High-precision sun sensor system design and calibration method based on PSD

Abstract

The invention discloses a PSD-based high-precision sun sensor system design and calibration method, which combines the performance of a PSD detector and the application scene of a sun sensor, analyzes matters needing attention in the design process of the PSD sun sensor, and provides an innovative method suitable for effective trepanning of a light shield of the PSD detector. And the influence of the saturation current of the PSD detector on the output solar incident angle is effectively solved. Meanwhile, errors existing in the PSD sun sensor are analyzed, a novel high-precision sun component angle calibration scheme is provided, angle calibration of the sun sensor is achieved by combining a curve fitting algorithm and a curved surface fitting algorithm, and the method can be completed only through a small amount of calculation in sun sensor hardware and is easy to achieve. Finally, the PSD sun sensor designed by the invention has the advantages of low energy consumption, fast response, low cost, small volume, strong radiation resistance and the like in the aspect of precision improvement.

Description

Technical Field

[0001] The invention belongs to the field of satellite technology, and in particular relates to a PSD-based high-precision solar sensor system design and calibration method. Background Art

[0002] The sun sensor is a common photoelectric attitude sensor, which is widely used in satellite attitude and control systems. Almost all satellites need to be equipped with a sun sensor. The sun sensor usually converts the received light signal into an electrical signal method, calculates the current data output by the sensor, and obtains the sun vector position at a certain moment, thereby determining the sun direction at this moment, and finally realizing the control of the satellite attitude.

[0003] Existing solar sensors mainly include high-precision digital solar sensors based on CCD or CMOS, which have the advantage of high accuracy in outputting attitude information, but may have problems of high power consumption and slow refresh rate; four-quadrant-based solar sensors have the advantages of simple structure, low cost, strong radiation resistance, etc., but have the problem of low measurement accuracy. A solar sensor based on PSD detector (position sensitive detector) that can combine the advantages of the above two types of solar sensors has the advantages of small size, low power consumption, low cost, etc., and can achieve high accuracy, simple structure, fast response, strong radiation resistance, etc. The research on this solar sensor is of great significance. This solar sensor can be widely used in space and energy-constrained Pina satellites. The improvement in accuracy indirectly improves the attitude accuracy and related performance of micro-nano satellites. Summary of the invention

[0004] In order to overcome the deficiencies of the prior art, the present invention provides a high-precision solar sensor system design and calibration method based on PSD. Combining the performance of the PSD detector and the application scenarios of the solar sensor, the present invention analyzes the matters that need to be paid attention to in the design process of the PSD solar sensor, and proposes an innovative method for effectively opening holes in the sunshade suitable for the PSD detector, which effectively solves the influence of the saturation current of the PSD detector on the output solar incident angle. At the same time, the errors existing in the PSD solar sensor are analyzed, and a new high-precision solar component angle calibration scheme is proposed. By combining the algorithms of curve fitting and surface fitting, the angle calibration of the solar sensor is realized. This method only requires a small amount of calculation inside the solar sensor hardware to complete, and is simple to implement. Finally, the PSD solar sensor designed by the present invention has the advantages of low energy consumption, fast response, low cost, small size, and strong radiation resistance in terms of the degree of accuracy improvement.

[0005] The technical solution adopted by the present invention to solve the technical problem is as follows:

[0006] Step 1: Design of a sunshade opening of a solar sensor based on a PSD detector; the solar sensor based on a PSD detector is referred to as a PSD solar sensor for short;

[0007] Step 1-1: Consider the sun as a black body with a surface temperature of 5770K. According to Planck's law, the solar spectrum radiation energy received by the earth's surface is:

[0008]

[0009] Where, λ is the wavelength of the sun, R is the solar half; L is the distance from the sun to the earth; c1 and c2 are constants, and T is the solar temperature; T is the solar temperature T = 5770K;

[0010] The radiation energy generated by the black body radiation reaching the earth's surface at T = 5770K is calculated by formula (1);

