CN113739823B - Mars APS sun sensor error compensation method - Google Patents
Mars APS sun sensor error compensation method Download PDFInfo
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Abstract
The invention relates to an error compensation method of an APS sun sensor of a Mars vehicle, which uses the thought of camera distortion correction to correct the centroid coordinates of a solar bright spot in advance, establishes a cubic polynomial of the theoretical coordinate position and the actual centroid position of the centroid of the solar bright spot, and uses a least square method to obtain the coefficients of the cubic polynomial. The angle residual error after coordinate compensation is solved by adopting the secondary compensation thought, and the problem of rapid positioning of an angle compensation curve is solved. The operation amount is reduced to 2 times of 3-order polynomial operation and 2 times of 7-order polynomial operation, the precision reaches 0.03 degrees (3 sigma) after error compensation, the operation amount is reduced, the product updating rate is improved, and the product precision is improved.
Description
Technical Field
The invention belongs to the field of optical attitude sensors, and relates to an error compensation method for an APS sun sensor of a Mars vehicle.
Background
The sun sensor is an optical attitude sensor for measuring the included angle between the attitude of a spacecraft and the vector of solar rays by taking the sun as a reference azimuth. The sun vector direction is measured by a sun sensor on the Mars, yaw direction is provided for the Mars to travel on the surface of the Mars, the Mars is ensured to advance according to a preset direction, and meanwhile correction of long-time drift of the gyroscope is completed.
An area array APS CMOS image sensor adopted by the Mars sun sensor is used as a photoelectric detector, light is introduced by utilizing a light-passing small hole on a light introducer, sun rays reach the APS image sensor through the small hole to form a sun bright spot, and the vector direction of the sun can be determined by extracting the energy center of the sun bright spot.
The APS sun sensor is calibrated by the sun simulator and the turntable due to refraction of the image sensor protective glass and systematic errors caused in the product assembling process, and the product angle errors are compensated by calibration data.
When the APS sun sensors of the goddess's three and the goddess's four are subjected to angle error compensation in development, the error introduced by refraction and assembly reaches more than 5 degrees, and the error is required to be compensated to be within 0.1 degrees, 7 times of operation of a 7-order polynomial are required to be performed, similar to patent CN103411580A (a two-axis angle determining method in the linear array APS sun sensor), the 7 times of polynomial operation are required to be subjected to iterative compensation for a plurality of times so as to select a proper compensation curve, and when the compensation curve is selected, weight distribution is performed between two adjacent compensation curves according to angle measurement values, namely, the compensation value is solved in a mode of weighting and summing the two error compensation polynomials, so that the single-machine internal single-chip microcomputer 80C32E operation time is overlong, the product update rate is low, only 2Hz, and finally, the angle compensation operation is only completed by a high-performance CPU in the integrated electronic.
Disclosure of Invention
The invention solves the technical problems that: the defect of the prior art is overcome, and an error compensation method for the APS sun sensor of the Mars vehicle is provided.
The solution of the invention is as follows:
an error compensation method for an APS sun sensor of a Mars vehicle, comprising the steps of:
the first step: solar bright spots obtained by using centroid methodActual position (x) Actual i ,y Actual i )；
And a second step of: establishing a lattice of (121 multiplied by 121) every 1 degree in a field of view of (+ -60 degrees X+/-60 degrees) by using a solar simulator and a biaxial turntable to obtain coordinate data of solar bright spots at 14641 angles under a calibration field, and obtaining a relation between the actual position and the zero position of the solar bright spots at the ith angle by using known calibration data (x 0, y0 and h), wherein x0 is the x-axis coordinate when the solar bright spots are at the zero position, y0 is the y-axis coordinate when the solar bright spots are at the zero position, h is the distance from a light sensitive surface of a detector to the lower surface of a light introducer, and i=1-14641;
and a third step of: the following mathematical model is established to represent the theoretical position (x) of the solar bright spot under the ith angle Theory i ，y Theory i ) And the actual position (x) Actual i ，y Actual i ) Is the relation of:
x theory i ＝x Actual i +x_p0*Δx i *r i +x_p1*Δx i *r i 2 +x_p2*Δx i *r i 3 ；
y Theory i ＝y Actual i +y_p0*Δy i *r i +y_p1*Δy i *r i 2 +y_p2*Δy i *r i 3 .
