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基于自适应噪声方差的卫星定位故障检测法

陈含智 孙蕊 邱明 毛继志 胡浩亮 张立东

陈含智,孙蕊,邱明,等. 基于自适应噪声方差的卫星定位故障检测法[J]. 北京航空航天大学学报,2023,49(2):406-421 doi: 10.13700/j.bh.1001-5965.2021.0222
引用本文: 陈含智,孙蕊,邱明,等. 基于自适应噪声方差的卫星定位故障检测法[J]. 北京航空航天大学学报,2023,49(2):406-421 doi: 10.13700/j.bh.1001-5965.2021.0222
CHEN H Z,SUN R,QIU M,et al. An adaptive noise variance based fault detection algorithm for GNSS positioning[J]. Journal of Beijing University of Aeronautics and Astronautics,2023,49(2):406-421 (in Chinese) doi: 10.13700/j.bh.1001-5965.2021.0222
Citation: CHEN H Z,SUN R,QIU M,et al. An adaptive noise variance based fault detection algorithm for GNSS positioning[J]. Journal of Beijing University of Aeronautics and Astronautics,2023,49(2):406-421 (in Chinese) doi: 10.13700/j.bh.1001-5965.2021.0222

基于自适应噪声方差的卫星定位故障检测法

doi: 10.13700/j.bh.1001-5965.2021.0222
基金项目: 国家自然科学基金(42174025,41974033);工信部民用飞机专项科研项目(MJ-2020-S-03);江苏省“六大人才高峰”项目(KTHY-014);中央高校基本科研业务费专项资金(KFJJ20200703);江苏省自然科学基金(BK20211569)
详细信息
    通讯作者:

    E-mail: rui.sun@nuaa.edu.cn

  • 中图分类号: V249.3

An adaptive noise variance based fault detection algorithm for GNSS positioning

Funds: National Natural Science Foundation of China (42174025,41974033); European Union’s Horizon 2020 Research and Innovation Programme Under Grant Agreement No 875154 GreAT (MJ-2020-S-03); Jiangsu Provincial Six Talent Peaks Project (KTHY-014); The Fundamental Research Funds for the Central Universities (KFJJ20200703); Natural Science Foundation of Jiangsu Province (BK20211569)
More Information
  • 摘要:

    不同观测环境的实际观测噪声可能存在较大差别,因此,固定的噪声方差矩阵可能使基于卡尔曼滤波故障检测法的故障检测效果下降。对此,提出自适应噪声方差的卫星定位故障检测算法,利用滑动窗内的历史新息实时估计观测噪声方差矩阵,在此基础上构建故障检测量与识别量对故障进行检测与识别,利用不含故障的新息更新状态向量并解算出定位结果。实验结果表明:所提算法在静态模式下,可100%检测和识别的最小单阶跃故障为3 m,对持续时间为100 s、斜坡故障增长速率为0.2 m/s的斜坡故障识别比率为51.4%,可100%检测和识别的最小多故障为4 m;在动态模式下,可100%检测和识别的最小单阶跃故障为10 m,对持续时间为200 s、斜坡故障增长速率为0.2 m/s的斜坡故障识别比率为66.25%,可100%检测和识别的最小多故障为12 m。所提算法性能优于基于最小二乘和卡尔曼滤波的故障检测法。

     

  • 图 1  本文算法框架

    Figure 1.  Framework of the proposed algorithm

    图 2  静态观测实验的环境

    Figure 2.  The environment of static observation experiment

    图 3  原始静态数据的故障检测量

    Figure 3.  Fault detection statistics based on the original static data

    图 4  原始静态数据下所提算法的定位误差

    Figure 4.  The positioning error of the proposed algorithm based on the original static data

    图 5  静态数据含5 m阶跃故障的故障检测量

    Figure 5.  Fault detection statistics with a 5 m step error added on observations in the static mode

