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Research ArticleOriginal Article
Open Access

An efficient tuning framework for Kalman filter parameter optimization using design of experiments and genetic algorithms

Alan Zhang and Mohamed Maher Atia
NAVIGATION: Journal of the Institute of Navigation December 2020, 67 (4) 775-793; DOI: https://doi.org/10.1002/navi.399
Alan Zhang
1Department of Systems and Computer Engineering, Carleton University Embedded and Multi-sensor Systems Lab, Carleton University, 1125 Colonel By Drive, Ottawa, ON K1S 5B6, Canada
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  • For correspondence: [email protected]
Mohamed Maher Atia
2Department of Systems and Computer Engineering, Carleton University Embedded and Multi-sensor Systems Lab, Carleton University, 1125 Colonel By Drive, Ottawa, ON K1S 5B6, Canada
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  • FIGURE 1
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    FIGURE 1

    Sensor fusion system

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    FIGURE 2

    Block diagram of tuning framework

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    FIGURE 3

    EKF Block Diagram

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    FIGURE 4

    Standard GA results

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    FIGURE 5

    Hardware setup

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    FIGURE 6

    Tuning Trajectory

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    FIGURE 7

    Simulated (left) and Real (right) nominal results with error plots

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    FIGURE 8

    Multiple GA runs for simulations and real data

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    FIGURE 9

    Simulated (left) and Real (right) GA results with error plots, comparison with Nominal results

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    FIGURE 10

    DoE parameter impact results

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    FIGURE 11

    Multiple DoE enhanced GA runs for simulated and real data

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    FIGURE 12

    Simulated (left) and Real Data (right) GA with DoE results with error plots, comparison with GA results

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    FIGURE 13

    IMU biases convergence to the true bias values in the simulated IMU data

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    FIGURE 14

    Trajectories used

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    FIGURE 15

    Tuning dataset (red), Test set #1 (yellow), and Test set #2 (blue) overlaid on Google Maps

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    FIGURE 16

    Pose Errors for Test set #1

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    FIGURE 17

    Pose Errors for Test set #2

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    FIGURE 18

    Innovations for Tuning Dataset

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    FIGURE 19

    Innovations for Test set #1

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    FIGURE 20

    Innovations for Test set #2

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    FIGURE 21

    IMU Bias for Tuning Dataset

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    FIGURE 22

    IMU Biases for Test set #1

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    FIGURE 23

    IMU Biases for Test set #2

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    FIGURE 24

    Outage Test for Test set #1

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    FIGURE 25

    DoE results on varying parameter configurations

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    FIGURE 26

    RMSE vs 6 selected parameters for 50 randomized parameter configurations

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    FIGURE 27

    RMSE vs 6 selected parameters for 50 randomized parameter configurations (zoomed in)

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    TABLE 1

    Nominal Parameters

    GM Standard DeviationGM Time Constant (s)AV Random Walk
    XYZXYZXYZ
    Gyro (rad/s)0.0340.0280.0255194406274390.130.140.14
    Accel (m/s2)0.0070.0340.00336191023263190.020.020.03
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    TABLE 2

    Nominal RMSE Results

    RMSESimulatedReal
    Position (m)Velocity (m/s)Orientation (deg)Position (m)Velocity (m/s)Orientation (deg)
    E/R0.950.340.280.860.320.59
    N/P1.350.430.422.200.660.51
    U/Y1.210.186.810.550.117.88
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    TABLE 3

    GA-tuned RMSE results

    RMSESimulated DataReal Data
    Position (m)Velocity (m/s)Orientation (deg)Position (m)Velocity (m/s)Orientation (deg)
    E/R0.050.030.070.110.100.50
    N/P0.070.050.100.290.180.33
    U/Y0.070.020.270.140.082.66
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    TABLE 4

    GA with DoE tuned RMSE results

    RMSESimulatedReal
    Position (m)Velocity (m/s)Orientation (deg)Position (m)Velocity (m/s)Orientation (deg)
    E/R0.030.030.090.200.120.48
    N/P0.040.040.080.090.080.33
    U/Y0.050.020.400.080.082.28
    RMSEGNSS Only (Single Point L1)
    Position (m)Velocity (m/s)
    E1.920.71
    N1.510.48
    U2.070.9
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    TABLE 5

    Datasets used

    Duration of data collection (s)Distance driven (m)
    Tuning dataset3104,541.93
    Test set #12001,905.83
    Test set #21701,748.10
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    TABLE 6

    RMSE results for Test sets

    RMSETest set #1Test set #2
    Position (m)Velocity (m/s)Orientation (deg) Position (m)Velocity (m/s)Orientation (deg)
    E/R0.080.090.340.100.100.44
    N/P0.050.070.310.070.080.65
    U/Y0.070.071.640.070.082.33
    RMSEGNSS Only (Single Point L1)GNSS Only (Single Point L1)
    Position (m)Velocity (m/s)Position (m)Velocity (m/s)
    E1.70.410.70.31
    N1.510.381.910.48
    U2.010.82.910.82

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NAVIGATION: Journal of the Institute of Navigation: 67 (4)
NAVIGATION: Journal of the Institute of Navigation
Vol. 67, Issue 4
Winter 2020
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An efficient tuning framework for Kalman filter parameter optimization using design of experiments and genetic algorithms
Alan Zhang, Mohamed Maher Atia
NAVIGATION: Journal of the Institute of Navigation Dec 2020, 67 (4) 775-793; DOI: 10.1002/navi.399

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An efficient tuning framework for Kalman filter parameter optimization using design of experiments and genetic algorithms
Alan Zhang, Mohamed Maher Atia
NAVIGATION: Journal of the Institute of Navigation Dec 2020, 67 (4) 775-793; DOI: 10.1002/navi.399
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Keywords

  • extended Kalman Filter < Multisensor Navigation
  • genetic algorithm < Algorithms and Methods
  • tightly-coupled data fusion < Land Based Applications

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