x_p0 is a first power compensation coefficient of the x-axis coordinate of the solar bright spot, x_p1 is a second power compensation coefficient of the x-axis coordinate of the solar bright spot, x_p2 is a third power compensation coefficient of the x-axis coordinate of the solar bright spot, y_p0 is a first power compensation coefficient of the y-axis coordinate of the solar bright spot, y_p1 is a second power compensation coefficient of the y-axis coordinate of the solar bright spot, and y_p2 is a third power compensation coefficient of the y-axis coordinate of the solar bright spot;
fourth step: the coordinate compensation coefficients (x_p0, x_p1, x_p2) and (y_p0, y_p1, y_p2) are calculated by least squares, and the sum of the values (x Actual i ，y Actual i ) Coordinate compensation is performed to obtain (x) Post-compensation i ，y Post-compensation i )，x Post-compensation i The position after the X-axis coordinate of the solar bright spot is compensated, y Post-compensation i Compensating the y-axis coordinate of the solar bright spot;
fifth step: with coordinates (x) Post-compensation i ，y Post-compensation i ) Obtaining an initial sun angle of the sun sensor:
α before compensation i Compensating the front angle, beta, for the alpha axis of the sun sensor Before compensation i The front angle is compensated for the sun sensor beta axis.
Sixth step: build alpha at the ith angle Before compensation i And beta Before compensation i Obtaining a residual error of the output angle of the sun sensor at the moment according to the corresponding relation between the sun sensor and the turntable angle, and obtaining a compensation coefficient table of the residual error at the moment by using a polynomial fitting method;
seventh step: rounding the angle before compensation of the sun sensor to obtain beta Before compensation i Int and alpha Before compensation i _int；β Before compensation i Int is beta Before compensation i Rounding the rounded values, alpha Before compensation i Int is alpha Before compensation i Rounding the rounded values;
eighth step: the field boundary is 60 degrees, m=β Before compensation i Int, at alpha Compensation coefficient A set of coefficients (alpha) corresponding to the m degree alpha axis is found m _p0，α m _p1，α m _p2，α m _p3，α m _p4，α m _p5，α m _p6，α m P 7) obtaining an alpha axis final angular output alpha from the set of coefficients Output of ；
n＝α Before compensation i Int, beta Compensation coefficient A set of coefficients (beta) corresponding to the beta axis of n degrees n _p0，β n _p1，β n _p2，β n _p3，β n _p4，β n _p5，β n _p6，β n P 7), obtaining the beta-axis final angular output beta from the set of coefficients Output of 。
In the first step, x Actual i ＝xa i /ga i ，y Actual i ＝ya i /ga i ；
xa i Is the gray product of sun bright spots in the x direction, ya i The gray product, ga, of the solar bright spots in the y direction i Is the gray sum of the solar bright spots.
In the second step of the process, the first step,
Δx i ＝x actual i -x0；
Δy i ＝y Actual i -y0；
x Theory i ＝h×tan(α Turntable i )+x0；
y Theory i ＝h×tan(β Turntable i )+y0；
Wherein Deltax is i Is the actual position x on the x axis of the solar bright spot under the ith angle Actual i Difference from zero position, Δy i Is the actual position y on the y axis of the solar bright spots Actual i Difference from zero position, r i Is the distance between the actual position and the zero position of the solar bright spots, x Theory i Alpha-axis turntable angle alpha is the ith angle Turntable i Theoretical position of solar bright spots, y Theory i The angle of the beta-axis turntable under the ith angle is beta Turntable i The theoretical position of the solar bright spots.
In the fourth step, (x) is paired using the following formula Actual i ，y Actual i ) Coordinate compensation is performed to obtain (x) Post-compensation i ，y Post-compensation i )：
x Post-compensation i ＝x Actual i +x_p0*Δx i *r i +x_p1*Δx i *r i 2 +x_p2*Δx i *r i 3 ；
y Post-compensation i ＝y Actual i +y_p0*Δy i *r i +y_p1*Δy i *r i 2 +y_p2*Δy i *r i 3 .。
In the sixth step, the angle alpha of the alpha-axis turntable Turntable i And alpha is Before compensation i Error Δα of (a) i ＝α Turntable i -α Before compensation i ，
Beta-axis turntable angle beta Turntable i And beta Before compensation i Error Δβ of (a) i ＝β Turntable i -β Before compensation i 。
Δα i Seven-order error compensation coefficient alpha of (2) Compensation coefficient j ＝polyfit(α Actual ji ,Δα ji ,7)(j＝-60～60,i＝-60～60)
Δβ i Seven-order error compensation coefficient beta Compensation coefficient j ＝polyfit(β Actual ji ,Δβ ji ,7)(j＝-60～60,i＝-60～60)
polyfit () is a polynomial fitting function.