    图 6  静态数据含5 m阶跃故障下所提算法的故障识别量

    Figure 6.  Fault identification statistics of the proposed algorithm with a 5 m step error added on the observations in the static mode

    图 7  静态数据含不同大小的阶跃故障时的故障检测比率、故障识别比率和3D均方根误差

    Figure 7.  The FDR, FIR and 3D accuracy (RMSE) for the candidate algorithms based on the static data with various step errors

    图 8  静态数据在${T_{{\text{SE}}}} = 100$ s,${V_{{\text{SE}}}} = 0.2$ m/s故障下的故障检测量

    Figure 8.  Fault detection statistics for the static data with a 0.2 m/s ramp error added for 100 s

    图 9  静态数据在${T_{{\text{SE}}}} = 100$ s,${V_{{\text{SE}}}} = 0.2$ m/s故障下所提算法的故障识别量

    Figure 9.  Fault identification statistics of the proposed algorithm with a 0.2 m/s ramp error added for 100 s in the static mode

    图 10  静态数据在${T_{{\text{SE}}}} = 100$ s,${V_{{\text{SE}}}} = 0.2$ m/s故障下基于卡尔曼滤波的故障检测法的故障识别量

    Figure 10.  Fault identification statistics of the KF-based method with a 0.2 m/s ramp error added for 100 s in the static mode

    图 11  静态数据在${T_{{\text{SE}}}} = 100$ s,${V_{{\text{SE}}}} = 0.2$ m/s故障下最小二乘残差法的故障识别量

    Figure 11.  Fault identification statistics of the least square residual based method with a 0.2 m/s ramp error added for 100 s in the static mode

    图 12  静态数据含不同大小的斜坡故障时的故障检测比率、故障识别比率和3D均方根误差

    Figure 12.  The FDR, FIR and 3D accuracy (RMSE) for candidate algorithms with various ramp errors in the static mode

    图 13  静态数据中卫星G09和G16的伪距同时含5 m的故障下的故障检测量

    Figure 13.  Fault detection statistics for 5 m step errors added on the pseudorange of G09 and G16 in the static mode

    图 14  静态数据中卫星G09和G16的伪距同时含有5 m的阶跃故障下所提算法的故障识别量

    Figure 14.  Fault identification statistics for 5 m step errors added on pseudorange of G09 and G16 in the static mode

    图 15  静态数据含不同大小的多故障时故障检测比率、故障识别比率和3D均方根误差

    Figure 15.  FDR, FIR and 3D accuracy (RMSE) for candidate algorithms with various step errors on two satellites in the static mode

    图 16  无人机的飞行轨迹

    Figure 16.  Flight trajectory of the unmanned aerial vehicle (UAV)

    图 17  原始动态数据的故障检测量

    Figure 17.  Fault detection statistics based on original dynamic data

    图 18  原始动态数据下所提算法的定位误差

    Figure 18.  Positioning error of the proposed algorithm based on original dynamic data

    图 19  动态数据含10 m阶跃故障下的故障检测量

    Figure 19.  Fault detection statistics with a 10 m step error added on observations in the dynamic mode

    图 20  动态数据含10 m阶跃故障下所提算法的故障识别量

    Figure 20.  Fault identification statistics with a 10 m step error added on observations in the dynamic mode

    图 21  动态数据含10 m阶跃故障下最小二乘残差法的故障识别量

    Figure 21.  Fault identification statistics of least square residual based method with a 10 m step error added on the observations in the dynamic mode

    图 22  动态数据含不同大小的阶跃故障时的故障检测比率、故障识别比率、3D均方根误差

    Figure 22.  The FDR, FIR and 3D accuracy (RMSE) for the candidate algorithms based on dynamic data with various step errors

    图 23  动态数据在${T_{{\text{SE}}}} = 200$ s,${V_{{\text{SE}}}} = 0.2$ m/s故障下的故障检测量

    Figure 23.  Fault detection statistics for the dynamic data with a 0.2 m/s ramp error added for 200 s

