International Journal of Naval Architecture and Ocean Engineering.
2014.
Sep,
6(3):
626-637

This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

- Published : September 30, 2014

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INTRODUCTION

On ship, high accurate information from Master Inertial Navigation System (MINS) can be used to fulfill initial alignment for Slave Inertial Navigation System (SINS) composed of low or medium inertial sensors (
Titterton and Weston, 2004
;
Wan and Fang, 1998
;
Kain and Cloutier, 1989
;
Shortelle et al., 1998
;
Grewal et al., 1991
). In the integrated system of M/S INS, Kalman filter is often used as an observer, and the differences of velocity, attitude, angular rate and acceleration between MINS and SINS are used as measurement data (
Titterton and Weston, 2004
;
Wan and Fang, 1998
).
In the M/S integration, the acceleration or velocity matching method can achieve its alignment goal in horizontal linear accelerated motion, as the angular rate or attitude matching method can do in horizontal angular motion (
Lyou and Lim, 2009
;
Yu, 1988
). A transfer alignment system based on combined matching methods can optimize the Kalman filter to outperform all others in arbitrary motions (
Lyou and Lim, 2009
;
Yu, 1988
). The best combined matching scheme is known to be the velocity plus attitude, or angular rate plus acceleration (
Lyou and Lim, 2009
;
Yu, 1988
;
Wan and Liu, 2005
;
Xiong et al., 2006
;
GoshenMeskin and Bar-Itazhack, 1992a
;
1992b
). Flexure deformation, lever-arm velocity and time-delay are known as major error sources for velocity and attitude matching (
Lyou and Lim, 2009
;
Yu, 1988
;
Wan and Liu, 2005
), as instrument error, noise and time-delay are for angular rate plus acceleration (
Yu, 1988
;
Hu et al., 2005
;
Huang et al., 2005
;
Lim and Lyou, 2002
).
Wan and Liu (2005)
gave the measurement data about deck flexure deformation of a medium-sized ship at six sea situation. The deformation around y-axis is 0.05~0.08° when it is about ±1.5
ATTITUDE MATCHING ERROR CAUSED BY FLEXURE DEFORMATION

- Attitude matching algorithm with no flexure deformation

Ship-based MINS is usually installed at the swing center to measure the overall attitude, velocity and position information, while SINS is usually installed at the head or tail of the ship to measure the attitude and velocity information of the installing position. The schematic diagram of the deck flexure deformation between MINS and SINS is shown in
Fig. 1
, where m is the MINS body frame, s is the SINS body frame, n is the local horizontal-geographical coordinate frame and navigation frame. In
Figs. 1(a)
and
(b)
denote the decks without and with flexure deformation. To a specific ship with limited size, the MINS and SINS have the same navigation frames.
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- Attitude matching algorithm with flexure deformation

As shown in
Fig. 1(b)
, m' is the flexural body frame and
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VELOCITY MATCHING ERROR CAUSED BY FLEXURE DEFORMATION

- Lever-arm velocity calculation between MINS and SINS

The installation relationship between MINS and SINS is shown in
Fig. 2
, where i is inertial frame;
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- Lever-arm velocity error caused by flexure deformation

Taking the flexure deformation around x-axis as an example, the lever-arm change caused by flexure deformation is shown in
Fig. 3
. In this figure,
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DESIGN OFH∞FILTER

- SINS error equations

System’s state equation and measurement equation are as follows:
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- Velocity error equation can be expressed as follows:

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- H∞sub-optimal filtering equation

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SIMULATION

- Simulation schemes

Ship swinging and translational motions are produced by motion trace simulator, and these motions are used as angle and velocity output by MINS.
Second-order Markov process is used to produce ship body flexure deformation and the flexure deformation angle added MINS angle are used as ideal angle output of SINS. Named lever-arm and flexure deformation angle are used to produce real lever-arm. Then lever-arm velocity can be calculated by real-lever arm size and angular rate of MINS. Lever-arm velocity added the velocity of MINS is used as ideal velocity output by SINS. The ideal inertial unit output of SINS can be calculated by these ideal outputs of SINS with back-stepping navigation solution, and these ideal inertial unit output added white noise are used as the real inertial unit output. With these inertial outputs, SINS solving can be carried, the accuracy of solution and the following filters can be evaluated by comparing these solving output with the ideal output.
Three simulation schemes are established, which are known flexure deformation and the standard Kalman filter, unknown flexure deformation and standard Kalman filter and unknown flexure deformation and
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- Simulation settings

In the simulation, the ship is assumed to be sailing 45° north by east at the speed of 5
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- Results and analysis

The simulation lasts 5,400
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Statistic of error (unit: angle (arc-min) and velocity (m/s)).

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CONCLUSION

On ship, especially on large ship, flexure deformation and lever-arm effect are the key factors which decide the actual accuracy of integrated system of M/S INS. Attitude and velocity matching errors caused by deformation is analyzed and simulation results indicate that with “attitude plus velocity”, effective combination of M/S INS cannot be fulfilled. To solve this problem, the
Acknowledgements

This work was supported in part by the National Natural Science Foundation (61004125, 61273056) and Chinese university research and operation expenses (104.205.2.5).

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Citing '$H_{\infty}$ filter for flexure deformation and lever arm effect compensation in M/S INS integration
'

@article{ E1JSE6_2014_v6n3_626}
,title={$H_{\infty}$ filter for flexure deformation and lever arm effect compensation in M/S INS integration}
,volume={3}
, number= {3}
, journal={International Journal of Naval Architecture and Ocean Engineering}
, publisher={The Society of Naval Architects of Korea}
, author={Liu, Xixiang
and
Xu, Xiaosu
and
Wang, Lihui
and
Li, Yinyin
and
Liu, Yiting}
, year={2014}
, month={Sep}