The residual compensation coefficients are shown below:
α k1 seven power compensation coefficient and alpha when p0 is alpha axis k1 degree k1 P1 is the sixth power compensation coefficient and alpha when the alpha axis is k1 degree k1 P2 is the compensation coefficient of the fifth power when the alpha axis is k1 degree, alpha k1 P3 is the fourth power compensation coefficient when the alpha axis is k1 degree, alpha k1 P4 is the third power compensation coefficient and alpha when the alpha axis is k1 degree k1 Second power compensation coefficient when p5 is alpha axis k1 degree, alpha k1 P6 is the first power compensation coefficient and alpha when the alpha axis is k1 degree k1 P7 is the compensation coefficient of a-axis k1 degree, k1= -60, -59, -58, … …,59, 60;
β k2 seven power compensation coefficient when p0 is k2 degree and beta is beta k2 P1 is the sixth power compensation coefficient when the beta axis is k2 degrees, beta k2 P2 is the compensation coefficient of the fifth power when the beta axis is k2 degrees, beta k2 Fourth power compensation coefficient when p3 is beta axis k2 degree, beta k2 Three times when p4 is k2 degrees on beta axisPower of power compensation coefficient, beta k2 Second power compensation coefficient when p5 is k2 degree and beta is beta k2 First power compensation coefficient when p6 is k2 degree and beta is beta k2 P7 is the compensation coefficient of k2 degrees by several times, k2= -60, -59, -58, … …,59, 60.
In the eighth step, alpha Output of ＝α Before compensation i +(α m _p0×α Before compensation i 7 +α m _p1×α Before compensation i 6 +α m _p2×α Before compensation i 5 +α m _p3×α Before compensation i 4 +α m _p4×α Before compensation i 3 +α m _p5×α Before compensation i 2 +α m _p6×α Before compensation i +α m _p7)；
α m P0 is alpha Compensation coefficient Seven power compensation coefficient when the middle alpha axis is m degrees, alpha m P1 is alpha Compensation coefficient Six power compensation coefficient when the middle alpha axis is m degrees, alpha m P2 is alpha Compensation coefficient Fifth power compensation coefficient when middle alpha axis is m degree, alpha m P3 is alpha Compensation coefficient Fourth power compensation coefficient when the middle alpha axis is m degrees, alpha m P4 is alpha Compensation coefficient Third power compensation coefficient when the middle alpha axis is m degrees, alpha m P5 is alpha Compensation coefficient Second power compensation coefficient when middle alpha axis is m degree, alpha m P6 is alpha Compensation coefficient The first power compensation coefficient when the middle alpha axis is m degrees, alpha m P7 is alpha Compensation coefficient The middle alpha axis is m degrees and is often a plurality of compensation coefficients.
β Output of ＝β Before compensation i +(β m _p0×β Before compensation i 7 +β m _p1×β Before compensation i 6 +β m _p2×β Before compensation i 5 +β m _p3×β Before compensation i 4 +β m _p4×β Before compensation i 3 +β m _p5×β Before compensation i 2 +β m _p6×β Before compensation i +β m _p7)；
β n P0 is beta Compensation coefficient Seven power compensation coefficient when the middle beta axis is n degrees, beta n P1 isβ Compensation coefficient Six power compensation coefficient when the middle beta axis is n degrees, beta n P2 is beta Compensation coefficient The middle beta axis is the fifth power compensation coefficient when n degrees, beta n P3 is beta Compensation coefficient Fourth power compensation coefficient when middle beta axis is n degree, beta n P4 is beta Compensation coefficient The third power compensation coefficient when the middle beta axis is n degrees, beta n P5 is beta Compensation coefficient The second power compensation coefficient when the middle beta axis is n degrees, beta n P6 is beta Compensation coefficient The first power compensation coefficient when the middle beta axis is n degrees, beta n P7 is beta Compensation coefficient The middle beta axis is n degrees and is often a plurality of compensation coefficients.
Compared with the prior art, the invention has the beneficial effects that:
(1) The invention firstly proposes to compensate the angle error of the APS sun sensor twice, firstly compensates the coordinates, then compensates the angle residual error, reduces the operation amount to 2 times of 3-order polynomial operation and 2 times of 7-order polynomial operation, and has the accuracy of 0.03 degrees (3 sigma) after error compensation, thereby reducing the operation amount, improving the product updating rate and improving the product accuracy.
(2) The invention uses the thought of camera distortion correction to correct the centroid coordinates of the solar bright spots in advance, establishes a cubic polynomial of the theoretical coordinate position and the actual centroid position of the centroid of the solar bright spots, and uses the least square method to obtain the coefficients of the cubic polynomial. The angle residual error of the sun sensor is reduced to be within 0.5 degrees after the correction of the coordinates.
(3) The invention adopts the idea of secondary compensation to solve the angle residual error after coordinate compensation and solve the problem of quick positioning of an angle compensation curve, and the invention can obtain a final compensation value by only carrying out angle compensation once on each coordinate axis without carrying out iterative compensation for a plurality of times so as to select a proper compensation curve, and simultaneously does not need to carry out weight distribution on an angle measurement value between two adjacent compensation curves, and then solves the compensation value in a mode of carrying out weighted summation on two error compensation polynomials.
