Fig. 1. Tetrahedron redundant configuration diagram
Fig. 2. Six-position transposition diagram
Fig. 3. Three-position rotation scheme
Fig. 4. Structure diagram of tetrahedral redundant inertial navigation system
Fig. 5. Experiment equipment and environment
Fig. 6. Attitude error of navigation solution
Fig. 7. Velocity error of navigation solution
Fig. 8. Position error of navigation solution
| Bias | Pos1 | Pos2 | Pos3 | Pos4 | Pos5 | Pos6 | | $\delta {\hat \omega _U}$ | $\delta \hat \omega _{x1}^b$ | $ - \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 1. IMU axial biases for each position estimation
| Parameter | Gyro
scope 1
| Gyro
scope 2
| Gyro
scope 3
| Gyro
scope 4
| | Bias/(°)·h−1 | 0.6 | 0.5 | −0.3 | 0.4 | | Scale factor/bits·((°)/s)−1 | 170000 | 170000 | 170000 | 170000 | | Installation error
$\delta {u_{gi}}$/(″)
| 40 | 40 | 40 | 40 | | Installation error
$\delta {v_{gi}}$/(″)
| 40 | 40 | 40 | 40 | | Noise/(°)·h−1/2 | 0.01 | 0.01 | 0.01 | 0.01 |
|
Table 2. Setting values of gyroscope error parameters
| Parameter | Accelerometer 1 | Accelerometer 2 | Accelerometer 3 | Accelerometer 4 | | Bias/mg | 0.3 | 0.2 | −0.4 | 0.5 | | Scale factor
/bits·((°)/s)−1 | 1 | 1 | 1 | 1 | | Installation error
$\delta {u_{fi}}$/(″)
| 40 | 40 | 40 | 40 | | Installation error
$\delta {v_{fi}}$/(″)
| 40 | 40 | 40 | 40 | | Noise/mg·h−1/2 | 0.02 | 0.02 | 0.02 | 0.02 |
|
Table 3. Setting values of accelerometer error parameters
| Fiber optic gyroscope parameters | Preset | Simulation results | Error | Accelerometer parameters | Preset | Simulation results | Error | | ${b_{g1} }/{(^\circ)\cdot {\rm{h} }^{-1} }$ | 0.6 | 0.5874 | 2.10% | ${b_{f1} }/{\rm{mg}}$ | 0.3 | 0.3056 | 1.87% | | ${b_{g2} }/{(^\circ)\cdot {\rm{h} }^{-1} }$ | 0.5 | 0.5098 | 1.96% | ${b_{f2} }/{\rm{mg}}$ | 0.2 | 0.1991 | 0.45% | | ${b_{g3} }/{(^\circ)\cdot {\rm{h} }^{-1} }$ | −0.3 | −0.2877 | 4.10% | ${b_{f3} }/{\rm{mg}}$ | −0.4 | −0.3926 | 1.85% | | ${b_{g4} }/{(^\circ)\cdot {\rm{h} }^{-1} }$ | 0.4 | 0.3753 | 6.18% | ${b_{f4} }/{\rm{mg}}$ | 0.5 | 0.4991 | 0.18% | | ${ {K}_{g1} }/{\rm{bits} }\cdot({(^\circ)/ {\rm{s} })^{-1} }$ | 170000 | 170142.54048690 | 0.0838% | ${ {K}_{f1} }/{\rm{bits} }\cdot{({\rm{m/s^2} }) ^{-1} }$ | 1 | 1.00000447 | 0.000004% | | ${ {K}_{g2} }/{\rm{bits} }\cdot({(^\circ)/ {\rm{s} })^{-1} }$ | 170000 | 170024.96320257 | 0.0147% | ${ {K}_{f2} }/{\rm{bits} }\cdot{({\rm{m/s^2} }) ^{-1} }$ | 1 | 0.99965628 | 0.0003% | | ${ {K}_{g3} }/{\rm{bits} }\cdot({(^\circ)/ {\rm{s} })^{-1} }$ | 170000 | 169981.63378409 | 0.0108% | ${ {K}_{f3} }/{\rm{bits} }\cdot{({\rm{m/s^2} }) ^{-1} }$ | 1 | 1.00019696 | 0.0002% | | ${ {K}_{g4} }/{\rm{bits} }\cdot({(^\circ)/ {\rm{s} })^{-1} }$ | 170000 | 169981.53174746 | 0.0109% | ${ {K}_{f4} }/{\rm{bits} }\cdot{({\rm{m/s^2} }) ^{-1} }$ | 1 | 0.99979333 | 