ZHENG Jia-xing, WU Wei, DAI Dong-kai

(College of Opto-Electronic Science and Engineering, National University of Defense Technology, Changsha 410073, China)

Influences of time synchronization error on angular flexure measurement of ship hull

ZHENG Jia-xing, WU Wei, DAI Dong-kai

(College of Opto-Electronic Science and Engineering, National University of Defense Technology, Changsha 410073, China)

For ship angular flexure measurement based on the ring laser units, the effects of time synchronization error between the two ring laser gyro units are analyzed and evaluated, and an algorithm is proposed to estimate the time synchronization error online. The inertial-frame attitude matching equation considering the time synchronization error is derived, which shows that the time synchronization error will result in extra fluctuation errors of Kalman filter observation as the ship moves in response of the motion of the waves and thus significantly degrade the accuracy of ship angular flexure measurement. In addition, based on the derived inertial-frame attitude matching equation, the delay state is augmented into conventional linear state equations, thus the time synchronization error can be estimated via Kalman filtering. Numerical simulations are carried out with the measured ship attitude data and the angular flexure data of ‘Yuan-Wang Ship’. The simulation results validate the effectiveness of the proposed time-delay estimation method and show that the longer time delay will result in the bigger angular flexure measurement error.

ship angular flexure measurement; time synchronization; ring laser gyro; attitude matching

The attitude of shipboard apparatus (radar antennas, optical systems, etc.), acquired from the central master inertial navigation system, may be corrupted significantly by the existence of ship angular flexure, thereby the ship angular flexure should be measured accurately.

Due to the reliable performance, the ring laser gyro units (LGUs) are attractive for ship angular flexure measurement[6], where the angular rate matching method[1-2]or the attitude matching method[3-5]may be applied to estimate the angular flexure via Kalman filtering. In this paper, based on the newly developed attitude matching method[3], the revised inertial-frame attitude matching equation considering the time synchronization error is strictly derived, from which the influences of time synchronization error between the two LGUs are assessed analytically. Additionally, to reduce the timesynchronization error’s influences on ship angular flexure measurement, an error compensation method is devised based on the delay state augmentation and the revised inertial-frame attitude matching equation. Finally, based on the real measured ship attitude data and angular flexure data of ‘Yuan-Wang Ship’, numerical simulations are carried out to assess the influences of the time synchronization error on ship angular flexure measurement and validate the effectiveness of the proposed time-delay estimation method.

1 Derivation of the revised attitude matching equation

LGU1 and LGU2 are rigidly fixed near the central MINS and any peripheral device, respectively. The angular misalignment (i.e. ship angular flexure) between LGU1 and LGU2 can be estimated via Kalman filtering based on the successive outputs of LGUs.

Equation (2) may be rearranged to give:

This Equation may be rearranged to give:

Rearranging gives:

Assuming that the corresponding Euler rotation angles are small, these DCMs can be approximated as skew symmetric matrices, as follows:

Substituting Equation (10) into Equation (9), rearranging and ignoring product terms, gives:

It can be shown from an element by element comparison that the above equation may be expressed invector form as:

2 T ime-delay estimation model

To reduce the ship angular flexure measurement errors induced by the time-delay, an error compensation method is devised based on the delay state augmentation and the revised inertial-frame attitude matching equation.

The small angular misalignment termis proportional to the angular turn ratessensed by LGU1. Substituting, and writing,and, Equation (12) may be expressed as:

The time delayδmay be modeled as a random constant (actually it’s a slow-varying bias):

Whereek-1,ek′′-1andek′′′-1are assumed to be white noises, andhis the period of Kalman filtering.

Equation (14), Equation (15) and Equation (16) may be combined to form the augmented Kalman filter model as follows:

Where

3 Simulation results

Numerical simulations are carried out to assess the influences of time synchronization error on ship angular flexure measurement and validate the effectiveness of the proposed time-delay estimation method.