Drawings
Fig. 1 shows that β= -60 °, and the angle error of α is from-60 ° to +60°;
fig. 2 is an angle error of β= -30 °, α from-60 ° to +60°;
fig. 3 is an angle error of β=0°, α ranging from-60 ° to +60°;
fig. 4 is an angle error of α= -30 °, β from-60 ° to +60°;
fig. 5 shows an angle error of α=0°, β ranging from-60 ° to +60°.
Detailed Description
The invention is further described below.
The APS sun sensor images the sun bright spots by using the APS image sensor, and calculates the centroid position of the sun bright spots to obtain the sun azimuth angle. In the Mars vehicle APS sun sensor, the refraction of the image sensor protection glass, hemispherical cover distortion and systematic errors in the product assembly link can reach more than 5 degrees at the field boundary.
The invention firstly proposes to compensate the angle error of the APS sun sensor twice, and then compensates the coordinates and compensates the angle residual error.
The specific implementation steps are as follows:
the first step: the barycenter method is used to obtain the coordinate position (x) of the solar bright spot Actual i ,y Actual i )；
x Actual i ＝xa i /ga i ；
y Actual i ＝ya i /ga i ；
xa i Is the gray product of sun bright spots in the x direction, ya i The gray product, ga, of the solar bright spots in the y direction i The gray sum of the solar bright spots;
and a second step of: establishing a lattice of (121 x 121) every 1 degree in a field of view of (+ -60 degrees X+/-60 degrees) by using a solar simulator and a biaxial turntable to obtain coordinate data of solar bright spots at 14641 angles under a calibration field, wherein i=1-14641, and obtaining a relation between the actual position and the zero position of the solar bright spots at the ith angle by using known calibration data (x 0, y0, h), wherein x0 is an x-axis coordinate when the solar bright spots are at the zero position, y0 is a y-axis coordinate when the solar bright spots are at the zero position, and h is a distance from a light sensitive surface of a detector to the lower surface of a light guide device:
Δx i ＝x actual i -x0；
Δy i ＝y Actual i -y0；
x Theory i ＝h×tan(α Turntable i )+x0；
y Theory i ＝h×tan(β Turntable i )+y0；
Wherein Deltax is i Is the actual position x on the x axis of the solar bright spot under the ith angle Actual i Difference from zero position, Δy i Is the actual position y on the y axis of the solar bright spots Actual i Difference from zero position, r i Is the distance between the actual position and the zero position of the solar bright spots, x Theory i Alpha-axis turntable angle alpha is the ith angle Turntable i Theoretical position of solar bright spots, y Theory i The angle of the beta-axis turntable under the ith angle is beta Turntable i The theoretical position of the solar bright spots.
And a third step of: establishing a mathematical model to represent the theoretical coordinate position (x) of the solar bright spot under the ith angle Theory i ，y Theory i ) And the actual coordinate position (x Actual i ，y Actual i ) Is the relation of:
x theory i ＝x Actual i +x_p0*Δx i *r i +x_p1*Δx i *r i 2 +x_p2*Δx i *r i 3 ；
y Theory i ＝y Actual i +y_p0*Δy i *r i +y_p1*Δy i *r i 2 +y_p2*Δy i *r i 3 .
x_p0 is a first power compensation coefficient of the x-axis coordinate of the solar light spot, x_p1 is a second power compensation coefficient of the x-axis coordinate, x_p2 is a third power compensation coefficient of the x-axis coordinate, y_p0 is a first power compensation coefficient of the y-axis coordinate, y_p1 is a second power compensation coefficient of the y-axis coordinate, and y_p2 is a third power compensation coefficient of the y-axis coordinate;
fourth step: obtaining coordinate compensation coefficients (x_p0, x_p1, x_p2) by least square) And (y_p0, y_p1, y_p2), for (x Actual i ，y Actual i ) The coordinate compensation can be performed by using the following formula to obtain (x) Post-compensation i ，y Post-compensation i )，x Post-compensation i Position after compensating for x-axis solar bright spot coordinates, y Post-compensation i And compensating the post-position for the y-axis solar bright spot coordinates.
x Post-compensation i ＝x Actual i +x_p0*Δx i *r i +x_p1*Δx i *r i 2 +x_p2*Δx i *r i 3 ；
y Post-compensation i ＝y Actual i +y_p0*Δy i *r i +y_p1*Δy i *r i 2 +y_p2*Δy i *r i 3 .
Fifth step: with coordinates (x) Post-compensation i ，y Post-compensation i ) Obtaining an initial sun angle of the sun sensor:
α before compensation i Compensating the sun alpha axis for the front angle beta Before compensation i The front angle is compensated for the sun's beta axis.