[0011] Step 1-2: Assume that the percentage of solar spectrum radiation energy at a certain wavelength less than the solar spectrum radiation at that wavelength in the total solar spectrum radiation is D λ ,λ p is the wavelength value; the percentage of radiation energy of each wavelength to the total solar radiation energy is P(λ);

[0012] Step 1-3: Assume that the output function of the current value of the PSD detector at different wavelengths is S(λ); each PSD detector responds to a different wavelength range, and assume that the wavelength of the PSD detector response is (λ min ~λ max ), then the unit current that the PSD detector can respond to under 1 solar constant is:

[0013]

[0014] Step 1-4: Assume the saturation current of the PSD detector is I s , the opening radius of the sunshade is r, then the following relationship should be satisfied:

[0015] I s ≥πr 2 ·I0 (4)

[0016] Therefore, the hood opening should meet the following requirements:

[0017] Step 2: Error compensation calibration of the solar sensor based on the PSD detector. The component of the solar incident angle in the x direction is α, that is, the angle between the projection of the solar ray on the x axis and the OZ axis; the component of the solar incident angle in the y direction is β, that is, the angle between the projection of the solar ray on the y axis and the OZ axis.

[0018] Step 2-1: Establish a curve relationship between the component angles of the solar incident angle output by the solar sensor and the component angles of the theoretical incident angle;

[0019] The curve fitting formula for establishing the solar sensor is as follows:

[0020]

[0021] In the formula, p i ,q i are the internal parameters of the sun sensor; α r , β r are the component angle test values ​​of the sun's incident angle in the x direction and the y direction respectively; s = 5; α m , β m are the theoretical values ​​of the component angles of the sun’s incident angle in the x-direction and the y-direction respectively;

[0022] Step 2-2: Assuming there are n component angle test values ​​of the solar incident angle, the curve fitting formula is substituted into formula (7) as follows:

[0023]

[0024]

[0025] set up

[0026]

[0027]

[0028] The resulting set of equations is:

[0029] Α1·P=α m (12)

[0030] The least square method is used to find the minimum error, and the calculation formula of P is as follows:

[0031] P=(Α1 T ·Α1) -1 ·Α1 T α m (13)

[0032] Similarly, there exists:

[0033]

[0034] The least square method is used to find the minimum error, and the calculation formula of Q is as follows:

[0035] Q = (A2 T ·Α2) -1 ·Α2 T β m(15)

[0036] Finally, the predicted value of the sun's incidence angle is:

[0037]

[0038] Among them, α k , β k are the intermediate predicted values ​​of the component angles of the solar incident angle in the x-direction and the y-direction, respectively, which are used as the input parameters of the least squares surface fitting;

[0039] Step 2-3: Establish the surface fitting formula of PSD sun sensor as follows:

[0040]

[0041] Among them, n ij ,m ij These are the internal calibration parameters of the sun sensor; e is a constant;

[0042] When e=3, the surface fitting formula of the PSD sun sensor is as follows:

[0043]

[0044] Let N = [n 00 n 01 n 02 n 03 n 10 n 11 n 12 n 20 n 21 n 30 ] T ,

[0045] M=[m 00 m 01 m 02 m 03 m 10 m 11 m 12 m 20 m 21 m 30 ] T ;

[0046] Finally, we need to get a set of parameters M and N so that With α m , With β m Infinitely close to each other;

[0047] Step 2-4: There are n groups of test data. Substitute them into formula (18) to get the residual formula for the l=1, 2, …, nth groups:

[0048]

[0049] To satisfy the minimum residuals for each set of equations, there exists the sum of squares of all residuals:

[0050]

[0051] When the minimum is reached, equation (20) is solved to obtain the values ​​of M and N, and the least squares surface calibration of the PSD sun sensor is realized;

[0052] Calculate the partial derivative of formula (20) and simplify it into a matrix form as follows:

[0053]

[0054]

[0055]

[0056] exist:

[0057]

[0058] The parameter solution is:

[0059]

[0060] The prediction equation is:

[0061]

[0062] Among them, α f ,β f are the component angles of the final solar incident angle output by the PSD solar sensor in the x-direction and the y-direction, i.e., the calibrated angles;

[0063] Step 2-5: Combine the equation after curve fitting with the equation after surface fitting, and the final calculation formula for the component angle of the solar incidence angle is as follows:

[0064]

[0065]

[0066] By combining curve fitting and surface fitting, we obtain formulas (24) and (25), which realize the error compensation of PSD sun sensor.

