Initial alignment of SINS on revolving base for antenna tracking stabilized platform

ZHANG Hua-qiang,XU Jing,ZHAO Yan

(1.School of Mechanical Engineering,Shandong University of Technology,Zibo 255049,China;2.School of Materials Science and Engineering,Shandong University of Technology,Zibo 255049,China;3.Beijing University of Aeronautics and Astronautics,Beijing 100191,China)

Initial alignment of SINS on revolving base for antenna tracking stabilized platform

ZHANG Hua-qiang1,XU Jing2,ZHAO Yan3

(1.School of Mechanical Engineering,Shandong University of Technology,Zibo 255049,China;2.School of Materials Science and Engineering,Shandong University of Technology,Zibo 255049,China;3.Beijing University of Aeronautics and Astronautics,Beijing 100191,China)

In order to improve the initial alignment precision of strapdown inertial navigation system(SINS) and reduce the initial alignment time,an initial alignment scheme based on revolving base is put forward according to the antenna tracking stabilized platform structure.Then the initial alignment mathematical models based on revolving base are built.The singular value decomposition(SVD) method is used to analyze the observability of SINS initial alignment.The experimental results show that the revolving base alignment method can improve observability degree of SINS,which can significantly improve the alignment precision and reduce the initial alignment time compared with stationary base alignment method.

revolving base;initial alignment;SINS;SVD;observability analysis

The attitude change of mobile carrier affects the pointing of satellite communication antenna,keeping the antenna platform stability is key technology of eliminating this disturbance.And the core technology of stabilized platform is attitude measurement and control of mobile carrier.

The SINS can measure the acceleration of the mobile carrier,after the acceleration integral,the carrier’s velocity and position can be calculated,so the initial value of integral which includes initial velocity and initial position must be known[1].If SINS takes the geography frame as navigation frame,either physics platform or math platform is chosen as the measurement benchmark of acceleration,the platform must be tracedto the geography frame accurately in order to reduce the acceleration measurement error.The three axes’ point of platform is discretionary after the SINS start-up,so it is need to align the three axes’ point of platform before navigation,which is called SINS initial alignment.The SINS initial alignment precision can directly affect the navigation precision,besides the time of initial alignment is another key index of SINS.

The organization of this paper proceeds as follows.In the next section,the scheme and structure design of revolving base alignment will be introduced.In section 3,the mathematic analysis of SINS initial alignment based on revolving base will be performed,which include the error model of SINS,the state and measurement equation,the observability analysis based on SVD method.At the last section,the experiment and analysis are presented.

1 The Scheme and Structure Design of Revolving Base Alignment

1.1 The scheme of revolving base alignment

In Ref.[2],the navigation system state vector is totally observable in the two-position initial alignment by changing azimuth,and the initial alignment precision especially the azimuth estimation precision can be improved effectively.After analyzing pertinent references [1,3-6],it can be concluded that the estimation precision of system state vector can be improved by changing azimuth.But only a few angles are changed in SINS multi-position initial alignment,so if more angles are changed,the estimation precision will be further improved.

The revolution-modulation principle of SINS is simple,and the implementation method is various[4].In this paper,the SINS will be rotated as a whole system,which is called system revolution-modulation.This scheme can be implemented simply in engineering and the SINS sensors’ orthogonality can be ensured easily.

According to the stabilized platform structure of antenna,which can rotate around the azimuth axis,a new initial alignment method based on revolving base is put forward in this paper.The scheme can be described as follows:

The definition of various coordinate frames are given as[8]:sensor frame s,body frame b,navigation frame n,the revolving base rotates around axiszwith angle velocityω.So the transformation matrix between the sensor frame s and body frame b has the following form:

The gyro and the accelerometer errors on the sensor frame can be described as:

According to Eq.(1),the gyro and the accelerometer errors on body frame can be written as:

Eq.(4) and Eq.(5) are the SINS error modulation principle based on revolving base.When the antenna platform rotates aroundzaxis with angle velocityω,the inertial devices errors onxaxis andyaxis but notzaxis are modulated to trigonometric function.If the rotation time is (2π?ω),the integral result of scale coefficient errors,the installation errors and the biases are zeros,so this method can eliminate the non-random errors by integral[8],which can improve the initial alignment precision.

