A Method of Dynamic Calibration for Installation Error of

Radar Payload Lin Wen, Zhong Liu, and Zhi-Kun Liu

Abstract—In order to eliminate the effects of radar payl-oad installation error to the degree of accuracy of radar payload detection, a dynamic calibration method of radar measurement data compensation is put forward. This me-thod based on the dynamic calibration principle, deduced the formulae of radar payload installation error identifica-tion, and error dynamic compensation in detail. The method is proved to be correct and practical by the final simulation experiments.

I. INTRODUCTIONN the modern high-tech war conditions, the mode that sea target detected by aerial platform equipped with radar payload has been widely used.The factors affecting the accuracy of radar payload de-

tection include systematic measurement error of radar payload, installation error that the mounting surface of the payload is not aligned with the aerial platform, and ran-dom measurement error.

Article [1] analyzed the influence of the payload sys-tematic measurement deviation to the location accuracy, conducted data statistic to the measured data and real-value data, identified systematic error and compen-sated the following measured data, but author did not consider the effects of installation error of the payload. Article [2] proposed a static calibration method which needed a large number of precision instruments and long time of measurement. It had a high degree of precision of error identification and compensation. Because the long time it takes, this method does not meet the request for the actual combat that the payload can be changed at any time needed.

According to the limitation of existing calibration me-thods for improving the accuracy of radar payload detec-tion, this paper based on the principle of photoelectric payload installation error dynamic calibration put forward from article [3], promoted and applied dynamic calibra-tion to radar payload, the method put forward from this article was suitable for practical applications of radar payload installation error dynamic calibration and the simulation experiment verified the correctness.

II. INSTALLATION ERROR DYNAMIC CALIBRATION OF

RADAR PAYLOAD

A. Installation Error Model of Radar Payload In practical applications, according to different tasks,

or when the payload breaks down, the payload often needs to be replaced temporarily, the process of replacing is artificial, the installation accuracy can not be guaran

Lin Wen, Zhong Liu, and Zhi-Kun Liu are with Electronics Engi-neering College, Naval University of Engineering, Wuhan, Hubei, Chi-na. (e-mail:fox_wl@sina.com, liuzhong@126.com,bill1302lzk@sina.com)

teed; the payload itself also has system measuring er-ror,the two aspects combined together form up the payl-oad installation error. Installation error represents itself as the discrepancy between radar payload coordinate system and aerial platform coordinate system.

In the radar payload coordinate system � �����o , as shown in figure 1, ��o is datum plane of the payload, � axis is called zero position of azimuth measurement. Suppose the target is T, T’s projection on the plane is p,

op�� is azimuth angle can be measured by radar payload and its range is [0°,360°), the pitching angle poT� of the target cannot be measured by radar payload, but the distance oT between the target and itself can be measure.

�

�

�

T

p

o

Fig. 1. Coordinate System of Radar Payload

As a result of the effect of installation error, discre-pancy exists between payload coordinates system and aerial platform coordinate system, as shown in figure 2:

o

�

�

�'�

'�

�

� �''�

� �''�

� �''� '�

� �1

� �3

� �2

����

��

Fig. 2. Diagram of Installation Error

Suppose the cardan angles from payload coordinates system to aerial platform are �� , �� and �� , their transformational relation is:

� �� �� � � �����

���

���

���

���

���

� � �

� �

� �

oo

o

o

oaroundrotate

oaroundrotate

oaroundrotate

''

'

''''

''

I

Fourth International Workshop on Advanced Computational Intelligence Wuhan, Hubei, China; October 19-21, 2011

978-1-61284-375-9/11/$26.00 @2011 IEEE 502

B. Installation Error Dynamic Identification Compared installation error dynamic calibration of ra-

dar payload with photoelectric payload, there are some distinctions as follows:

1) Radar payload can not measure the target azimuth angle, in the photoelectric payload calibration algorithm, target azimuth angle is important parameters to plane parallel correction. With the lack of azimuth angle, hori-zontal error of radar payload can not be calibrated ac-cording to the algorithm used in photoelectric payload installation error calibration.