[0067] Preferably, the solar radius R = 6.995*108 m, the distance from the sun to the earth L = 1.496*10 11 m.

[0068] Preferably, c1=3.7418*10 20 ,Unit: W*m 2 *nm.

[0069] Preferably, c2=1.4388*10 7 , unit: nm*K.

[0070] Preferably, the solar temperature is T=5770K.

[0071] A computer program enables a computer to execute the above-mentioned solar sensor system design and calibration method.

[0072] An electronic device comprises: a processor and a memory; the memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory, so that the electronic device executes the above-mentioned solar sensor system design and calibration method.

[0073] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the above-mentioned solar sensor system design and calibration method.

[0074] A chip includes: a processor for calling and running a computer program from a memory, so that a device equipped with the chip executes the above-mentioned solar sensor system design and calibration method.

[0075] A computer program product, the computer program product comprising a computer storage medium, the computer storage medium storing a computer program, the computer program comprising instructions executable by at least one processor, and the above-mentioned solar sensor system design and calibration method is implemented when the instructions are executed by the at least one processor.

[0076] The beneficial effects of the present invention are as follows:

[0077] 1. The overall design process of the PSD solar sensor provided by the present invention takes into account the saturation current of the PSD detector according to the performance of the PSD detector itself, and proposes a method for designing the aperture of the sunshade under the condition of satisfying the photoelectric linearity, so as to ensure that the PSD detector outputs valid data under 1 solar constant. A PSD solar sensor design framework scheme is also provided, including preliminary analysis, electrical design, and a calculation scheme from output voltage to the final solar component angle. By analyzing the influence of the errors generated in each link on the resulting solar component angle, an error compensation scheme is proposed, which makes the accuracy of the solar component angle output by the compensated PSD solar sensor higher. The error compensation scheme is highly feasible, has a small amount of calculation, and can be widely used. The PSD solar sensor compensates the accuracy of its own measurement of the α angle from 5.2912° to 0.2262°, and compensates the accuracy of the measurement of the β angle from 7.7766° to 0.1561°.

[0078] 2. The present invention proposes an error compensation scheme suitable for PSD solar sensor, which calculates calibration parameters by combining curve fitting and surface fitting methods. The scheme mainly implements complex operations on an external computer, writes the calibration parameters into the PSD solar sensor, and only requires a small amount of calculation to complete the compensation operation of the solar component angle, which is easy to implement.

[0079] 3. The calibration scheme provided by the present invention can save a lot of manpower and time, making the PSD solar sensor easier to mass produce. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] Figure 1 is the solar radiation corresponding to each wavelength;

[0081] Figure 2 (a) is the plan view of the two-dimensional pillow-shaped PSD detector. Figure 2 (b) is the cross-sectional view of the PSD sun sensor;

[0082] Figure 3 is the solar incidence angle component diagram;

[0083] Figure 4 System framework for the electrical design of the PSD sun sensor. DETAILED DESCRIPTION

[0084] The present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0085] The present invention designs a high-precision solar sensor system design method based on PSD, which ensures fast response rate and high resolution of the system while improving the accuracy; at the same time, the conditions that should be met in the selection of the sunshade opening when designing the solar sensor system are given, and a corresponding calculation method is proposed to meet the effective field of view data of the solar sensor; and an error compensation calibration algorithm applied to the output solar component angle of the PSD solar sensor is given, which can effectively improve the accuracy of the solar sensor.

[0086] The present invention is achieved through the following technical solutions:

[0087] In the design process of PSD solar sensor, knowledge of optics, mechanical structure and circuit is needed. Firstly, according to the working environment requirements of PSD solar sensor, the aperture requirements of sunshade processing are analyzed. The design concept of sunshade used by PSD solar sensor is basically the same as that of conventional sun sensor sunshade, and the main thing to pay attention to is the size of the opening area of ​​the sunshade.