1.2 The structure and navigation algorithm of revolving base alignment

According to the tracking stabilized platform structure and working principle of antenna,the SINS can be fixed on antenna platform base as shown in Fig.1.

Fig.1 The structure of SINS initial alignment revolving base

The SINS can rotate aroundzaxis with the rotation of antenna platform base,so the method of initial alignment based on revolving base can be used here.

2 The mathematic analysis of SINS initial alignment based on revolving base

2.1 The error model of SINS

For the SINS initial alignment based on revolving base,the carrier is stationary,so the error equations of the initial alignment based on revolving base can be simplified as follows.

The misalignment angle equation can be described as:

The position error equation can be written as:

In order to define the relationship of inertial device random errors between navigation frame and sensor frame,the following relationship can be used:

2.2 The state and measurement equations

Generally,the first stage of SINS initial alignment is coarse alignment,which can be accomplished by least square method[9],all the state vector errors are very little after coarse alignment[10],so the SINS initial alignment error model can be considered as a liner model.

In order to shorten the alignment time and improve the filtering speed,the dimension of filter must be reduced.The position error can be ignored in the error model because the SINS position is known accurately when the SINS initial alignment.Because the SINS is not stable on vertical direction,so only the velocity error and accelerometer error on horizontal plane are used in SINS error model.The dimension of the SINS state vector can be reduced from fifteen to ten.In the navigation frame,the SINS initial alignment error model can be described as[11-14]:

During the initial alignment,two velocity errors δVEand δVNon horizontal plane are considered as measurements.So the measurement equation of SINS[13-15]can be expressed as:

2.3 The observability analysis of SINS initial alignment based on SVD method

The observability can reflect the estimate ability of the system state.The precision and efficiency of state estimation are affected by system observability degree[16].Eq.(11) and Eq.(13) can formulate the state equation and measurement equation of SINS initial alignment based on revolving base as follows:

The linear system can be seemed to stabilization system in limited time interval,which can be analyzed as piece wise constant system (PWCS)[3].If Stripped observability matrix (SOM) extracted from Total observability matrix (TOM) is used to analyze thesystem observability substituted the TOM,the analysis process will be simplified greatly[13].

For the system of [A(t),H],the observability matrixQjofcan be described as:

采用SPSS 21.0統計學軟件對本組研究對象的臨床數據進行分析統計工作,以均數±標準差表示計量數據,以t檢驗;計數資料采用[n(%)]表示,采用卡方檢驗。若p<0.05,則表示組間數據對比差異顯著,有統計學意義。

The TOMQ(j) and SOMcan be determined using the following equations:

Using SVD method[13],the matrixR(m×n) can be factorized as:

whereU=[u1,u2,…,um]andV=[v1,v2,…,vt]are unitary matrixes.,,is theith singular value.

The SVD method is more suitable for analyzing observability degree of PWCS,and the step can be described as follows:

1) Choosing the first timet1and calculatingA(t1),H1andQ1,according to the error characteristics and system measurement precision,Z1can be calculated.

2) Using the same method,QjandZjcan be calculated,and then the SOMof PWCS can be calculated,the single valuecan be calculated by SVD method.

3) Using Eq.(19),every element of state variableX0can be calculated corresponding every single value.The observability of every state vector component can be determined by element value ofX0.

3 Experimental results

3.1 Experimental conditions

In order to verify the performance of SINS initial alignment based on revolving base,some experiments have been performed.In order to simplify the experiment,the antenna base is replaced by turntable,the experimental parameters are given in Tab.1.

Tab.1 Experimental parameters

In Tab.1,ω-Rotation angle velocity of antenna base.r-The distance between SINS and antenna base center.