    图 24  动态数据在${T_{{\text{SE}}}} = 200$ s,${V_{{\text{SE}}}} = 0.2$ m/s故障下所提算法的故障识别量

    Figure 24.  Fault identification statistics of the proposed algorithm with a 0.2 m/s ramp error added for 200 s in the dynamic mode

    图 25  动态数据在${T_{{\text{SE}}}} = 200$ s,${V_{{\text{SE}}}} = 0.2$ m/s故障下基于卡尔曼滤波的故障检测法的故障识别量

    Figure 25.  Fault identification statistics of the KF-based method with a 0.2 m/s ramp error added for 200 s in the dynamic mode

    图 26  动态数据在${T_{{\text{SE}}}} = 200$ s,${V_{{\text{SE}}}} = 0.2$ m/s故障下最小二乘残差法的故障识别结果

    Figure 26.  Fault identification result of the least square residual based method with a 0.2 m/s ramp error added for 200 s in dynamic mode

    图 27  动态数据含不同大小的斜坡故障时的故障检测比率、故障识别比率和3D均方根误差

    Figure 27.  The FDR, FIR and 3D accuracy (RMSE) for candidate algorithms with various ramp errors in the dynamic mode

    图 28  动态数据中卫星G10和G12同时含有10 m的故障下的故障检测量

    Figure 28.  Fault detection statistics for 10 m step errors added on pseudorange of G10 and G12 in the dynamic mode

    图 29  动态数据中卫星G10和G12的伪距同时含有10 m的阶跃故障下所提算法的故障识别量

    Figure 29.  Fault identification statistics of the proposed algorithm with 10 m step errors added on the pseudorange of G10 and G12 in dynamic mode

    图 30  动态数据中卫星G10和G12的伪距同时含有10 m的阶跃故障下基于卡尔曼滤波的故障检测法的故障识别量

    Figure 30.  Fault identification statistics of KF-based method with 10 m step errors added on pseudorange of G10 and G12 in dynamic mode

    图 31  动态数据含不同大小的多故障时故障检测比率、故障识别比率和3D均方根误差

    Figure 31.  The FDR, FIR and 3D accuracy RMSE for candidate algorithms with various step errors on two satellites

    表  1  本文的实验场景

    Table  1.   The designed scenarios

    实验章节数据类型故障类型具体描述
    2.1.1节静态数据
    (采样率10 Hz)
    无故障原始的静态观测数据。
    2.1.2节单阶跃故障往卫星G09在观测时刻150~200 s(含150 s和200 s,共501个历元)内的伪距中添加阶跃故障
    2.1.3节单斜坡故障往卫星G09在观测时刻100~200 s(不含100 s,含200 s,共1 000个历元)内的伪距中添加斜坡故障
    2.1.4节多故障往卫星G09和G16在观测时刻150~200 s(含150 s和200 s,共501个历元)内的伪距中添加阶跃故障
    2.2.1节动态数据
    (采样率10 Hz)
    无故障原始的动态观测数据
    2.2.2节单阶跃故障往卫星G10在观测时刻300~400 s(含300 s和400 s,共1001个历元)内的伪距添加阶跃故障
    2.2.3节单斜坡故障往卫星G10在观测时刻400~600 s(不含400 s,含600 s,共2 000个历元)内的伪距添加斜坡故障
    2.2.4节多故障往卫星G10和G12在观测时刻400~500 s(含400 s和500 s,共1 001个历元)内的伪距中添加阶跃故障
    下载: 导出CSV

    表  2  原始静态数据的定位精度指标

    Table  2.   The positioning accuracy for the candidate algorithms based on the original static data m