[0088] The PSD detector has a saturation current. Within the saturation current, there is a certain linear relationship between the light intensity and the output current. If the saturation current is exceeded, the linearity of the light intensity and the output current deviates. When designing the size of the sunshade opening, it is important to note that the current generated by the maximum light irradiation energy entering the field of view of the solar sensor is less than the saturation current of the PSD.

[0089] The PSD solar sensor is installed on the spacecraft. When it is running on a certain orbit, the solar energy received is approximately within one solar constant. It is necessary to calculate the unit current generated by the PSD under one solar constant. First, we need to understand the energy generated by the sun's rays reaching the earth's surface. In general, the sun can be regarded as a black body with a surface temperature of 5770K. According to Planck's law, the solar spectrum radiation energy received by the earth's surface is:

[0090]

[0091] Where λ is the wavelength of the sun, and the radius of the sun is R = 6.995*10 8 m;

[0092] The distance from the sun to the earth is L = 1.496*10 11 m;

[0093] Constant c1=3.7418*10 20 ,Unit: W*m 2 *nm;

[0094] Constant c2=1.4388*10 7 , unit: nm*K;

[0095] The temperature of the sun is T = 5770K.

[0096] The radiation energy generated by the black body radiation reaching the earth's surface at T = 5770K can be obtained by formula (1). Figure 1 .

[0097] The solar spectrum radiation energy of a certain wavelength is less than the percentage of the solar spectrum radiation of this wavelength in the total solar spectrum radiation. λ , see Table 1:

[0098] Table 1

[0099]

[0100]

[0101] It can be seen from Table 1 that the proportion of each wavelength is different. The various wavelengths within the range of two adjacent wavelengths in the table can be regarded as having the same proportion when calculating. Then the percentage of each wavelength in the entire solar spectrum is calculated as:

[0102]

[0103] The photosensitivity of the PSD detector is that the output current is different under different wavelengths. The output function of the current value of the PSD detector at different wavelengths is S(λ), and the unit is (A / W). If there is no direct correspondence in the technical documentation of the selected PSD detector, the response function relationship can be obtained by taking data points and fitting the provided photosensitivity diagram. Each PSD detector can respond to a different wavelength range. Assuming that a PSD detector is selected that can respond to a wavelength of (λ min ~λ max ), then the unit current that the PSD detector can respond to under 1 solar constant is:

[0104]

[0105] Assume that the saturation current of the selected PSD is I s , the opening radius of the sunshade is r, then the following relationship should be satisfied:

[0106] I s ≥πr 2 ·I0 (4)

[0107] Therefore, the hood opening should meet the following requirements:

[0108] according to Figure 2The bottom of the PSD sun sensor is a pillow-shaped two-dimensional PSD detector with a side length of L. The center of the detector is the center point O of the coordinate system, and the entire PSD detector plane constitutes an Oxyz coordinate system. A light shield with a circular light introducer with a radius of r is set above the PSD detector, and the center of the light hole is aligned with the center of the circular hole of the light shield.

[0109] When sunlight shines on the photosensitive plane through the circular hole in the center of the sunshade at a certain incident angle, a light spot is formed on the PSD detector, and the currents generated on the four electrodes are I1, I2, I3, and I4 respectively. The currents of the four electrodes corresponding to the light spot falling on different positions of the PSD detector are different. The coordinates of the center of the light spot are (dx, dy), and the calculation formula is as follows:

[0110]

[0111]

[0112] Wherein, dx is the horizontal coordinate value of the center of the solar spot, and dy is the vertical coordinate value of the center of the solar spot.