0.0002% | | $ {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 | −0.999999 | 0.0001% | $ {H_{f1 z}} $ | $ - 1$ | −0.999999 | 0.0001% | | $ {H_{g2 x}} $ | 0.942633 | 0.942775 | 0.0151% | $ {H_{f2 x}} $ | 0.942633 | 0.942775 | 0.0151% | | $ {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}} $ | 0.333378 | 0.333428 | 0.0150% | $ {H_{f2 z}} $ | 0.333378 | 0.333429 | 0.0153% | | $ {H_{g3 x}} $ | −0.471261 | −0.471270 | 0.0019% | $ {H_{f3 x}} $ | −0.471261 | −0.471236 | 0.0053% | | $ {H_{g3 y}} $ | 0.816626 | 0.816554 | 0.0088% | $ {H_{f3 y}} $ | 0.816626 | 0.816583 | 0.0053% | | $ {H_{g3 z}} $ | 0.333378 | 0.333384 | 0.0018% | $ {H_{f3 z}} $ | 0.333378 | 0.333361 | 0.0051% | | $ {H_{g4 x}} $ | −0.471373 | −0.471427 | 0.0115% | $ {H_{f4 x}} $ | −0.471373 | −0.471418 | 0.0095% | | $ {H_{g4 y}} $ | −0.816379 | −0.816450 | 0.0087% | $ {H_{f4 y}} $ | −0.816379 | −0.816458 | 0.0097% | | $ {H_{g4 z}} $ | 0.333378 | 0.333416 | 0.0114% | $ {H_{f4 z}} $ | 0.333378 | 0.333409 | 0.0093% |
|
Table 4. Simulation results
| Parameter name | Parameter 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 5. Technical specification of fiber optic gyroscope and accelerometer
| Fiber optic gyroscope parameters | Calibration results | Fiber optic gyroscope parameters | Calibration 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 6. Gyroscope error calibration results
| Accelerometer parameters | Calibration results | Accelerometer parameters | Calibration 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 7. Accelerometer error calibration results
| Rotating way | Standard value/(°)·s−1 | Factory parameter | | Calibration parameter | | Compensation result
/(°)·s−1 | Relative error | Compensation result
/(°)·s−1 | Relative error | | x（clockwise）
| 10 | 10.0126 | 0.00126 | | 9.9932 | −0.00068 | | x（counterclockwise）
| −10 | −9.9687 | −0.00313 | −10.0011 | 0.00011 | | y（clockwise）
| 10 | 9.9842 | −0.00158 | 9.9967 | −0.00037 | | y（counterclockwise）
| −10 | −9.9825 | −0.00175 | −9.9903 | −0.00097 | | z（clockwise）
| 10 | 9.9709 | −0.00291 | 9.9995 | −0.00005 | | z（counterclockwise）
| −10 | −9.9599 | −0.00401 | −10.0046 | 0.00046 |
|
Table 8. Gyroscope turntable test results
| Position | Standard value/m·s2 | Factory parameter | | Calibration parameter | | | Compensation result/m·s2 | Relative error | Compensation result | Relative error | | x（up）
| 9.8014 | 9.8046 | 3.2648 E-4 | | 9.8022 | −8.1621 E-5 | | x（down）
| −9.8014 | −9.7952 | −6.3256 E-4 | −9.8014 | 0 | | y（up）
| 9.8014 | 9.8020 | 6.1216 E-5 | 9.8011 | 3.06079 E-5 | | y（down）
| −9.8014 | −9.7987 | −2.7547 E-4 | −9.8017 | −3.0608 E-5 | | z（up）
| 9.8014 | 9.7957 | −5.8155 E-4 | 9.8029 | −1.5304 E-4 | | z（down）
| −9.8014 | −9.7994 | −2.0405 E-4 | −9.8029 | −1.5304 E-4 |
|
Table 9. Accelerometer turntable test results