    故障检测算法方向误差
    最大值
    95%分位误差均方根误差
    最小二乘残差法竖直1.4671.2940.900
    水平0.4220.3950.222
    3D1.4671.2970.927
    基于卡尔曼滤波
    的故障检测法
    竖直1.4331.2970.892
    水平0.4200.3960.222
    3D1.4341.2980.919
    所提算法竖直1.4181.1260.657
    水平0.3350.2920.191
    3D1.4201.1310.685
    下载: 导出CSV

    表  3  静态数据含5 m阶跃故障下的故障检测指标

    Table  3.   Fault detection performance for a 5 m step error added on the static data %

    故障检测
    算法
    FDRFIRFARMDR
    最小二乘残差法000100
    基于卡尔曼滤波的
    故障检测法
    000100
    所提算法10010000
    下载: 导出CSV

    表  4  静态数据含5 m阶跃故障下的定位精度指标

    Table  4.   The positioning accuracy for the candidate algorithms based on the static data with a 5 m step error m

    故障检测算法方向误差
    最大值
    95%分位误差均方根误差
    最小二乘残差法竖直5.1225.0082.174
    水平2.7942.7111.075
    3D5.7415.6642.425
    基于卡尔曼滤波
    的故障检测法
    竖直5.5565.0252.174
    水平2.9252.7041.077
    3D6.2705.6572.426
    所提算法竖直1.4181.1260.659
    水平0.3350.2860.192
    3D1.4201.1310.687
    下载: 导出CSV

    表  5  静态数据在TSE = 100 s,VSE = 0.2 m/s故障下的故障检测指标

    Table  5.   Fault detection performance for the candidate algorithms with a 0.2 m/s ramp error added for 100 s in the static mode %

    故障检测
    算法
    FDRFIRFARMDR
    最小二乘残差法57.820042.2
    基于卡尔曼滤波的
    故障检测法
    57.835.2042.2
    所提算法61.651.4038.4
    下载: 导出CSV

    表  6  静态数据在TSE = 100 s,VSE = 0.2 m/s故障下的定位精度指标

    Table  6.   The positioning accuracy for the candidate algorithms with a 0.2 m/s ramp error added for 100 s in the static mode m

    故障检测算法方向误差最
    大值
    95%分位点定
    位误差
    均方根
    误差
    最小二乘残差法竖直4.1983.5951.595
    水平6.7195.4712.006
    3D7.9236.5482.563
    基于卡尔曼滤波
    的故障检测法
    竖直3.6702.9971.357
    水平5.4444.2191.472
    3D6.5175.1612.002
    所提算法竖直1.4181.1250.657
    水平1.1500.4240.275
    3D1.4201.1340.712
    下载: 导出CSV

    表  7  静态数据中卫星G09和G16的伪距同时有5 m的阶跃故障下的故障检测指标

    Table  7.   Fault detection performance for candidate algorithms with 5 m step errors added on pseudorange of G09 and G16 in static mode %

    故障检测算法FDRFIRFARMDR
    基于卡尔曼滤波的故障检测法 0 00100
    所提算法10010000
    下载: 导出CSV

    表  8  静态数据中卫星G09和G16的伪距同时含有5 m的阶跃故障下的定位精度指标

    Table  8.   Positioning accuracy performance for candidate algorithms with 5 m step errors added on pseudorange of G09 and G16 in static mode m

    故障检测算法方向误差
    最大值
    95%分位点定位误差均方根误差
    基于卡尔曼滤波
    的故障检测法
    竖直1.4321.3010.813
    水平4.3163.9571.576
    3D4.3283.9651.773
    所提算法竖直1.4181.1250.655
    水平0.6870.5530.260
    3D1.4201.1310.704
    下载: 导出CSV

    表  9  原始动态数据的定位精度指标

    Table  9.   Positioning accuracy performance for candidate algorithms based on original dynamic data m

    故障检测算法方向误差
    最大值
    95%分位误差均方根误差
    最小二乘残差法竖直6.4814.7652.955
    水平4.5902.8811.585
    3D7.2895.0693.353
    基于卡尔曼滤波
    的故障检测法
    竖直9.9204.4662.891
    水平5.9762.9331.558
    3D11.2674.7433.284
    所提算法竖直9.9203.0071.591
    水平5.9763.2421.567
    3D11.2674.0522.233
    下载: 导出CSV