[0113] like Figure 3 As shown, the component of the solar incident angle in the x direction is defined as α, that is, the angle between the projection of the solar ray on the x axis and the OZ axis; the component of the solar incident angle in the y direction is β, that is, the angle between the projection of the solar ray on the y axis and the OZ axis; H is the height between the sunshade and the photosensitive surface of the PSD detector. The calculation formula of the component angle of the solar incident angle is as follows:

[0114] α=arctan(dx / H)

[0115] β=arctan(dy / H) (6)

[0116] The design principle of the PSD solar sensor electrical system is the same as that of the four-quadrant solar sensor electrical system. Figure 4 , mainly including an optical system, a PSD detector, a signal processing module (signal amplification circuit, A / D conversion circuit), and a data processing module (output voltage detection unit, component angle calculation unit of the solar incident angle, component angle calibration unit of the solar incident angle).

[0117] For the signal processing module: the current value output by each electrode of the PSD needs to be amplified and converted to analog / digital (Analog to Digital, A / D). The signal processing module and the data processing module use SPI mode communication, which can ensure the synchronization of sending and receiving data on the serial communication bus. The signal processing module adopts a common processing method. When amplifying the signal, attention should be paid to the selection of the amplification factor, which should be determined in combination with the diameter of the sunshade opening. The signal processing module of the PSD sun sensor is consistent with the implementation principle of the signal processing module of the traditional four-quadrant-based sun sensor.

[0118] For the data processing module: including the output voltage detection unit, the solar component angle calculation unit, and the solar component angle calibration unit, all of which are implemented using algorithm software.

[0119] The calculation formulas of the component angles of the solar incident angle are shown in (5) and (6). The component angle calibration unit of the solar incident angle is specifically shown in the following steps.

[0120] During the processing and assembly of the PSD solar sensor, some errors will be generated, mainly including: assembly error between the solar sensor and the PSD detector, assembly error of the PSD detector on the PCB, and assembly error of the PSD and PCB as a whole with the solar sensitive housing. These errors will cause a certain deviation between the calculated component angles of the solar incident angle and the actual component angles of the solar incident angle. The assembly error between the solar sensor and the PSD detector includes the center offset error of the sunshade relative to the PSD detector, the rotation error (the rotation angle of the sunshade relative to the PSD detector around the z-axis) and the plane tilt error (the rotation angle of the sunshade relative to the PSD detector around the x- and y-axes). The assembly error of the PSD detector on the PCB board mainly includes: rotation error (the PSD detection board rotates around the z-axis relative to the PCB board) and tilt error (the PSD detector rotates around the x- and y-axes relative to the PCB board). The assembly error of the PSD and PCB as a whole with the solar sensitive housing mainly includes: rotation error (the PSD detector and PCB as a whole rotate around the z-axis relative to the solar sensor housing) and tilt error (the PSD detector and PCB as a whole rotate around the x- and y-axes relative to the solar sensor housing). The above errors are errors caused by external parameters. There are also some PSD detector output noise, signal acquisition and processing circuit noise, which will directly affect the data output by the solar sensor.

[0121] Some errors can be tested using high-precision measuring instruments, while some errors require a lot of experimental analysis. In practical applications, the confirmation and measurement of errors requires a lot of manpower and material resources, which does not meet the needs of low-cost, mass-produced products. The present invention mainly analyzes the direct impact of errors and uses a fitting method to uniformly compensate for data errors.

[0122] By analyzing the error, we know that the component angle α of the solar incident angle output by the solar sensor is r , β r There is a nonlinear relationship with the component angles α and β of the theoretical solar incident angle, and they are mutually coupled. Therefore, there is a certain error in the solar component angle data initially calculated by the PSD solar sensor, and the accuracy of the output angle needs to be further improved through testing and appropriate calibration algorithms.

[0123] The component angle α of the solar incidence angle r They are affected by two aspects of data: on the one hand, the component angle α of the sun's incident angle is tested. r The nonlinear relationship between the component angle α of the theoretical solar incident angle and the component angle α of the tested solar incident angle is r The nonlinear relationship between the component angles α and β of the theoretical solar incident angle. Similarly, the component angle β of the solar incident angle r It is also affected by this aspect. Through practical and measured analysis, this paper uses two algorithms to calibrate the solar incidence angle, namely least squares curve fitting and least squares surface fitting.

