IMU Errors Analysis

[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:

• IMU Noise Model (kalibr)

• IMU Noise Model（游）

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

• IMU误差模型与校准