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Compared to the error factors of the Linear Array Digital Sun Sensor (DSS), those of the Area Array DSS are complicated and methods used for error compensation are not valid or simple enough. This paper presents the main error factors of the Area Array DSS and proposes an effective method to compensate them. The procedure of error compensation of Area Array DSS includes three steps. First, the geometric error of calibration is compensated; second, the coordinate map method is used to compensate the error caused by optical refraction; third, the high order polynomialfitting method is applied to calculate the tangent of the sun angles; finally, the arc tangent method is used to calculate the sun angles. Experimental results of the product of the High Accuracy Sun Sensor indicate that the precision is better than 0.02° during the cone field of view (CFOV) of 10°, and the precision is better than 0.14° during the CFOV 10° to 64°. The proposed compensation method effectively compensates the major error factors and significantly improves the measure precision of the Area APS DSS.
Sun Sensor, a device for satellite attitude control, is used to calculate the attitude angle between the sun and the satellite. The sun sensor, applied widely in various kinds of aerospace controllers, is one kind of common attitude control sensor [
The research on DSS focuses on system integration and the centroid algorithm of sun spots, without error compensation and calibration, which inevitably results in errors during the process of fixing. In order to achieve high measurement accuracy, it is necessary to research the error compensation of Area DSS. Using the method provided in thesis [
Based on the shortcomings of the above error compensation method, this study thoroughly analyzes the error factors and provides a means to compensate the error factors, especially (the) main error factors. In summary, our method compensates the geometry rotation error and optical refraction error respectively, followed by calculating the tangent values using a high order polynomialfitting method to reduce the random error.
The optical refraction caused by the surface protecting glass of the image detector results in the change of coordinate values that makes oneaxis coordinate values in the same incident angle of the relative axis be different from the different incident angles of another axis. Therefore methods which are based on the theoretical measurement model, generate large errors between the measured and true values. Furthermore, the larger the incident angles are, the larger the errors are. In the FOV 64°, the largest error is 2°∼3°.
The principle of measuring Area DSS is shown in
According to the measurement model, it is not difficult to summarize the formula as follows:
The feature of theoretical measurement model: when either
In reality, sun rays have to pass through air, quartz glass, air, protecting glass of the image detector surface and air to the image detector surface, as shown in
In
According to the geometric projection rule, the twoaxis coordinates are:
From the shift trend, the shift of
Because of machining errors and fixing errors, the image detector surface deflects and rotates round the optical axis. DSS uses a calibration method to improve measurement accuracy. Our studies show it is ineffective to eliminate errors only through the fitting method.
DSS calibration facility (
According to the above analysis, the main factors of error in DSS are optical refraction, and deflection and rotation of the image detector around the optical axis. Therefore, error compensated is used and its flow chart is presented in
Because of the rotation error and optical refraction, the coordinate value of the angle
From the optical refraction rule as shown in
According to the rule of coordinate system rotation, the formula to calculate the rotation angle is as follows:
In order to the rotation angle more accurate, the arithmetic mean value of the rotation angle
The rotation angle
In
According to the analysis in Section 2.1.2, concerning the shift trend of coordinate values caused by refraction, the change of oneaxis coordinate value depends on both the twoaxis coordinate values. As a result, Dualfit serves to map the coordinate values for correlation of optical refraction. The purpose of the map method is to make the coordinate values of the angle
In
From
Zoning in the first quadrant is shown in
In order to reduce random errors such as deflection, the method of single axis high order interpolation polynomials serves to calculate the tangent values of oneaxis angle. Then, the values of twoaxis angles are calculated through an antitangent operation. The detailed method is as follows: the tangent values are calculated from the coordinate values either after the rotation correlation in the small CFOV or after the coordinate map correlation in the large CFOV.
The formula to calculate the tangent value is as follows:
In
The proposed method of error compensation was applied in a real High Accuracy Sun Sensor (HASS) product to be installed on board a satellite under development (
When HASS calculates the angle only through high order interpolation polynomials method, without using compensation, the measurement error is shown in
Before using the proposed method to compensate HASS, the shift trend of coordinate values shown in the
Because the state of every sun sensor is not the same, the compensation index of every sun sensor is not same either.
The rotation angle is calculated through the coordinate values when angle
Based on a width of 10° of stripshaped area, the map indexes of each stripshaped area are listed in
The calibration experiment collects the relative coordinate values of the incident angle. Then the calibration data including the coordinate value and angle value serves to calculate the index of high order interpolation polynomials in Matlab.
After compensation, the errors of the sun sensor in the cone FOV 64° (reference
Previous works on Area Array DSS other than this paper do not undertake definite measurements to compensate for the two major error factors, which are the geometry error of fixing and the optical refraction caused by the surface protection glass of the image detector. Thus, it is difficult to attain high accuracy. According to the analysis mentioned above, the optical refraction is the most important error factor of DSS, and the method proposed in this paper compensates the geometry rotation error and optical refraction error, respectively.
HASS uses a high order interpolation polynomials method to compute the twoaxis angles and produces a maximal error larger than 3°. By applying the proposed method of error compensation, the accuracy of HASS is greatly improved. The measurement error in FOV 10° is smaller than 0.02° and that in FOV 10°∼64° is smaller than 0.14°. The proposed method of error compensation is thus proven to be effective.
This work was performed in The State Key Laboratory of Precision Measurement Technology and Instruments at Tsinghua University, Beijing, China.
The principle of DSS. (
The optical refraction model of DSS.
The trend of coordinate shift. In order to highlight the shift trend of the
The calibration system schematic diagram and facilities of DSS.
The flow chart of error compensation of DSS.
The sketch map of rotation of coordinate system.
The sketch map of stripshaped areas.
High Accuracy Sun Sensor with cubic prism.
The error of HASS before compensation. (
The coordinate shift trend of HASS before compensation.
The error of HASS after compensation. (
The values of rotation angle.
0  5  0.083  12.998  0.3634 
0  10  0.155  25.850  0.3452 
0  15  0.219  39.224  0.3211 
0  20  0.302  53.020  0.3267 
0  25  0.376  67.594  0.3183 
0  30  0.458  83.249  0.3152 
0  35  0.559  100.021  0.3201 
0  40  0.659  118.644  0.3185 
0  45  0.779  139.685  0.3194 
0  50  0.898  164.061  0.3135 
0  55  1.063  193.273  0.315 
0  60  1.246  229.612  0.3109 
0  64  1.429  266.858  0.3068 
 