2) Compared to photoelectric payload, radar payload can measure the distance to the target, the distance is a very important parameter in the location, but for calibra-tion, as the GPS information of aerial platform and coop-erative target are known, the distance is known also, the distance measured by radar can not be used in the calibra-tion algorithm [4].

3) Dynamic calibration dose not conduct physical in-stallation adjustment to the payload [5], the installation error identified by dynamic calibration is used to com-pensate the measurement data in the calculation process of location. Because the radar payload can only measure the azimuth angle, the one-dimensional measurements cannot be transformed from payload coordinate system to geographic coordinate system of aerial platform[6~8].

According to the problems mentioned above and based on the dynamic calibration principle, this paper designedinstallation error dynamic calibration method suitable for radar payload. This method deducted the formula of in-stallation error calibration by using azimuth angle in ac-cordance with the principle of spatial coordinate trans-formation, broke through the limitation of traditional ca-libration algorithm that can not help but use pitching an-gle to horizontal error calibration.

By making an observation on the cooperative target, the target azimuth angle GPS� and pitching angle GPS� in the geographic coordinates system of aerial platform can be obtained, converted from aerial platform and coopera-tive target GPS positional information. Suppose heading angle of aerial platform is IMUH and scroll angle is

IMUS and pitching angle is IMUP , the formulae con-vert GPS� and GPS� to target azimuth �� and pitching angle �� in the coordinate system of aerial platform are as follows:

� � � �� � � �� ��

��

���

�

�

��

��

GPSgps

GPSGPSgps

GPSGPSgps

z

y

x

�

��

��

sin

coscos

sincos

(1)

���

�

�

���

�

�

�������

�

�

���

�

�

gps

gps

gps

zyx

ChCpCszyx

�

�

�

(2)

� � � �

� � � � ���

�

�

���

�

� ��

IMUIMU

IMUIMU

SS

SSCs

cos0sin010

sin0cos

� � � �� � � ��

��

�

�

���

�

�

��

IMUIMU

IMUIMUPPPPCp

cossin0sincos0

001

� � � �� � � �

���

�

�

���

�

� ��

1000cossin0sincos

IMUIMU

IMUIMUHHHH

Ch

� �� ���

���

�

�

���

��

�

�

yxa

za

,2tan

sin(3)

According to the cardan angles �� , �� and �� of in-stallation error, �� and �� can be converted to target azimuth ���� and pitching angle ���� in the coordinate system of radar payload.

���

�

�

���

�

�

�������

�

�

���

�

�

�

�

�

���

���

������

zyx

CCCzyx

(4)

� � � �

� � � �

� � � �� � � �

� � � �� � � �

���

�

�

���

�

� ��

���

�

�

���

�

�

��

���

�

�

���

�

� ��

1000cossin0sincos

cossin0sincos0

001

cos0sin010

sin0cos

��������

�

���������

����

�����

C

C

C

� �� ���

���

�

�

���������

������

�

�

yxa

za

,2tan

sin(5)

Because of the high precision of GPS measurement,the ���� converted from data of GPS is identified to be the truth-value in theory. After contain times of mea-surements, two groups of data which are actually meas-ured target azimuth angle � � � � � �� �n

opopop ��� ,,, 21 � measured by radar payload and theoretical true-value of target azimuth angle � � � � � �� �n

��������� ��� ,,, 21 � are gained, establish optimiza-tion function J:

� � � � � �� � �

��n

i

iop

iJ1

2,, �������� ��� (6)

J is the function of installation error, when the installa-tion error reaches to its real value, function value reaches to minimum. By using intelligent swarm algorithm to search in the solution space, the installation error can be found when J reaches to minimum.

C. Installation Error Dynamic Compensation As shown in figure 3, suppose the target is T on the sea

level, o is the projection of aerial platform, the distance Dbetween aerial platform and target is measured by radar payload, according height information H measured by GPS of the aerial platform, oT can be confirmed, the final target position can be determined by the target azimuth angle NoT� in the geographical coordinate system of aerial platform.