[0124] According to the actual situation of the PSD solar sensor, a curve relationship between the component angles of the output incident angle of the solar sensor and the component angles of the theoretical incident angle is established to reduce the measurement error of the solar sensor.

[0125] The curve fitting formula for establishing the solar sensor is as follows:

[0126]

[0127] In the formula, p i ,q i is the internal parameter of the solar sensor, which is related to its own performance and is different for each sensor; s is determined by the product performance and is calculated based on the test data. It is generally 3 to 5. Here, s = 5;

[0128] Assuming there are n component angle test values ​​of the solar incident angle, the curve fitting formula is substituted as follows:

[0129]

[0130]

[0131] in,

[0132]

[0133]

[0134] The system of equations is:

[0135] Α1·P=αm (12)

[0136] The least square method is used to find the minimum error, and the calculation formula of P is as follows:

[0137] P=(Α1 T ·Α1) -1 ·Α1 T α m (13)

[0138] Similarly, there exists:

[0139]

[0140] The least square method is used to find the minimum error, and the calculation formula of Q is as follows:

[0141] Q = (A2 T ·Α2) -1 ·Α2 T β m (15)

[0142] Finally, the predicted values ​​of the component angles of the solar incidence angle are:

[0143]

[0144] Among them, α k , β k It is the intermediate predicted value of the component angle of the solar incident angle in the x-direction and the y-direction, which is used as the input parameter of the least squares surface fitting.

[0145] The surface fitting formula for establishing the PSD sun sensor is as follows:

[0146]

[0147] The parameter e is usually 3 to 5;

[0148] When e=3, the surface fitting formula of the PSD sun sensor is as follows:

[0149]

[0150] Let N = [n 00 n 01 n 02 n 03 n 10 n 11 n 12 n 20 n 21 n 30 ] T ,

[0151] M=[m 00 m 01 m 02 m 03 m 10 m 11 m 12 m 20 m 21 m 30 ] T .

[0152] Finally, we need to get a set of parameters M and N so that With α m , With β m Infinitely close.

[0153] There are n groups of test data. Substituting them into the above formula, we can get the lth (l=1,2,…,n) residual formula as follows:

[0154]

[0155] ε αl , ε βl The smaller the value, the closer it is to the theoretical value and the better the fitting effect. To ensure that the residuals of each set of equations are minimized, the sum of squares of all residuals must be

[0156]

[0157] Reaching the minimum, solving the above equations, and obtaining the values ​​of M and N, the least squares surface calibration of the PSD sun sensor is realized.

[0158] By taking partial derivatives of the above formula and simplifying it into a matrix form as follows:

[0159]

[0160]

[0161]

[0162] exist:

[0163]

[0164] The parameter solution is:

[0165]

[0166] At this time, the prediction equation is:

[0167]

[0168] Among them, αf ,β f The output of the PSD sun sensor ultimately predicts the component angles of the solar incidence angle.

[0169] Combining the equation after curve fitting with the equation after surface fitting, the final formula for the component angle prediction value of the solar incidence angle is as follows:

[0170]

[0171]

[0172] By combining curve fitting and surface fitting, we obtain formulas (24) and (25), which realize the error compensation of PSD sun sensor. Through this error compensation scheme, the fitted calibration parameters are written into the Flash of the sun sensor, which significantly improves the accuracy of PSD sun sensor.

[0173] Example:

[0174] The embodiment of the present invention provides a design and error calibration scheme for a PSD sun sensor, and the implementation steps are as follows:

[0175] Step 1: Determine the aperture of the sunshade according to the requirements. According to the saturation current of the PSD detector and the application scenario of the PSD sun sensor, calculate the unit current of the PSD detector and determine the aperture diameter of the sunshade.

[0176] I s ≥πr 2 ·I0

[0177] Among them, I s is the saturation current of the PSD detector, and I0 is the unit current of the PSD detector in a certain application environment.

[0178] Step 2, calculate the incident component angles α and β with errors.

