Inertial Measurement Unit Error Modeling Tutorial: Inertial Navigation System State Estimation with Real-Time Sensor Calibration

Abstract

Autonomous vehicle technology is rapidly advancing (see “Summary”). A key enabling factor is the advancing capabilities and declining cost of computing and sensing systems that enable sensor fusion for awareness of the vehicle’s state and surroundings (see “Nontechnical Article Summary”). For control purposes, the vehicle’s state must be estimated accurately, reliably, at a sufficiently high sample rate, and with a sufficiently high bandwidth. For systems with a high bandwidth, these requirements are often achieved by an aided inertial navigation system (INS) (see “Aided Inertial Navigation System History”) <xref ref-type="bibr" rid="ref1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[1]</xref> , <xref ref-type="bibr" rid="ref2" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[2]</xref> , <xref ref-type="bibr" rid="ref3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[3]</xref> , <xref ref-type="bibr" rid="ref4" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[4]</xref> , <xref ref-type="bibr" rid="ref5" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[5]</xref> , <xref ref-type="bibr" rid="ref6" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[6]</xref> . An INS integrates data from an inertial measurement unit (IMU) through a kinematic model at the high sampling rate of the IMU to compute the state estimate. An aided INS corrects this state estimate using data from aiding sensors [for example, vision, lidar, radar, and global navigation satellite systems (GNSS)]. State estimation by sensor fusion may be accomplished using a variety of methods: Kalman filter (KF) <xref ref-type="bibr" rid="ref7" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[7]</xref> , <xref ref-type="bibr" rid="ref8" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[8]</xref> , <xref ref-type="bibr" rid="ref9" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[9]</xref> , <xref ref-type="bibr" rid="ref10" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[10]</xref> , <xref ref-type="bibr" rid="ref11" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[11]</xref> , extended KF (EKF) <xref ref-type="bibr" rid="ref12" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[12]</xref> , <xref ref-type="bibr" rid="ref13" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[13]</xref> , <xref ref-type="bibr" rid="ref14" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[14]</xref> , <xref ref-type="bibr" rid="ref15" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[15]</xref> , unscented KF (UKF) <xref ref-type="bibr" rid="ref16" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[16]</xref> , <xref ref-type="bibr" rid="ref17" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[17]</xref> , <xref ref-type="bibr" rid="ref18" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[18]</xref> , particle filter (PF) <xref ref-type="bibr" rid="ref19" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[19]</xref> , <xref ref-type="bibr" rid="ref20" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[20]</xref> , <xref ref-type="bibr" rid="ref21" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[21]</xref> , and maximum a posteriori (MAP) optimization <xref ref-type="bibr" rid="ref22" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[22]</xref> , <xref ref-type="bibr" rid="ref23" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[23]</xref> , <xref ref-type="bibr" rid="ref24" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[24]</xref> , <xref ref-type="bibr" rid="ref25" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[25]</xref> , <xref ref-type="bibr" rid="ref26" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[26]</xref> , <xref ref-type="bibr" rid="ref27" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[27]</xref> .