503

Sea LevelN

D

T

o

H

Fig. 3. Location Diagram of Radar Payload The target azimuth angle op� in radar payload coordi-

nates system must be converted to target azimuth an-gle st� before being used to target location algorithm. As for photoelectric payload, when the installation error is identified, the target azimuth angl op� and pitching angle

op� measured by payload will be converted to the coordi-nates system of aerial platform through installation error compensation, and then to geographic coordinates system of aerial platform through flight attitude correction. The intermediate steps actually are coordinate transformation, convert the known quantity op� and op� to unknown quantity st� and st� through known intermediate steps.

� �

� �

� �

� �!!!!

"

#

$$$$

%

&

� !!!!

"

#

$$$$

%

&

unknownst

unknownst

tiontransforma coordinate

knownop

knownop

�

�

�

�

The transformation formulae are as follows: � � � �� � � �� ��

��

���

�

�

��

��

opop

opopop

opopop

z

y

x

�

��

��

sin

coscos

sincos

(7)

���

�

�

���

�

�

����������

�

�

���

�

�

op

op

op

st

st

st

zyx

CCCCsCpChzyx

'''''' ��� (8)

� �� ��

��

��

ststst

ststyxa

za,2tan

sin��

(9)

As for radar payload, the pitching angle op� is anunknown quantity, so formulae 7 to 9 can be applied to radar payload. But the distance D between target and aerial platform can be measured by radar payload, com-bined with height information H measured by GPS of aerial platform, the target pitching angle st� can be got, as shown in figure 4.

HD

The Earth

st�

Fig. 4. Diagram of Transformation Theory

!"#

$%&��

DH

st arcsin�

� �DH

st ���sin(10)

The formula 11 derived from formula 8: opopopst zCyBxAz �'�'�� (11)

A � (� cos( IMUP ) � sin( IMUS ) � cos( �� ) � sin( IMUP ) � sin( �� )) � cos( �� ) � (� (� cos( IMUP ) � sin( IMUS ) � sin( �� ) +sin( IMUP ) � cos( �� )) � sin( �� ) +cos( IMUP ) � cos( IMUS ) � cos( �� )) � sin( �� ) B � (� cos( IMUP ) � sin( IMUS ) � sin( �� ) +sin( IMUP ) � cos( �� )) � cos( �� ) +cos( IMUP ) � cos( IMUS ) � sin( �� ) C � (� cos( IMUP ) � sin( IMUS ) � cos( �� ) � sin( IMUP ) � sin( �� )) � sin( �� ) +(� (� cos( IMUP ) � sin( IMUS ) � sin( �� ) +sin( IMUP ) � cos( �� )) � sin( �� ) +cos( IMUP ) � cos( IMUS ) � cos( �� )) � cos( �� )

Formula 12 is defined by 11: � � � �� � � �� � 0sin

coscossin

�'�'

��'�

DHC

BA

op

opopop

�

���(12)

� ��� 0,90�(op�

In the formula 12, every quantity is known except op� ,when op� is worked out, put it back into formulae 7, 8 and 9 to work out st� .

D. Verification of Simulation Experiment In this simulation, the initial coordinate of aerial plat-

form in geodetic coordinate system is set, the longitude is E 121.9111°, the latitude is N 29.7546° and the altitude is 3000m. The speed is 20 m/s, the course is 0° and 90° after 180s, and total simulation time is 360s. Set initial coordi-nate of co-operational target in geodetic coordinate system, the longitude is E 121.7947°, the latitude is N 29.7650° and altitude is 0m. The speed is 5 m/s, the course is 60°, as shown in figure 5:

Fig. 5. The Situation of Aerial Platform and Co-operational Target

After the 100 times of Monte Carlo simulation experi-ments, the results as shown in Table I:

TABLE I RESULT OF SIMULATION EXPERIMENTS

Set Value Results of identification �� �� �� �� �� ��

-1 -1 1 -0.9762 -0.9870 1.0036 5 3 1 5.0022 3.0304 1.0138

504

III. CONCLUSION

The method of dynamic calibration for installation error of radar payload put forward in this article based on the dynamic calibration principle, the formulae ofradar payload installation error identification, and error dynamic compensation are deduced in detail. The new way of calibration for radar payload is developed and itwill be great help to engineering practice.

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