    表  10  动态数据含10 m阶跃故障下的故障检测指标

    Table  10.   Fault detection performance for candidate algorithms with a 10 m step error added on the observations in the dynamic mode %

    故障检测
    算法
    FDRFIRFARMDR
    最小二乘残差法98.756.401.3
    基于卡尔曼滤波的
    故障检测法
    000100
    所提算法10010000
    下载: 导出CSV

    表  11  动态数据含10 m阶跃故障下的定位精度指标

    Table  11.   Positioning accuracy performance for candidate algorithms with a 10 m step error added on observations in dynamic mode m

    故障检测算法方向误差
    最大值
    95%分位误差均方根误差
    最小二乘残差法竖直22.46014.0694.800
    水平4.5902.9471.635
    3D22.66814.4015.071
    基于卡尔曼滤波
    的故障检测法
    竖直18.82314.6226.180
    水平5.9763.0201.646
    3D19.23914.8546.396
    所提算法竖直9.9204.8582.600
    水平5.9765.2391.592
    3D11.2673.2083.049
    下载: 导出CSV

    表  12  动态数据在${{\boldsymbol{T}}_{{\bf{SE}}}} $= 200 s,${{\boldsymbol{V}}_{{\bf{SE}}}} $ = 0.2 m/s故障下的故障检测指标

    Table  12.   Fault detection performance for candidate algorithm with a 0.2 m/s ramp error added for 200 s in dynamic mode %

    故障检测
    算法
    FDRFIRFARMDR
    最小二乘残差法75.138.2024.9
    基于卡尔曼滤波的
    故障检测法
    66.7554.3033.25
    所提算法66.2566.25033.75
    下载: 导出CSV

    表  13  动态数据在${{\boldsymbol{T}}_{{\bf{SE}}}} $= 200 s,${{\boldsymbol{V}}_{{\bf{SE}}}}$ = 0.2 m/s故障下定位精度指标

    Table  13.   Positioning accuracy for candidate algorithms with a 0.2 m/s ramp error added for 200 s indynamic mode m

    故障检测算法方向误差最大值95%分位误差均方根误差
    最小二乘残差法竖直18.7434.5702.575
    水平11.8458.7433.385
    3D20.6818.8144.253
    基于卡尔曼滤波
    的故障检测法
    竖直9.9204.4532.776
    水平8.8455.9562.429
    3D11.2676.1243.689
    所提算法竖直9.9203.9421.975
    水平5.9763.3471.616
    3D11.2674.6292.552
    下载: 导出CSV

    表  14  动态数据中卫星G10和G12的伪距同时含有10 m阶跃故障下的故障检测指标

    Table  14.   Fault detection performance for candidate algorithms with 10 m step errors added on pseudorange of G10 and G12 in dynamic mode %

    故障检测
    算法
    FDRFIRFARMDR
    基于卡尔曼滤波的
    故障检测法
    3.70096.3
    所提算法10085.600
    下载: 导出CSV

    表  15  动态数据中卫星G10和G12的伪距同时含有10 m的故障下的定位精度指标

    Table  15.   Positioning accuracy performance for candidate algorithms with 10 m step errors added on pseudorange of G10 and G12 in dynamic mode m

    故障检测算法方向误差
    最大值
    95%分位误差均方根误差
    基于卡尔曼滤波
    的故障检测法
    竖直17.31615.2376.382
    水平5.9763.0181.756
    3D17.47615.4966.618
    所提算法竖直11.8514.1182.064
    水平5.9763.3401.654
    3D12.5725.1022.645
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-05-06
  • 录用日期:  2021-08-09
  • 网络出版日期:  2021-09-14
  • 整期出版日期:  2023-02-28

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