Servo pointing error correction method based on nonlinear semi-parameter model least square estimation

Abstract

The invention relates to a servo pointing error correction method based on nonlinear semi-parameter model least square estimation. The method comprises the following steps: acquiring a series of actual azimuth angle observation values and pitch angle observation values # imgabs0 # and # imgabs1 # to construct azimuth angle and pitch angle error correction functions f (alpha i, beta i) and g (alpha i, beta i); constructing a semi-parameter model of the azimuth angle error delta alpha i and the pitch angle error delta beta i, performing parameter identification of the semi-parameter model by adopting a least square iteration method to obtain an undetermined parameter pi, and obtaining a first-stage estimated value pi * of the pi; substituting pi * into the semi-parametric model, and estimating the non-parametric quantity by adopting a kernel estimation method to obtain a first-stage estimated value h alpha i * of the non-parametric quantity h alpha i and a first-stage estimated value h beta i * of the non-parametric quantity h beta i; and the pointing error correction model is used for accurately calculating an azimuth angle error delta alpha i and a pitch angle error delta beta i. A nonlinear semi-parameter model is adopted to correct errors, the ability of the model to suppress interference of nonlinear error factors is enhanced, and error parameters are positioned more accurately.

Description

Technical Field

[0001] The present invention belongs to the technical field of servo pointing error correction, and more specifically, relates to a servo pointing error correction method based on the least squares estimation of a non-linear semi-parametric model. Background Art

[0002] Servo pointing systems are mainly applied in industries, aviation, military, surveying and mapping, etc., serving multiple platform devices such as numerically controlled machine tools, coordinate measuring machines, and optoelectronic stabilization platforms. The pointing accuracy not only affects its own performance, but also affects the accuracy and reliability of the entire platform. The present invention analyzes various error sources of the servo pointing mechanism, establishes a servo pointing model, uniformly selects several points in the full field of view area, compares the deviation between the theoretical outgoing light beam and the actual outgoing light beam, estimates the non-linear error through the least squares estimation theory of the non-linear semi-parametric model, so as to achieve precise correction of various linear errors and effectively improve the pointing accuracy of the servo system. Currently, the methods adopted by servo pointing correction models include methods based on the product of exponentials formula, genetic algorithm estimation, least squares calibration, Monte Carlo theory, etc., and various pointing error models based on multi-body system theory. However, the above models mostly only consider the model error in the physical sense and ignore the random error, resulting in inaccurate parameter estimation and further affecting the improvement of the pointing accuracy. The error influencing factors of optoelectronic detection systems are very complex. The existing L-M model can only model and analyze the main linear error factors. Refer to Patent 202210097369.3 "Rotation Double Prism Pointing Deviation Correction Method Based on Levenberg-Marquardt Algorithm", which unifies all non-linear factors into the observation noise, which does not conform to the actual situation, thus restricting the further improvement of the pointing accuracy and the model parameter identification accuracy. In order to make up for the deficiencies of the L-M model and enhance the ability of the model to suppress the interference of non-linear error factors, it is urgent to propose a new servo pointing error correction method. Summary of the Invention

[0003] Aiming at the shortcomings of the above-mentioned existing technologies, on the basis of considering various linear errors, a method of constructing a semi-parametric model is adopted to remove random errors, so as to obtain error parameters that more conform to the actual situation and improve the correction accuracy.

[0004] In a first aspect, an embodiment of the present invention provides a servo pointing error correction method based on the least squares estimation of a non-linear semi-parametric model, including:

[0005] Obtaining a series of actual azimuth angle observation values and elevation angle observation values and

[0006] Constructing an azimuth angle and elevation angle error correction function f(α i, β i ), and g(α i , β i ), where, in addition to known parameter quantities, there are also unknown parameter quantities that cannot be measured;

[0007] Construct a semi - parametric model of the azimuth error δα i and the elevation angle error δβ i . The azimuth error δα i and the elevation angle error δβ i can be expressed as:

[0008]

[0009] where α i is the theoretical calculated value of the azimuth angle, β i is the theoretical calculated value of the elevation angle, is the azimuth error correction value brought by non - parametric quantities, is the elevation angle error correction value brought by non - parametric quantities; f(α i , β i ; p i ) is the theoretical calculated value of the azimuth angle considering parameter quantities, g(α i , β i ; p i ) is the theoretical calculated value of the elevation angle considering parameter quantities;

[0010] Adopt the least - squares iteration method to identify the parameters of the semi - parametric model, obtain the undetermined parameter (quantity) pi, and obtain the first - stage estimated value pi* of pi;

