−11111
      Installation error $\delta {u_{fi}}$/(″) 40404040
      Installation error $\delta {v_{fi}}$/(″) 40404040
      Noise/mg·h−1/20.020.020.020.02
    • Table 4. Simulation results

      View table
      View in Article

      Table 4. Simulation results

      Fiber optic gyroscope parametersPresetSimulation resultsErrorAccelerometer parametersPresetSimulation resultsError
      ${b_{g1} }/{(^\circ)\cdot {\rm{h} }^{-1} }$0.60.58742.10%${b_{f1} }/{\rm{mg}}$0.30.30561.87%
      ${b_{g2} }/{(^\circ)\cdot {\rm{h} }^{-1} }$0.50.50981.96%${b_{f2} }/{\rm{mg}}$0.20.19910.45%
      ${b_{g3} }/{(^\circ)\cdot {\rm{h} }^{-1} }$−0.3−0.28774.10%${b_{f3} }/{\rm{mg}}$−0.4−0.39261.85%
      ${b_{g4} }/{(^\circ)\cdot {\rm{h} }^{-1} }$0.40.37536.18%${b_{f4} }/{\rm{mg}}$0.50.49910.18%
      ${ {K}_{g1} }/{\rm{bits} }\cdot({(^\circ)/ {\rm{s} })^{-1} }$170000170142.540486900.0838%${ {K}_{f1} }/{\rm{bits} }\cdot{({\rm{m/s^2} }) ^{-1} }$11.000004470.000004%
      ${ {K}_{g2} }/{\rm{bits} }\cdot({(^\circ)/ {\rm{s} })^{-1} }$170000170024.963202570.0147%${ {K}_{f2} }/{\rm{bits} }\cdot{({\rm{m/s^2} }) ^{-1} }$10.999656280.0003%
      ${ {K}_{g3} }/{\rm{bits} }\cdot({(^\circ)/ {\rm{s} })^{-1} }$170000169981.633784090.0108%${ {K}_{f3} }/{\rm{bits} }\cdot{({\rm{m/s^2} }) ^{-1} }$11.000196960.0002%
      ${ {K}_{g4} }/{\rm{bits} }\cdot({(^\circ)/ {\rm{s} })^{-1} }$170000169981.531747460.0109%${ {K}_{f4} }/{\rm{bits} }\cdot{({\rm{m/s^2} }) ^{-1} }$10.999793330.0002%
      $ {H_{g1 x}} $$1.939\;255 \times {10^{ - 4}}$${{1}}{{.939\;254}} \times {10^{ - 4}}$0.0001%$ {H_{f1 x}} $$1.939\;255 \times {10^{ - 4}}$${{1}}{{.939\;257}} \times {10^{ - 4}}$0.0001%
      $ {H_{g1 y}} $$1.939\;255 \times {10^{ - 4}}$$1.939\;254 \times {10^{ - 4}}$0.0001%$ {H_{f1 y}} $$1.939\;255 \times {10^{ - 4}}$$1.939\;258 \times {10^{ - 4}}$0.0002%
      $ {H_{g1 z}} $−1−0.9999990.0001%$ {H_{f1 z}} $$ - 1$−0.9999990.0001%
      $ {H_{g2 x}} $0.9426330.9427750.0151%$ {H_{f2 x}} $0.9426330.9427750.0151%
      $ {H_{g2 y}} $$ {{ - }}2.474\;740 \times {10^{ - 4}} $${{ - 2}}{{.472\;355}} \times {10^{ - 4}}$0.0964%$ {H_{f2 y}} $$ - 2.474\;740 \times {10^{ - 4}} $${{ - 2}}{{.472\;524}} \times {10^{ - 4}}$0.0896%
      $ {H_{g2 z}} $0.3333780.3334280.0150%$ {H_{f2 z}} $0.3333780.3334290.0153%
      $ {H_{g3 x}} $−0.471261−0.4712700.0019%$ {H_{f3 x}} $−0.471261−0.4712360.0053%
      $ {H_{g3 y}} $0.8166260.8165540.0088%$ {H_{f3 y}} $0.8166260.8165830.0053%
      $ {H_{g3 z}} $0.3333780.3333840.0018%$ {H_{f3 z}} $0.3333780.3333610.0051%
      $ {H_{g4 x}} $−0.471373−0.4714270.0115%$ {H_{f4 x}} $−0.471373−0.4714180.0095%
      $ {H_{g4 y}} $−0.816379−0.8164500.0087%$ {H_{f4 y}} $−0.816379−0.8164580.0097%
      $ {H_{g4 z}} $0.3333780.3334160.0114%$ {H_{f4 z}} $0.3333780.3334090.0093%
    • Table 5. Technical specification of fiber optic gyroscope and accelerometer

      View table
      View in Article

      Table 5. Technical specification of fiber optic gyroscope and accelerometer

      Parameter nameParameter indicator
      Fiber optic gyroscope bias stability $/{(^\circ)\cdot {\rm{h} }^{-1} }$$ \leqslant $0.1
      Fiber optic gyroscope scale factor $/{\rm{bits} }\cdot({(^\circ)/ {\rm{s} })^{-1} }$176000±5000
      Accelerometer bias stability $/\text{μ} {\rm{g}}$50
      Accelerometer scale factor $/{\rm{mA} } \cdot{{ g} }^{-1}$1.1-1.5
    • Table 6. Gyroscope error calibration results