3.1 Simulation conditions

Ship motions and angular flexure are both generated based on the real ship data of the ‘YUAN-WANG’ space instrumentation ship in which the attitude data may be acquired from the central main inertial navigation system and the angular flexure is the output of the ‘Optical Deformation Measurement System’. Fig.1 and Fig.2 show 300s-long real measured ship attitude data and the synchronized angular flexure data.

LGU1’s attitude may be simulated by the real attitude data (shown in Fig.1). The angular misalignment between the two LGUs may be simulated by the real angular data (shown in Fig.2) plus a constant angular misalignment (installation misalignment). The installation misalignment is set to 0.1° along each axis. Based on the simulated LGUs’ attitude data, the gyro data outputs may be calculated, and the two LGUs’ gyro bias difference is set to 0.01(°)/h.

Fig.1 Ship attitude

Fig.2 Ship angular flexure

3.2 Effects of the time synchronization error

To strictly assess the influences of the time synchronization error, a group of simulations are carried out where the time delays ranges from -2 ms to 2 ms, as shown in Fig.3. The corresponding root mean square angular flexure estimation errors are illustrated in Fig.4.

Fig.3 Angular flexure errors

Fig.4 Root mean square errors of flexure

From Fig.4, the time synchronization error degrades angular flexure estimation significantly, and the longer time delay may result in the bigger angular flexure error. Additionally, it’s clear that if the time delay is shorter than 0.2 ms, the change of the root mean square flexure error is less than 5″.

3.3 T ime delay estimation

Based on the augmented Kalman filter model provided by Equation (17) and Equation (18), the time delay may be estimated in less than 20 s as illustrated in Fig.5, where the time delay ranges from -10 ms to 10 ms. The corresponding time delay estimation errors are illustrated in Fig.6.

From Fig.6, the time delay estimation error may be less than 0.2 ms, implying that with the time delay compensation, the time synchronization error has little influence on ship angular flexure measurement.

Fig.5 Time-delay estimation results

Fig.6 Time-delay estimation errors

4 Conclusions

The revised inertial-frame attitude matching equation considering the time synchronization error has been strictly derived, from which the influences of the time synchronization error between the two LGUs are assessed analytically. The time synchronization error degrades the angular flexure estimation significantly, and the longer time delay may result in bigger angular flexure error.

To reduce the time synchronization error influences on ship angular flexure measurement, an error compensation method is devised based on the delay state augmentation and the revised inertial-frame attitude matching equation. With the time delay compensation, the time synchronization error has little influence on ship angular flexure measurement.

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1005-6734(2017)02-0151-05

時(shí)間同步誤差對船體角形變測量的影響

鄭佳興，吳 偉，戴東凱

（國防科技大學(xué) 光電科學(xué)與工程學(xué)院，長沙 410073）

針對激光陀螺船體角形變測量，分析評估了兩組激光陀螺組合體時(shí)間同步誤差的影響，并提出了一種時(shí)間同步誤差的在線估計(jì)算法。嚴(yán)格推導(dǎo)了考慮了時(shí)間同步誤差的慣性姿態(tài)匹配方程，從方程可見，船體在波浪搖擺條件下時(shí)間同步誤差將導(dǎo)致額外的 Kalman濾波觀測量波動(dòng)誤差，直接影響船體角形變測量精度。另一方面，基于新推導(dǎo)的慣性姿態(tài)匹配方程，在濾波狀態(tài)中增加時(shí)間延遲變量，通過Kalman濾波能夠在線估計(jì)時(shí)間延遲大小?；趯?shí)測遠(yuǎn)望船體姿態(tài)和角變形數(shù)據(jù)進(jìn)行了仿真，仿真測試表明大的時(shí)間延遲將導(dǎo)致大的船體角形變測量誤差，同時(shí)驗(yàn)證了時(shí)間延遲在線估計(jì)方法的有效性。

船體角形變測量；時(shí)間同步；激光陀螺；姿態(tài)匹配

U666.1

A

2017-01-16；

2017-03-24

國家自然科學(xué)基金（61275002）

鄭佳興（1984—），男，工學(xué)博士，講師，從事慣性技術(shù)應(yīng)用研究。E-mail: 362422833@qq.com

10.13695/j.cnki.12-1222/o3.2017.02.003