IMU Errors and Rectification


[TOC]

Overview

  • 确定性误差(六面法 标定)
    • 开机后恒定的零偏误差(bias)
    • 比例因子误差(scale factor)
    • 轴偏及非正交误差(misalignment errors and non-orthogonality)
    • 非线性误差(non-linearity)
    • 温度误差(thermal noise)
    • 陀螺仪还包含加速度的变化引起的误差(g-dependent noise)
  • 随机性误差(Allan方差 标定)
    • 高斯白噪声(Noise Density)
    • 零偏不稳定性(Bias Instability or Random Walk)


IMU Stochastic Errors

  • a high frequency additive White Noise
  • a slower varying sensor Bias

continuous-time model:

Ref:

How To Get

the Datasheet of the IMU

  • White Noise Terms
    • Rate Noise Density (Angular Random Walk - ARW)
    • Acceleration Noise Density (Velocity Random Walk - VRW)
  • Bias Terms
    • In-Run Bias (Bias Stability)

the Allan standard deviation (AD)

  • “white noise” is at tau=1 (slope -1/2 in a log-log AD plot)
  • “random walk” is at tau=3 (slope +1/2 in a log-log AD plot)

Noise Samples (Continuous-time)

  • MPU6000 / MPU6050

    core_noise_acc: 0.003924    # [m/s^2/sqrt(Hz)] mpu6000 datasheet
    core_noise_gyr: 0.00008726  # [rad/s/sqrt(Hz)] mpu6000 datasheet
    
  • ADIS 16448

    # avg-axis
    gyr_n: 1.8582082627718251e-04
    gyr_w: 7.2451532648461174e-05
    acc_n: 1.9862287242243099e-03
    acc_w: 1.2148497781522122e-03
    
  • MYNT-EYE-S1030 IMU

    gyr_n: 0.00888232829671
    gyr_w: 0.000379565782927
    acc_n: 0.0268014618074
    acc_w: 0.00262960861593
    

Performance Analysis Software

  • IMU-TK: Inertial Measurement Unit ToolKit
  • gaowenliang/imu_utils: A ROS package tool to analyze the IMU performance
    <?xml version="1.0"?>
    <launch>
        <node pkg="imu_utils" type="imu_an" name="imu_an" output="screen">
            <param name="imu_topic" type="string" value= "/camera/imu/data_raw"/>
            <param name="imu_name" type="string" value= "ZR300"/>
            <param name="data_save_path" type="string" value= "$(find imu_utils)/data/"/>
            <param name="max_time_min" type="int" value= "80"/>
            <param name="max_cluster" type="int" value= "100"/>
        </node>
    </launch>
    
  • rpng/kalibr_allan: IMU Allan standard deviation charts for use with Kalibr and inertial kalman filters
  • XinLiGH/GyroAllan: 陀螺仪随机误差的 Allan 方差分析
  • AllanTools: A python library for calculating Allan deviation and related time & frequency statistics.

Reference




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