      View table
      View in Article

      Table 6. Gyroscope error calibration results

      Fiber optic gyroscope parametersCalibration resultsFiber optic gyroscope parametersCalibration results
      ${b_{g1} }/{(^\circ)\cdot {\rm{h} }^{-1} }$0.0541${ {K}_{g1} }/{\rm{bits} }\cdot({(^\circ)/ {\rm{s} })^{-1} }$172207.11
      ${b_{g2} }/{(^\circ)\cdot {\rm{h} }^{-1} }$0.0524${ {K}_{g2} }/{\rm{bits} }\cdot({(^\circ)/ {\rm{s} })^{-1} }$177573.77
      ${b_{g3} }/{(^\circ)\cdot {\rm{h} }^{-1} }$0.0780${ {K}_{g3} }/{\rm{bits} }\cdot({(^\circ)/ {\rm{s} })^{-1} }$179823.99
      ${b_{g4} }/{(^\circ)\cdot {\rm{h} }^{-1} }$−1.1961${ {K}_{g4} }/{\rm{bits} }\cdot({(^\circ)/ {\rm{s} })^{-1} }$171997.12
      $ {H_{g1 x}} $−0.0015$ {H_{g3 x}} $−0.4703
      $ {H_{g1 y}} $−0.0034$ {H_{g3 y}} $0.8168
      $ {H_{g1 z}} $−1.0000$ {H_{g3 z}} $0.3340
      $ {H_{g2 x}} $0.9418$ {H_{g4 x}} $−0.4673
      $ {H_{g2 y}} $0.0016$ {H_{g4 y}} $−0.8186
      $ {H_{g2 z}} $0.3362$ {H_{g4 z}} $0.3339
    • Table 7. Accelerometer error calibration results

      View table
      View in Article

      Table 7. Accelerometer error calibration results

      Accelerometer parametersCalibration resultsAccelerometer parametersCalibration results
      ${b_{f1} }/{{g} }$−0.0167${ {K}_{f1} }/{\rm{bits} }\cdot{({\rm{m/s^2} }) ^{-1} }$0.9680
      ${b_{f2} }/{{g} }$0.0087${ {K}_{f2} }/{\rm{bits} }\cdot{({\rm{m/s^2} }) ^{-1} }$0.9687
      ${b_{f3} }/{{g} }$0.0109${ {K}_{f3} }/{\rm{bits} }\cdot{({\rm{m/s^2} }) ^{-1} }$0.9907
      ${b_{f4} }/{{g} }$−0.0029${ {K}_{f4} }/{\rm{bits} }\cdot{({\rm{m/s^2} }) ^{-1} }$0.9516
      $ {H_{f1 x}} $${ { - } }3.159\;0 \times {10^{ - 5} }$$ {H_{f3 x}} $−0.4734
      $ {H_{f1 y}} $${ { - } }1.225\;7 \times {10^{ - 4} }$$ {H_{f3 y}} $−0.8152
      $ {H_{f1 z}} $−1.0000$ {H_{f3 z}} $0.3337
      $ {H_{f2 x}} $0.9428$ {H_{f4 x}} $−0.4696
      $ {H_{f2 y}} $−0.0019$ {H_{f4 y}} $−0.8173
      $ {H_{f2 z}} $0.3335$ {H_{f4 z}} $0.3338
    • Table 8. Gyroscope turntable test results

      View table
      View in Article

      Table 8. Gyroscope turntable test results

      Rotating wayStandard value/(°)·s−1Factory parameterCalibration parameter
      Compensation result /(°)·s−1Relative errorCompensation result /(°)·s−1Relative error
      x(clockwise) 1010.01260.001269.9932−0.00068
      x(counterclockwise) −10−9.9687−0.00313−10.00110.00011
      y(clockwise) 109.9842−0.001589.9967−0.00037
      y(counterclockwise) −10−9.9825−0.00175−9.9903−0.00097
      z(clockwise) 109.9709−0.002919.9995−0.00005
      z(counterclockwise) −10−9.9599−0.00401−10.00460.00046
    • Table 9. Accelerometer turntable test results

      View table
      View in Article

      Table 9. Accelerometer turntable test results

      PositionStandard value/m·s2Factory parameterCalibration parameter
      Compensation result/m·s2Relative errorCompensation resultRelative error
      x(up) 9.80149.80463.2648 E-49.8022−8.1621 E-5
      x(down) −9.8014−9.7952−6.3256 E-4−9.80140
      y(up) 9.80149.80206.1216 E-59.80113.06079 E-5
      y(down) −9.8014−9.7987−2.7547 E-4−9.8017−3.0608 E-5
      z(up) 9.80149.7957−5.8155 E-49.8029−1.5304 E-4
      z(down) −9.8014−9.7994−2.0405 E-4−9.8029−1.5304 E-4
    Tools

    Get Citation

    Copy Citation Text

    Xuerui Zhai, Yuan Ren, Lifen Wang, Ting Zhu, Chen Wang. Full parameter rapid field calibration method for regular tetrahedral redundant inertial navigation[J]. Infrared and Laser Engineering, 2022, 51(7): 20210784

    Download Citation

    EndNote(RIS)BibTexPlain Text
    Save article for my favorites
    Paper Information

    Category: Photoelectric measurement

    Received: Oct. 26, 2021

    Accepted: --

    Published Online: Dec. 20, 2022

    The Author Email:

    DOI:10.3788/IRLA20210784

    Topics