Citation: Xing, J.; Yang, G.; Cai, T.
Modeling and Calibration for
Dithering of MDRLG and
Time-Delay of Accelerometer in SINS.
Sensors 2022, 22, 278. https://
doi.org/10.3390/s22010278
Academic Editors: Kamil Krasuski
and Damian Wierzbicki
Received: 23 November 2021
Accepted: 28 December 2021
Published: 30 December 2021
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Article
Modeling and Calibration for Dithering of MDRLG and
Time-Delay of Accelerometer in SINS
Jinlong Xing
1,†
, Gongliu Yang
1,2,†
and Tijing Cai
1,
*
1
School of Instrument Science and Engineering, Southeast University, Nanjing 210018, China;
230198299@seu.edu.cn (J.X.); yanggongliu@buaa.edu.cn (G.Y.)
2
School of Instrumentation and Optoelectronic Engineering, Beihang University, Beijing 100191, China
* Correspondence: caitij@seu.edu.cn
† These authors contributed equally to this work.
Abstract:
At present, the design and manufacturing technology of mechanically dithered ring laser
gyroscope (MDRLG) have matured, the strapdown inertial navigation systems (SINS) with MDRLG
have been widely used in military and business scope. When the MDRLG is working, high-frequency
dithering is introduced, which will cause the size effect error of the accelerometer. The accelerometer
signal has a time delay relative to the system, which will cause the accelerometer time delay error.
In this article, in order to solve the above-mentioned problem: (1) we model the size effect error
of the mechanically dithering of the MDRLG and perform an error analysis for the size effect error
of the mechanically dithering of the MDRLG; (2) we model the time delay error of accelerometer
and perform an error analysis for the time delay error of accelerometer; (3) we derive a continuous
linear 43-D SINS error model considering the above-mentioned two error parameters and expand the
temperature coefficients of accelerometers, inner lever arm error, outer lever arm error parameters
to achieve high-precision calibration of SINS. We use the piecewise linear constant system (PWCS)
method during the calibration process to prove that all calibration parameters are observable. Finally,
the SINS with MDRLG is used in laboratory conditions to test the validity of the calibration method.
Keywords: size effect; system-level calibration; inertia lnavigation; lasergyro; dither
1. Introduction
Error parameters of the inertial device are important factors affecting the navigation
accuracy of SINS. Any small error parameter of the inertial device will cause a large navi-
gation error through the divergence of the algorithm error, which needs to be compensated
by calibration. Error parameter calibration methods mainly include discrete calibration
and systematic calibration. The discrete calibration relies on the accurate azimuth, position,
and angular rate reference provided by the high-precision turntable, and by referring to the
local gravity acceleration and the earth’s rotation angular rate, placing the IMU in different
positions can calibrate the error terms of the gyroscopes and accelerometers [
1
,
2
]. However,
the calibration accuracy of the discrete calibration is fundamentally limited by the accuracy
of the turntable [
3
], and the cost of high-precision turntable equipment is too high, which
makes it difficult to greatly improve the accuracy of the discrete calibration.
The systematic calibration method is the process of estimating the SINS error pa-
rameters from the navigation error (attitude error, velocity error, position error) of the
SINS that is based on the error model of the SINS. Systematic calibration does not rely on
high-precision turntables, so it has been widely used in self-calibration and field calibration
of SINS. Pittman [
4
] pointed out the four major advantages of the systematic calibration
method: it can realize the on-site calibration of the SINS; it can realize the self-calibration
of the SINS; it does not require high-precision turntables and other high-precision test
equipment; it does not need to measure and record the output of the gyroscope or ac-
celerometer. At present, the research on systematic calibration mainly focuses on the
Sensors 2022, 22, 278. https://doi.org/10.3390/s22010278 https://www.mdpi.com/journal/sensors