[0179]

[0180] Among them, α is the angle between the projection of the solar incident angle on xoz and the oz axis; β is the angle between the projection of the solar incident angle on yoz and the oz axis; L is the side length of the photosensitive surface of the selected PSD detector; H is the distance from the sun hood to the photosensitive surface of the PSD detector; I1, I2, I3, and I4 are the currents output by the four electrodes of the PSD detector.

[0181] The embodiment of the present invention provides a solar component angle calibration method for a PSD solar sensor, and a method for calculating various parameters in the calibration method. The implementation steps are as follows:

[0182] Step 1: Write a program inside the PSD solar sensor to collect the current of the four electrodes and convert it into a voltage value through the current pressure. Calculate the solar component angle according to formulas (5) and (6) and wait for calibration.

[0183] Step 2: Full-field automated calibration data collection: fix the PSD solar sensor to a two-dimensional turntable, and control the rotation of the turntable through a computer to traverse the entire field of view. Taking the positive and negative field of view of 60° as an example, a dual-axis turntable is used with a step size of 3° to generate solar component angles α and β covering the entire field of view. At each angle, collect a few seconds of data, and automatically record the angle of the turntable and the four-way voltage value output by the PSD solar sensor. A PSD solar sensor needs to collect 1681 sets of calibration point data, that is, there are i component angles (α ri ,β ri ) corresponds to the component angle (α mi ,β mi ), some data are shown in Table 2.

[0184] Table 2

[0185]

[0186]

[0187] Step 3, calibration parameter calculation, calculate a set of calibration parameters according to formula (13), substitute it into formula (22), and then calculate another set of calibration parameters according to formula (22). Substitute the two sets of calibration parameters into formula (23), and this formula is written into the internal calibration program of the PSD sun sensor.

[0188] The calibrated coefficients are shown in Table 3:

[0189] Table 3

[0190]

[0191] The measurement accuracy before and after calibration is shown in Table 4:

[0192] Table 4

[0193] α angle β angle Before calibration 5.2912°(1σ) 7.7766°(1σ) After calibration 0.2262°(1σ) 0.1561°(1σ)

[0194] As can be seen from the above table, the PSD sun sensor improves the accuracy of measuring the α angle from 5.2912° to 0.2262°, and improves the accuracy of measuring the β angle from 7.7766° to 0.1561°.