[0011] Substitute pi* into the semi - parametric model, and use the kernel estimation method to estimate the non - parametric quantities, obtaining the first - stage estimated value h αi * of the non - parametric quantity h αi and the first - stage estimated value h βi * of the non - parametric quantity h βi *;

[0012] Substitute the non - parametric errors h αi * and h βi * of the first stage into the semi - parametric model, and use the least - squares method again to obtain the second - stage estimated value i of the undetermined parameter p At the same time, substitute into the semi - parametric model to calculate and obtain and That is, the pointing error correction model is obtained;

[0013] The pointing error correction model is used to accurately calculate the azimuth error δα i and the elevation angle error δβi 。

[0014] In some possible embodiments, the obtaining of a series of actual azimuth angle observations and elevation angle observations and includes: setting up a test device for actual azimuth angle observations and elevation angle observations and The test device includes a laser, an optoelectronic servo platform and a receiving screen arranged along the optical path. The distance between the exit port of the optoelectronic servo platform and the receiving screen is L mm. The receiving screen is fixed on a two-dimensional translation stage, and the receiving screen is used to measure the pointing angle information of the optoelectronic servo platform, that is, the azimuth angle observation and the elevation angle observation; establish a right-handed receiving screen coordinate system O1-X1Y1Z1;

[0015] According to the calibrated zero position of the optoelectronic servo platform and the coordinate system, a series of measurement points are tested to obtain a series of actual azimuth angle observations and elevation angle observations and

[0016] In some possible embodiments, the receiving screen uses a large area array CCD.

[0017] In some possible embodiments, the to-be-determined parameter quantity pi includes: laser incident angle X (laser incident angle in the X1 direction), laser incident angle Y (laser incident angle in the Y1 direction), the distance between the optoelectronic servo platform and the receiving screen, scanning coordinate system rotation (compared with the horizontal coordinate system, there may be a certain rotation in the coordinate system of the servo), the tilt error of the optoelectronic servo platform in the X1 direction, and the tilt error of the optoelectronic servo platform in the Y1 direction. Among them, the laser incident angle X and the laser incident angle Y can be measured and are known parameter quantities, and the others are unknown parameter quantities;

[0018] In some possible embodiments, substituting pi* into the semi-parametric model and using the kernel estimation method to estimate the non-parametric quantity, the obtained first-stage estimated value h of the non-parametric quantity h αi of the first-stage estimated value h αi * and the first-stage estimated value h of the non-parametric quantity h βi of the first-stage estimated value h βi *, specifically includes: substituting p i * into the semi-parametric model, and the following can be obtained

[0019]

[0020] According to the above formula, it can be obtained that

[0021]

[0022] where

[0023] The non-parametric quantity is estimated by the kernel estimation method. K is the selected kernel function. Considering the distribution property of the measurement data, the Gaussian kernel function is adopted here. H is the window width, which is a constant related to n, and n is the constant obtained by fitting. The mean square error is used to measure the accuracy of the kernel estimation. When the mean square error is the smallest, the non-parametric quantity h αi The first-stage estimated value h αi * and the non-parametric quantity h βi The first-stage estimated value h βi *.

[0024] In a second aspect, an embodiment of the present invention provides a servo pointing error correction device based on the least squares estimation of a non-linear semi-parametric model. The device includes:

[0025] An acquisition module for acquiring a series of actual azimuth angle observation values and elevation angle observation values and

[0026] A model construction module for constructing azimuth angle and elevation angle error correction functions f(α i , β i ) and g(α i , β i ), where, in addition to the known parameter quantities, there are also unknown parameter quantities that cannot be measured;

[0027] For constructing a semi-parametric model for the azimuth angle error δα i and the elevation angle error δβ i . The azimuth angle error δα i and the elevation angle error δβ i can be expressed as:

[0028]

[0029] where, α i is the azimuth angle calculated value, β i is the elevation angle calculated value, is the azimuth angle error correction value brought by the non-parametric quantity, that is, the unknown parameter quantity, is the elevation angle error correction value brought by the non-parametric quantity, that is, the unknown parameter quantity;

[0030] A parameter identification module for identifying the parameters of the semi-parametric model by using the least squares iteration method to obtain the undetermined parameter pi and the first-stage estimated value pi* of pi;

[0031] A non-parametric quantity estimation module for substituting pi* into the semi-parametric model and estimating the non-parametric quantity by using the kernel estimation method to obtain the non-parametric quantity hαi The first-stage estimated value h αi * and the non-parametric quantity h βi The first-stage estimated value h βi *;

[0032] Obtain a pointing error correction model module for substituting the non-parametric errors h αi * and h βi * of the first stage into the semi-parametric model, and again using the least squares method to obtain the undetermined parameter p i The second-stage estimated value Meanwhile, substitute into the semi-parametric model for calculation to obtain and That is, the pointing error correction model is obtained;

[0033] An application module for accurately calculating the azimuth error δα i and the elevation angle error δβ i .