Sixth step: build alpha at the ith angle Before compensation i And beta Before compensation i Obtaining a residual error of the output angle of the sun sensor at the moment according to the corresponding relation between the sun sensor and the turntable angle, and obtaining a compensation coefficient table of the residual error at the moment by using a polynomial fitting method;
alpha-axis turntable angle alpha Turntable i And alpha is Before compensation i Error Δα of (a) i ＝α Turntable i -α Before compensation i
Beta-axis turntable angle beta Turntable i And beta Before compensation i Error Δβ of (a) i ＝β Turntable i -β Before compensation i
Δα i Seven-order error compensation system of (2)Number alpha Compensation coefficient j ＝polyfit(α Actual ji ,Δα ji ,7)(j＝-60～60,i＝-60～60)
Δβ i Seven-order error compensation coefficient beta Compensation coefficient j ＝polyfit(β Actual ji ,Δβ ji ,7)(j＝-60～60,i＝-60～60)
polyfit () is a polynomial fitting function in MATLAB.
α -60 Seven power compensation coefficient and alpha when p0 is alpha axis of-60 DEG -60 P1 is the sixth power compensation coefficient and alpha when alpha axis is-60 DEG -60 P2 is the compensation coefficient of the fifth power when the alpha axis is-60 degrees, alpha -60 P3 is the fourth power compensation coefficient and alpha when alpha axis is-60 DEG -60 P4 is the third power compensation coefficient and alpha when alpha axis is-60 degrees -60 P5 is the second power compensation coefficient and alpha when alpha axis is-60 DEG -60 P6 is the first power compensation coefficient and alpha when alpha axis is-60 DEG -60 And p7 is a constant compensation coefficient when the alpha axis is-60 degrees.
α -59 Seven power compensation coefficient and alpha when p0 is alpha-59 DEG -59 P1 is the sixth power compensation coefficient and alpha when alpha axis is-59 degrees -59 P2 is the compensation coefficient of the fifth power when the alpha axis is-59 degrees, alpha -59 P3 is the fourth power compensation coefficient and alpha when alpha axis is-59 DEG -59 P4 is the third power compensation coefficient and alpha when alpha axis is-59 degrees -59 P5 is the second power compensation coefficient and alpha when alpha axis is-59 DEG -59 P6 is the first power compensation coefficient and alpha when alpha axis is-59 DEG -59 P7 is a constant compensation coefficient for-59 degrees on the alpha axis.
α 60 Seven power compensation coefficient when p0 is 60 degrees and alpha is 60 P1 is the sixth power compensation coefficient when the alpha axis is 60 degrees, alpha 60 Fifth power compensation system when p2 is 60 DEG alpha axisNumber, alpha 60 P3 is the fourth power compensation coefficient when the alpha axis is 60 degrees, alpha 60 P4 is the third power compensation coefficient and alpha when the alpha axis is 60 DEG 60 P5 is the second power compensation coefficient and alpha when the alpha axis is 60 DEG 60 P6 is the first power compensation coefficient and alpha when the alpha axis is 60 DEG 60 P7 is the 60 degree constant compensation coefficient for the alpha axis.
β -60 Seven power compensation coefficient and beta when p0 is beta axis at-60 DEG -60 P1 is the sixth power compensation coefficient when the beta axis is-60 degrees, beta -60 P2 is the compensation coefficient of the fifth power when the beta axis is-60 degrees, beta -60 P3 is the fourth power compensation coefficient when the beta axis is-60 degrees, beta -60 P4 is the third power compensation coefficient and beta when the beta axis is-60 DEG -60 P5 is the second power compensation coefficient and beta when the beta axis is-60 DEG -60 P6 is the first power compensation coefficient and beta when the beta axis is-60 DEG -60 P7 is a constant compensation coefficient for a β axis of-60 degrees.
β -59 Seven power compensation coefficient when p0 is beta axis at-59 degree, beta -59 P1 is the sixth power compensation coefficient when the beta axis is-59 degrees, beta -59 P2 is the compensation coefficient of the fifth power when the beta axis is-59 degrees, beta -59 P3 is the fourth power compensation coefficient when the beta axis is minus 59 degrees, beta -59 P4 is the third power compensation coefficient and beta when the beta axis is-59 DEG -59 P5 is the second power compensation coefficient when the beta axis is-59 degrees, beta -59 P6 is the first power compensation coefficient when the beta axis is-59 degrees, beta -59 P7 is a constant compensation coefficient with a beta axis of-59 degrees.
β 60 Seven power compensation coefficient when p0 is 60 degrees and beta is 60 P1 is the six power compensation coefficient when the beta axis is 60 degrees, beta 60 P2 is the compensation coefficient of the fifth power when the beta axis is 60 degrees, beta 60 P3 is the fourth power compensation coefficient when the beta axis is 60 degrees, beta 60 P4 is the third power compensation coefficient and beta when the beta axis is 60 DEG 60 P5 is the second power compensation coefficient when the beta axis is 60 degrees, beta 60 P6 is the first power compensation coefficient when the beta axis is 60 degrees, beta 60 P7 is the 60 degree constant compensation coefficient for the beta axis.