Claims

1. A high-precision solar sensor system design and calibration method based on PSD, characterized in that: The steps include: Step 1: Design of a sunshade opening of a solar sensor based on a PSD detector; the solar sensor based on a PSD detector is referred to as a PSD solar sensor for short; Step 1-1: Consider the sun as a black body with a surface temperature of 5770K. According to Planck's law, the solar spectrum radiation energy received by the earth's surface is: Where, λ is the wavelength of the sun, R is the solar half; L is the distance from the sun to the earth; c1 and c2 are constants, and T is the solar temperature; T is the solar temperature T = 5770K; The radiation energy generated by the black body radiation reaching the earth's surface at T = 5770K is calculated by formula (1); Step 1-2: Assume that the percentage of solar spectrum radiation energy at a certain wavelength less than the solar spectrum radiation at that wavelength in the total solar spectrum radiation is D λ ,λ p is the wavelength value; the percentage of radiation energy of each wavelength to the total solar radiation energy is P(λ); Step 1-3: Assume that the output function of the current value of the PSD detector at different wavelengths is S(λ); each PSD detector responds to a different wavelength range, and assume that the wavelength of the PSD detector response is (λ min ~λ max ), then the unit current that the PSD detector can respond to under 1 solar constant is: Step 1-4: Assume the saturation current of the PSD detector is I s , the opening radius of the sunshade is r, then the following relationship should be satisfied: I s ≥πr 2 ·I0 (4) Therefore, the hood opening should meet the following requirements: Step 2: Error compensation calibration of the solar sensor based on the PSD detector. The component of the solar incident angle in the x direction is α, that is, the angle between the projection of the solar ray on the x axis and the OZ axis; the component of the solar incident angle in the y direction is β, that is, the angle between the projection of the solar ray on the y axis and the OZ axis. Step 2-1: Establish a curve relationship between the component angles of the solar incident angle output by the solar sensor and the component angles of the theoretical incident angle; The curve fitting formula for establishing the solar sensor is as follows: In the formula, p i ,q i are the internal parameters of the sun sensor; α r , β r are the component angle test values ​​of the sun's incident angle in the x direction and the y direction respectively; s = 5; α m , β m are the theoretical values ​​of the component angles of the sun’s incident angle in the x-direction and the y-direction respectively; Step 2-2: Assuming there are n component angle test values ​​of the solar incident angle, the curve fitting formula is substituted into formula (7) as follows: set up The resulting set of equations is: A1·P=a m (12) The least square method is used to find the minimum error, and the calculation formula of P is as follows: P=(A1 T ·A1) -1 ·A1 T ·a m (13) Similarly, there exists: The least square method is used to find the minimum error, and the calculation formula of Q is as follows: Q=(A2 T ·A2) -1 ·A2 T ·b m (15) Finally, the predicted value of the sun's incidence angle is: Among them, α k , β k are the intermediate predicted values ​​of the component angles of the solar incident angle in the x-direction and the y-direction, respectively, which are used as the input parameters of the least squares surface fitting; Step 2-3: Establish the surface fitting formula of PSD sun sensor as follows: Among them, n ij ,m ij These are the internal calibration parameters of the sun sensor; e is a constant; When e=3, the surface fitting formula of the PSD sun sensor is as follows: Let N = [n 00 n 01 n 02 n 03 n 10 n 11 n 12 n 20 n 21 n 30 T ,​ M=[m 00 m 01 m 02 m 03 m 10 m 11 m 12 m 20 m 21 m 30 ] T ; Finally, we need to get a set of parameters M and N so that With α m , With β m Infinitely close to each other; Step 2-4: There are n groups of test data. Substitute them into formula (18) to get the residual formula for the l=1, 2, …, nth groups: To satisfy the minimum residuals for each set of equations, there exists the sum of squares of all residuals: When the minimum is reached, equation (20) is solved to obtain the values ​​of M and N, and the least squares surface calibration of the PSD sun sensor is realized; Calculate the partial derivative of formula (20) and simplify it into a matrix form as follows: exist: The parameter solution is: The prediction equation is: Among them, α f ,β f are the component angles of the final solar incident angle output by the PSD solar sensor in the x-direction and the y-direction, i.e., the calibrated angles; Step 2-5: Combine the equation after curve fitting with the equation after surface fitting, and the final calculation formula for the component angle of the solar incidence angle is as follows: By combining curve fitting and surface fitting, we obtain formulas (24) and (25), which realize the error compensation of PSD sun sensor.

2. The method for designing and calibrating a high-precision solar sensor system based on PSD according to claim 1, characterized in that: The solar radius R = 6.995*10 8 m, the distance from the sun to the earth L = 1.496*10 11 m.

3. The method for designing and calibrating a high-precision solar sensor system based on PSD according to claim 1, characterized in that: c1=3.7418*10 20 ,Unit: W*m 2 *nm.

4. The method for designing and calibrating a high-precision solar sensor system based on PSD according to claim 1, characterized in that: c2=1.4388*10 7 , unit: nm*K.

5. The method for designing and calibrating a high-precision solar sensor system based on PSD according to claim 1, characterized in that: The solar temperature T = 5770K.

6. A computer program, characterized in that The computer program enables a computer to execute the method according to any one of claims 1 to 5.

7. An electronic device, characterized in that: include: Processor and memory; The memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory, so that the electronic device executes the method as claimed in any one of claims 1 to 5.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method according to any one of claims 1 to 5 is implemented.

9. A chip, characterized in that: include: A processor, configured to call and run a computer program from a memory, so that a device equipped with the chip executes a method as claimed in any one of claims 1 to 5.

10. A computer program product, characterized in that The computer program product comprises a computer storage medium storing a computer program, wherein the computer program comprises instructions executable by at least one processor, and when the instructions are executed by the at least one processor, the method according to any one of claims 1 to 5 is implemented.

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