[0034] Thirdly, an embodiment of the present invention provides an electronic device, including:

[0035] At least one processor, at least one memory, and a communication interface; wherein,

[0036] The processor, the memory, and the communication interface communicate with each other;

[0037] The memory stores program instructions executable by the processor, and the processor invokes the program instructions to execute the method described in the first aspect.

[0038] Fourthly, an embodiment of the present invention provides a non-transitory computer-readable storage medium, and the non-transitory computer-readable storage medium stores computer instructions, and the computer instructions cause the computer to execute the method described in the first aspect.

[0039] The servo pointing error correction method based on the least squares estimation of the non-linear semi-parametric model of the present invention has the following advantages:

[0040] Aiming at the deficiencies of numerous error sources in the existing servo system and difficulty in achieving accurate pointing, the present invention establishes a non-linear semi-parametric model of servo pointing error, uniformly selects several points in the full field of view area, compares the deviation between the theoretical outgoing beam and the actual outgoing beam of the servo, and corrects the system error of the servo through the least squares estimation theory of the non-linear semi-parametric model, realizing high-precision pointing of the servo.

[0041] On the basis of completing the servo pointing error measurement, a non-linear semi-parametric model is used to correct this error. At the same time, considering the deficiencies of previous models in ignoring non-linear factors, the ability of the model to suppress the interference of non-linear error factors is enhanced, and the error parameters can be located more accurately. On the basis of considering various linear errors, the method of constructing a non-linear semi-parametric model is used to remove random errors, so as to obtain error parameters that more conform to the actual situation and improve the correction accuracy. Brief Description of the Drawings

[0042] Figure 1 It is a schematic flowchart of the method of the present invention;

[0043] Figure 2 It is the actual azimuth angle observation value and elevation angle observation value of the present invention and The structural schematic diagram of the test device.

[0044] Figure 3 It is a schematic diagram of the measurement point distribution of the present invention. In the figure, the asterisks represent the theoretical calculation results, and the squares represent the actual measurement results.

[0045] In the figure, 1 - laser source, 2 - optoelectronic servo platform, 3 - receiving screen, 4 - two-dimensional translation stage. Specific Embodiments

[0046] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0047] Example 1

[0048] As Figure 1 shown, the servo pointing error correction method based on the least square estimation of the non-linear semi-parametric model in this embodiment includes:

[0049] Obtain a series of actual azimuth angle observation values and elevation angle observation values and

[0050] In this embodiment, obtaining a series of actual azimuth angle observation values and elevation angle observation values and includes: building a test device for actual azimuth angle observation values and elevation angle observation values and as Figure 2As shown, the test device includes a laser, an optoelectronic servo platform, and a receiving screen arranged along the optical path. The distance between the exit port of the optoelectronic servo platform and the receiving screen is L mm. The receiving screen is fixed to a two-dimensional translation stage, and a right-handed receiving screen coordinate system O1-X1Y1Z1 is established.

[0051] According to the calibrated zero position of the optoelectronic servo platform and the coordinate system, a series of measurement points are tested to obtain a series of actual azimuth angle observation values and elevation angle observation values. and

[0052] The incident light uses a 532 nm laser. A receiving screen is set at a distance L from the exit port of the optoelectronic servo platform. A right-handed receiving screen coordinate system O1-X1Y1Z1 is established. The receiving screen uses a large area array CCD. The receiving screen is fixed on a two-dimensional translation stage. The travel of the translation stage is 300 mm × 300 mm, and the single-step resolution accuracy is 2.5 μm. The receiving screen is used to measure the pointing angle information of the optoelectronic servo platform, that is, the azimuth angle observation value and the elevation angle observation value.

[0053] The specific test steps include: Select typical servo pointing angles, input the corresponding angles in the servo control software, and control the optoelectronic servo platform to rotate to the corresponding angles; Move the two-dimensional translation stage according to the theoretical simulation results so that the camera measures the images at the corresponding angles; For all the light points on the image, convert the pixel values into distance values; According to the calibrated servo zero position (the zero position of the optoelectronic servo platform) and the coordinate system, rotate multiple groups of measurement points for testing. To ensure the accuracy of the measurement, the more measurement points, the more accurately the pointing accuracy of the servo can be measured. In this experiment, 136 groups of measurements are selected. These 136 groups of experiments cover the ±x-axis, ±y-axis, ±45°, and ±135° diagonals. The distribution of the measurement points is shown in the following figure. The asterisks in the figure represent the theoretical calculation results, and the squares represent the actual measurement results. It can be seen that according to the method of the present invention, the theoretical calculation value and the actual measurement result are in good agreement, indicating that the method of the present invention has a high correction accuracy, as Figure 3 shown.