3.2 Experimental results and discussion

According to the Experimental parameters shown in Tab.1,the gyro data and accelerometer data of SINS initial alignment based on revolving base are illustratedin Fig.2 and Fig.3 respectively.

This paper analyzes the change of SOM minimal single value based on revolving base and stationary base respectively,the results of which are shown in Fig.4 and Fig.5 respectively.The SOM minimal single value based on revolving base increases continuously with the change of azimuth,which is about decuple of the minimal single value based on stationary base.Because the system observability degree is high when the single value is large,so the observability degree of SINS initial alignment based on revolving base is higher than the one based on stationary base.

Fig.1 Gyro data of SINS initial alignment based on revolving base

Fig.2 Accelerometer data of SINS initial alignment based on revolving base

Fig.4 The change of minimal single value based on revolving base

Fig.5 The change of minimal single value based on stationary base

Fig.6 The mean-squared error of azimuth estimation

Fig.7 The mean-squared error of roll estimation

Fig.8 The mean-squared error of pitch estimation

Tab.1 The alignment precision of azimuth

Tab.2 The alignment precision of roll

Tab.3 The alignment precision of pitch

Fig.6 and Tab.2 show that the estimation precision of azimuth error based on stationary base is poor because of the low observability degree.The estimation azimuth is 28.10′ at 100 s and 26.74′ at 150 s,and then drives to stabilization after that.But the SINS initial alignment based on revolving base can get more information by changing the azimuth continuously,which can improve the observability degree of system state.The estimation azimuth is 12.50′ at 100 s,6.54′ at 150 s,4.14′ at 200 s and then drives to stabilization after that.

Fig.7～Fig.8 and Tab.3～Tab.4 show that the estimation precision of horizon attitude error based on stationary base is high,which can converge to less than2′.The horizon attitude error mainly relates to.Because the single value corresponding tobased on revolving base is high,so the estimation precision of horizon attitude error can converge to less than 40′.

4 Conclusion

This paper analyzed the structure of the antenna tracking stabilized platform firstly,then the initial alignment scheme of revolving base alignment is put forward,and the mathematical models of revolving base alignment are built and simulated.In order to analyze the observability of SINS revolving base alignment,the SVD method is used.at the end of the paper,the experimental results and analysis are given,which show that the SINS initial alignment precision can be improved evidently on revolving base,the estimation azimuth is 6.54′ at 150 s,4.14′ at 200 s and then drives to stabilization after that and the estimation precision of horizon attitude error can converge to less than 50′ in 20 s.

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1005-6734(2014)01-0032-06

一種用于天線跟蹤穩定平臺的SINS轉動基座初始對準方法

張華強1，許 敬2，趙 剡3
（1.山東理工大學 機械工程學院，淄博 255049；2.山東理工大學 材料科學與工程學院，淄博 255049；3.北京航空航天大學 儀器科學與光電工程學院，北京 100191）

提出一種應用于天線跟蹤穩定平臺的捷聯慣導轉動基座初始對準方法。首先對衛星天線跟蹤穩定平臺的結構進行分析，得出在不改變系統現有硬件結構條件下，可充分利用天線跟蹤穩定平臺的結構特點進行轉動基座初始對準的結論；建立完整的捷聯慣導旋轉基座初始對準數學模型，并采用奇異值分解法分析捷聯慣導轉動基座初始對準的可觀測性。實驗結果表明，該方法初始對準中系統可觀測矩陣的最小奇異值比靜基座初始對準可觀測矩陣最小奇異值大一個多數量級，能提高捷聯慣導系統的可觀測性，并能有效地提高姿態角尤其是航向角的對準精度，為提高通信衛星天線跟蹤穩定平臺的性能提供了有價值的參考。

旋轉基座；初始對準；捷聯慣導；奇異值分解法；可觀測性分析

U666.1

：A

2013-10-18；

：2014-01-02

國家自然科學基金（51105026）

張華強（1982—），男，博士，講師，從事檢測與導航技術研究。E-mail：huaqiang.zhang@163.com

10.13695/j.cnki.12-1222/o3.2014.01.008