Seventh step: the obtained initial angle of the sun sensor is rounded, and the formula is as follows:
β before compensation i _int＝round(β Before compensation i )；
α Before compensation i _int＝round(α Before compensation i )；
β Before compensation i Int is beta Before compensation i Rounding off the rounded values.
α Before compensation i Int is alpha Before compensation i Rounding off the rounded values.
Eighth step: the field boundary is 60 degrees, m=β Before compensation i Int, at alpha Compensation coefficient A set of coefficients (alpha) corresponding to the m degree alpha axis is found m _p0，α m _p1，α m _p2，α m _p3，α m _p4，α m _p5，α m _p6，α m P 7), substituting the formula to obtain alpha Output of As a final angular output.
α Output of ＝α Before compensation i +(α m _p0×α Before compensation i 7 +α m _p1×α Before compensation i 6 +α m _p2×α Before compensation i 5 +α m _p3×α Before compensation i 4
+α m _p4×α Before compensation i 3 +α m _p5×α Before compensation i 2 +α m _p6×α Before compensation i +α m _p7)；
α m P0 is alpha Compensation coefficient Seven power compensation coefficient when the middle alpha axis is m degrees, alpha m P1 is alpha Compensation coefficient Six power compensation coefficient when the middle alpha axis is m degrees, alpha m P2 is alpha Compensation coefficient Fifth power compensation coefficient when middle alpha axis is m degree, alpha m P3 is alpha Compensation coefficient Fourth power compensation coefficient when the middle alpha axis is m degrees, alpha m P4 is alpha Compensation coefficient Third power compensation coefficient when the middle alpha axis is m degrees, alpha m P5 is alpha Compensation coefficient Second power compensation coefficient when middle alpha axis is m degree, alpha m P6 is alpha Compensation coefficient The first power compensation coefficient when the middle alpha axis is m degrees, alpha m P7 is alpha Compensation coefficient The middle alpha axis is m degrees and is often a plurality of compensation coefficients.
n＝α Before compensation i Int, beta Compensation coefficient A set of coefficients (beta) corresponding to the beta axis of n degrees n _p0，β n _p1，β n _p2，β n _p3，β n _p4，β n _p5，β n _p6，β n P 7), substituting the formula to obtain beta Output of As a final angular output.
β Output of ＝β Before compensation i +(β m _p0×β Before compensation i 7 +β m _p1×β Before compensation i 6 +β m _p2×β Before compensation i 5 +β m _p3×β Before compensation i 4 +β m _p4×β Before compensation i 3 +β m _p5×β Before compensation i 2 +β m _p6×β Before compensation i +β m _p7)；
β n P0 is beta Compensation coefficient Seven power compensation coefficient when the middle beta axis is n degrees, beta n P1 is beta Compensation coefficient Six power compensation coefficient when the middle beta axis is n degrees, beta n P2 is beta Compensation coefficient The middle beta axis is the fifth power compensation coefficient when n degrees, beta n P3 is beta Compensation coefficient Fourth power compensation coefficient when middle beta axis is n degree, beta n P4 is beta Compensation coefficient The third power compensation coefficient when the middle beta axis is n degrees, beta n P5 is beta Compensation coefficient The second power compensation coefficient when the middle beta axis is n degrees, beta n P6 is beta Compensation coefficient The first power compensation coefficient when the middle beta axis is n degrees, beta n P7 is beta Compensation coefficient The middle beta axis is n degrees and is often a plurality of compensation coefficients.
The error conditions of the Mars sun sensor after coordinate error compensation and angle error compensation according to the method of the invention are shown in figures 1, 2, 3, 4 and 5. As can be seen from the graph, the accuracy of the Mars sun sensor is better than 0.02 degrees after the method.
What is not described in detail in the present specification is a known technology to those skilled in the art.
Claims (9)
1. The error compensation method for the Mars APS sun sensor is characterized by comprising the following steps of:
the first step: the actual position (x) of the solar bright spot is obtained by using a centroid method Actual i ,y Actual i )；
And a second step of: establishing a lattice of (121 multiplied by 121) every 1 degree in a field of view of (+ -60 degrees X+/-60 degrees) by using a solar simulator and a biaxial turntable to obtain coordinate data of solar bright spots at 14641 angles under a calibration field, and obtaining a relation between the actual position and the zero position of the solar bright spots at the ith angle by using known calibration data (x 0, y0 and h), wherein x0 is the x-axis coordinate when the solar bright spots are at the zero position, y0 is the y-axis coordinate when the solar bright spots are at the zero position, h is the distance from a light sensitive surface of a detector to the lower surface of a light introducer, and i=1-14641;
and a third step of: the following mathematical model is established to represent the theoretical position (x) of the solar bright spot under the ith angle Theory i ，y Theory i ) And the actual position (x) Actual i ，y Actual i ) Is the relation of:
x theory i ＝x Actual i +x_p0*Δx i *r i +x_p1*Δx i *r i 2 +x_p2*Δx i *r i 3 ；
y Theory i ＝y Actual i +y_p0*Δy i *r i +y_p1*Δy i *r i 2 +y_p2*Δy i *r i 3 .