0.3226 
Values of index M.
 

0–10  10–64  959.942  2.325  1.027  71.297 
10–64  0–10  999.818  4.093  0.027  6.7755 
10–20  10–64  972.889  7.332  0.645  −476.931 
20–64  10–20  998.005  11.146  0.099  −164.034 
20–30  20–64  951.478  6.945  0.671  458.043 
30–64  20–30  988.327  8.890  0.228  415.243 
30–40  30–64  953.791  17.295  0.520  465.957 
40–64  30–40  981.513  22.595  0.216  545.475 
40–50  40–64  957.596  34.327  0.332  698.877 
50–64  40–50  968.727  38.571  0.234  518.038 
50–60  50–64  967.158  50.032  0.190  317.087 
Values of index M.
 

0–10  10–64  999.834  7.747  0.179  27.971 
10–64  0–10  973.931  0.576  0.714  −16.651 
10–20  10–64  997.435  5.043  0.135  39.810 
20–64  10–20  970.039  0.067  0.653  216.528 
20–30  20–64  990.156  9.915  0.217  275.415 
30–64  20–30  964.378  4.041  0.597  355.476 
30–40  30–64  983.609  21.922  0.221  350.355 
40–64  30–40  966.815  15.921  0.450  107.906 
40–50  40–64  979.153  38.063  0.180  124.986 
50–64  40–50  968.361  34.565  0.265  133.359 
50–60  50–64  971.270  41.640  0.200  458.288 
The max error in Field of view.
 

α  0.018°  0.138° 
β  0.0193°  0.1208° 