Pseudo loosely-integrated navigation of low-cost MEMS-INS/GPS with insufficient observable satellites
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摘要:
为了解决GPS可观测卫星不足情况下低成本微电子机械-惯性导航系统/全球定位系统（MEMS-INS/GPS）组合导航精度维持问题，提出基于灰色模型和自适应卡尔曼滤波的MEMS-INS/GPS伪松组合导航方法。以MEMS-INS/GPS松组合导航模式为框架，建立了伪松组合导航系统的状态空间模型。基于MEMS-INS/GPS的历史观测数据，使用灰色模型对MEMS-INS/GPS观测差值进行预测，称为系统伪观测量。当GPS可观测卫星充分时，使用噪声自适应估计卡尔曼滤波对MEMS-INS/GPS进行松组合导航；当GPS可观测卫星不足时，使用噪声自适应估计卡尔曼滤波依据系统伪观测量，将MEMS-INS/GPS进行伪松组合导航。以车载低成本MEMS-INS/GPS组合导航系统为例进行仿真和实验验证，结果表明：当GPS可观测卫星不足时，传统的MEMS-INS/GPS松组合导航精度迅速下降并发散，而MEMS-INS/GPS伪松组合导航精度与GPS正常工作时的导航精度相差不大，维持了较高精度的导航状态。
Abstract:To solve the problem of accuracy maintenance of low-cost MEMS-INS/GPS integrated navigation under the condition of insufficient observable GPS satellites, a MEMS-INS/GPS pseudo loosely-integrated navigation method is proposed based on grey model and adaptive Kalman filter. In the framework of the proposed navigation mode, a state space model of integrated navigation system is established. Based on the MEMS-INS/GPS historical observation data, grey model is used to predict the difference between GPS and MEMS-INS, and this prediction is named system pseudo-observation. When the observable GPS satellites are sufficient, noise adaptive estimating Kalman filter is used for MEMS-INS/GPS integrated navigation; otherwise, this filter is used for MEMS-INS/GPS pseudo loosely-integrated navigation based on the system pseudo-observation. An example of low-cost MEMS-INS/GPS integrated vehicle navigation system is used in simulation and experimental verification. The results show that when the observable GPS satellites are insufficient, the traditional MEMS-INS/GPS loosely-integrated navigation decreases in accuracy rapidly and diverges, but the MEMS-INS/GPS pseudo loosely-integrated navigation is not significantly different from the normal GPS navigation in terms of accuracy, maintaining a high precision navigation state.
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图 2 基于灰色模型的GPS伪观测量预测
Figure 2. Grey-model based prediction of pseudo observing quantity of GPS
图 4 东向和北向速度差值预测结果
Figure 4. Prediction result of difference between eastward and northward speeds
图 8 不同导航方案导航量的变化情况
Figure 8. Navigation parameter changes of different navigation schemes
表 1 灰色模型预测精度等级
Table 1. Prediction accuracy grade of grey model
模型精度等级 小误差概率$ p $ 后验差比值$ C $ 1级（好） $ p \geqslant 0.95 $ $ C \leqslant 0.35 $ 2级（合格） $ 0.80 \leqslant p \lt 0.95 $ $ 0.35 \lt C \leqslant 0.5 $ 3级（勉强） $ 0.70 \leqslant p \lt 0.80 $ $ 0.5 \lt C \leqslant 0.65 $ 4级（不合格） $ p \lt 0.70 $ $ C \gt 0.65 $ 
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表 2 MEMS仪表性能指标参数
Table 2. Property index parameters of MEMS
MEMS陀螺仪 MEMS加速度计 GPS 量程/
（（°）·s−1）零偏/
（（°）·s−1）零偏稳定性/
（（°）·s−1）零偏重复性/
（（°）·s−1）量程 零偏 零偏稳定性 零偏重复性 授时精度/
ns位置精度
（CEP DGPS）/m速度精度/
（m·s−1）数据更新率/
Hz注：CEP为原概率偏差，DGPS是差分GPS工作模式。
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表 3 380~410 s位置误差统计
Table 3. Statistics of location error among 380~410 s
m 双测状态 经度 纬度 高度 均值 SD 均值 SD 均值 SD 卫星正常 0.20818 1.0587 −0.25183 1.19667 −0.37409 1.21927 卫星不足 −6.85383 14.33106 −0.98421 4.06205 −6.51393 13.87575 观测量预测 0.81243 2.37502 −0.72929 1.89076 0.25046 1.31343
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表 4 380~410 s速度误差统计
Table 4. Statistics of speed error among 380~410 s
m/s 双测状态 ${V_{\rm{E}}}$ ${V_{\rm{N}}}$ ${V_{\rm{U}}}$ 均值 SD 均值 SD 均值 SD 卫星正常 0.01727 0.04224 −0.00426 0.05191 −0.00291 0.02113 卫星不足 0.00796 0.12605 −0.06687 0.44914 −0.02372 0.14846 观测量预测 0.01221 0.06536 0.00564 0.09993 0.00835 0.05092
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表 5 伪松组合导航下的最大位置误差
Table 5. Maximum position error under pseudo loosely-integrated navigation
参数 时刻/s 5 10 15 20 25 30 35 40 45 50 最大误差/m 3.6 4.1 5.0 6.2 7.6 9.2 12.2 15.7 19.8 23.9
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表 6 卫星失效范围内速度误差统计
Table 6. Statistics of speed error among satellite failure ramge
m/s 实验 ${V_{\rm{E}}}$ ${V_{\rm{N}}}$ 均值 SD 均值 SD 实验2 3.25361 5.78239 2.63561 4.64385 实验3 0.06327 0.09532 0.00863 0.10936
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表 7 卫星失效范围内位置误差统计
Table 7. Statistics of location error among satellite failure ramge
m 实验 经度 纬度 均值 SD 均值 SD 实验2 8.06001 18.21367 5.34918 10.40109 实验3 1.01342 2.63926 1.01232 2.20167
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