x_p0 is a first power compensation coefficient of the x-axis coordinate of the solar bright spot, x_p1 is a second power compensation coefficient of the x-axis coordinate of the solar bright spot, x_p2 is a third power compensation coefficient of the x-axis coordinate of the solar bright spot, y_p0 is a first power compensation coefficient of the y-axis coordinate of the solar bright spot, y_p1 is a second power compensation coefficient of the y-axis coordinate of the solar bright spot, and y_p2 is a third power compensation coefficient of the y-axis coordinate of the solar bright spot;
fourth step: the coordinate compensation coefficients (x_p0, x_p1, x_p2) and (y_p0, y_p1, y_p2) are calculated by least squares, and the sum of the values (x Actual i ，y Actual i ) Coordinate compensation is performed to obtain (x) Post-compensation i ，y Post-compensation i )，x Post-compensation i The position after the X-axis coordinate of the solar bright spot is compensated, y Post-compensation i Is the y-axis coordinate of the solar bright spotsCompensated position;
fifth step: with coordinates (x) Post-compensation i ，y Post-compensation i ) Obtaining an initial sun angle of the sun sensor:
α before compensation i Compensating the front angle, beta, for the alpha axis of the sun sensor Before compensation i Compensating a front angle for a beta axis of the sun sensor;
sixth step: build alpha at the ith angle Before compensation i And beta Before compensation i Obtaining a residual error of the output angle of the sun sensor at the moment according to the corresponding relation between the sun sensor and the turntable angle, and obtaining a compensation coefficient table of the residual error at the moment by using a polynomial fitting method;
seventh step: rounding the angle before compensation of the sun sensor to obtain beta Before compensation i Int and alpha Before compensation i _int；β Before compensation i Int is beta Before compensation i Rounding the rounded values, alpha Before compensation i Int is alpha Before compensation i Rounding the rounded values;
eighth step: the field boundary is 60 degrees, m=β Before compensation i Int, at alpha Compensation coefficient A set of coefficients (alpha) corresponding to the m degree alpha axis is found m _p0，α m _p1，α m _p2，α m _p3，α m _p4，α m _p5，α m _p6，α m P 7) obtaining an alpha axis final angular output alpha from the set of coefficients Output of ；
n＝α Before compensation i Int, beta Compensation coefficient A set of coefficients (beta) corresponding to the beta axis of n degrees n _p0，β n _p1，β n _p2，β n _p3，β n _p4，β n _p5，β n _p6，β n P 7), obtaining the beta-axis final angular output beta from the set of coefficients Output of 。
2. The method for compensating for errors in an APS sun sensor of a Mars vehicle according to claim 1, wherein: in the first step, x Actual i ＝xa i /ga i ，y Actual i ＝ya i /ga i ；
xa i Is the gray product of sun bright spots in the x direction, ya i The gray product, ga, of the solar bright spots in the y direction i Is the gray sum of the solar bright spots.
3. The method for compensating for errors in an APS sun sensor of a Mars vehicle according to claim 1, wherein: in the second step of the process, the first step,
Δx i ＝x actual i -x0；
Δy i ＝y Actual i -y0；
x Theory i ＝h×tan(α Turntable i )+x0；
y Theory i ＝h×tan(β Turntable i )+y0；
Wherein Deltax is i Is the actual position x on the x axis of the solar bright spot under the ith angle Actual i Difference from zero position, Δy i Is the actual position y on the y axis of the solar bright spots Actual i Difference from zero position, r i Is the distance between the actual position and the zero position of the solar bright spots, x Theory i Alpha-axis turntable angle alpha is the ith angle Turntable i Theoretical position of solar bright spots, y Theory i The angle of the beta-axis turntable under the ith angle is beta Turntable i The theoretical position of the solar bright spots.
4. The method for compensating for errors in an APS sun sensor of a Mars vehicle according to claim 1, wherein: in the fourth step, (x) is paired using the following formula Actual i ，y Actual i ) Coordinate compensation is performed to obtain (x) Post-compensation i ，y Post-compensation i )：
x Post-compensation i ＝x Actual i +x_p0*Δx i *r i +x_p1*Δx i *r i 2 +x_p2*Δx i *r i 3 ；
y Post-compensation i ＝y Actual i +y_p0*Δy i *r i +y_p1*Δy i *r i 2 +y_p2*Δy i *r i 3 .。
5. The method for compensating for errors in an APS sun sensor of a Mars vehicle according to claim 1, wherein: in the sixth step, the angle alpha of the alpha-axis turntable Turntable i And alpha is Before compensation i Error Δα of (a) i ＝α Turntable i -α Before compensation i ，
Beta-axis turntable angle beta Turntable i And beta Before compensation i Error Δβ of (a) i ＝β Turntable i -β Before compensation i 。
6. The method for compensating for errors in an APS sun sensor of a Mars car according to claim 5, wherein: Δα i Seven-order error compensation coefficient alpha of (2) Compensation coefficient j ＝polyfit(α Actual ji ,Δα ji ,7)(j＝-60～60,i＝-60～60)
Δβ i Seven-order error compensation coefficient beta Compensation coefficient j ＝polyfit(β Actual ji ,Δβ ji ,7)(j＝-60～60,i＝-60～60)
polyfit () is a polynomial fitting function.
7. The method for compensating for errors in the APS sun sensor of a mars car according to claim 6, wherein the residual compensation coefficients are shown as follows:
α k1 seven power compensation coefficient and alpha when p0 is alpha axis k1 degree k1 P1 is the sixth power compensation coefficient and alpha when the alpha axis is k1 degree k1 P2 is the compensation coefficient of the fifth power when the alpha axis is k1 degree, alpha k1 P3 is the fourth power compensation coefficient when the alpha axis is k1 degree, alpha k1 P4 is the third power compensation coefficient and alpha when the alpha axis is k1 degree k1 Second power compensation coefficient when p5 is alpha axis k1 degree, alpha k1 P6 is the first power compensation coefficient and alpha when the alpha axis is k1 degree k1 P7 is the compensation coefficient of a-axis k1 degree, k1= -60, -59, -58, … …,59, 60;
β k2 seven power compensation coefficient when p0 is k2 degree and beta is beta k2 P1 is the sixth power compensation coefficient when the beta axis is k2 degrees, beta k2 P2 is the compensation coefficient of the fifth power when the beta axis is k2 degrees, beta k2 Fourth power compensation coefficient when p3 is beta axis k2 degree, beta k2 P4 is the third power compensation coefficient when the beta axis is k2 degrees, beta k2 Second power compensation coefficient when p5 is k2 degree and beta is beta k2 First power compensation coefficient when p6 is k2 degree and beta is beta k2 P7 is the compensation coefficient of k2 degrees by several times, k2= -60, -59, -58, … …,59, 60.
8. The method for compensating for errors in a Mars car APS sun sensor according to claim 7, wherein in said eighth step,
α output of ＝α Before compensation i +(α m _p0×α Before compensation i 7 +α m _p1×α Before compensation i 6 +α m _p2×α Before compensation i 5 +α m _p3×α Before compensation i 4 +α m _p4×α Before compensation i 3 +α m _p5×α Before compensation i 2 +α m _p6×α Before compensation i +α m _p7)；
α m P0 is alpha Compensation coefficient Seven power compensation coefficient when the middle alpha axis is m degrees, alpha m P1 is alpha Compensation coefficient Six power compensation coefficient when the middle alpha axis is m degrees, alpha m P2 is alpha Compensation coefficient Fifth power compensation coefficient when middle alpha axis is m degree, alpha m P3 is alpha Compensation coefficient Fourth power compensation coefficient when the middle alpha axis is m degrees, alpha m P4 is alpha Compensation coefficient Third power compensation coefficient when the middle alpha axis is m degrees, alpha m P5 is alpha Compensation coefficient Second power compensation coefficient when middle alpha axis is m degree, alpha m P6 is alpha Compensation coefficient The first power compensation coefficient when the middle alpha axis is m degrees, alpha m P7 is alpha Compensation coefficient The middle alpha axis is m degrees and is often a plurality of compensation coefficients.
9. The method for compensating for errors in a Mars APS sun sensor according to claim 8, wherein,
β output of ＝β Before compensation i +(β m _p0×β Before compensation i 7 +β m _p1×β Before compensation i 6 +β m _p2×β Before compensation i 5 +β m _p3×β Before compensation i 4 +β m _p4×β Before compensation i 3 +β m _p5×β Before compensation i 2 +β m _p6×β Before compensation i +β m _p7)；
β n P0 is beta Compensation coefficient Seven power compensation coefficient when the middle beta axis is n degrees, beta n P1 is beta Compensation coefficient Six power compensation coefficient when the middle beta axis is n degrees, beta n P2 is beta Compensation coefficient The middle beta axis is the fifth power compensation coefficient when n degrees, beta n P3 is beta Compensation coefficient Fourth power compensation coefficient when middle beta axis is n degree, beta n P4 is beta Compensation coefficient The third power compensation coefficient when the middle beta axis is n degrees, beta n P5 is beta Compensation coefficient The second power compensation coefficient when the middle beta axis is n degrees, beta n P6 is beta Compensation coefficient The first power compensation coefficient when the middle beta axis is n degrees, beta n P7 is beta Compensation coefficient The middle beta axis is n degrees and is often a plurality of compensation coefficients.
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