[0054] Construct the azimuth angle and elevation angle error correction functions f(α i , β i ) and g(α i , β i ), where, in addition to the known parameter quantities, there are also unknown parameter quantities that cannot be measured. Considering the unmeasurable unknown parameter quantities will achieve accurate estimation;

[0055] Construct the semi-parametric models of the azimuth angle error δα i and the elevation angle error δβ i . The azimuth angle error δα i and the elevation angle error δβ i can be expressed as:

[0056]

[0057] Among them, α i is the theoretical calculated value of the azimuth angle, f(α i ,β i ; p i ) is the theoretical calculated value of the azimuth angle considering the undetermined parameter quantity pi (including known parameter quantities and unknown parameter quantities); β i is the theoretical calculated value of the elevation angle, g(α i ,β i ; p i ) is the theoretical calculated value of the elevation angle considering the undetermined parameter quantity pi, is the azimuth angle error correction value brought by non-parameter quantities, is the elevation angle error correction value brought by non-parameter quantities; and are the model error quantities describing the unknown functional relationship, used to represent the non-linear error factors, thus not only inheriting the empirical advantages of the error analysis model but also overcoming the limitations of the basic parameter model. On the one hand, it can make the mathematical model closer to the objective reality, and on the other hand, it can numerically obtain the estimates of parameters and non-parameters respectively, and can make more full use of the information provided by the pointing error observation data;

[0058] The least squares iterative method is used for parameter identification of the semi-parameter model to obtain the correction of the undetermined parameters, that is, pi (including known parameter quantities and unknown parameter quantities), and the first-stage estimated value pi* of pi is obtained; in this embodiment, the undetermined parameter quantity pi includes: the laser incident angle X (the laser incident angle in the X1 direction), the laser incident angle Y (the laser incident angle in the Y1 direction), the distance between the optoelectronic servo platform and the receiving screen, the rotation of the scanning coordinate system (compared with the horizontal coordinate system, there may be a certain rotation in the coordinate system of the servo), the tilt error of the optoelectronic servo platform in the X1 direction, and the tilt error of the optoelectronic servo platform in the Y1 direction. Among them, the laser incident angle X and the laser incident angle Y can be measured and are known parameter quantities, and the others are unknown parameter quantities;

[0059] Substitute pi* into the semi-parameter model, and use the kernel estimation method to estimate the non-parameter quantities, and obtain the first-stage estimated value h αi * of the non-parameter quantity h αi and the first-stage estimated value h βi * of the non-parameter quantity h βi *; in this embodiment, specifically include: substitute p i * into the semi-parameter model, and

[0060]

[0061] According to the above formula, it can be obtained that

[0062]

[0063] wherein

[0064] The method of kernel estimation is adopted to estimate the non-parametric quantity. K is the selected kernel function. Considering the distribution property of the measurement data, the Gaussian kernel function is adopted here. H is the window width, which is a constant related to n, and n is a constant obtained by fitting. The mean square error is used to measure the accuracy of the kernel estimation. When the mean square error is the smallest, the non-parametric quantity h αi The first-stage estimated value h αi * and the non-parametric quantity h βi The first-stage estimated value h βi *.

[0065] Substitute the non-parametric errors h αi * and h βi * into the semi-parametric model, and use the least squares method again to obtain the undetermined parameter p i The second-stage estimated value At the same time, substitute into the semi-parametric model and calculate to obtain and That is, the pointing error correction model is obtained;

[0066] The pointing error correction model is used to accurately calculate the azimuth error δα i and the elevation angle error δβ i .

[0067] Embodiment 2

[0068] The servo pointing error correction device based on the least squares estimation of the non-linear semi-parametric model in this embodiment includes:

[0069] An acquisition module, configured to acquire a series of actual azimuth angle observation values and elevation angle observation values and

[0070] A model construction module, configured to construct the azimuth angle and elevation angle error correction functions f(α i , β i ) and g(α i , β i ), wherein, in addition to the known parameter quantities, there are also unknown parameter quantities that cannot be measured;

[0071] For constructing the semi-parametric model of the azimuth error δα i and the elevation angle error δβ i The azimuth error δαi and the pitch angle error δβ i can be expressed as:

[0072]

[0073] where α i is the azimuth angle calculated value, β i is the pitch angle calculated value, is the azimuth angle error correction value brought by non-parametric quantities, i.e., unknown parameter quantities, is the pitch angle error correction value brought by non-parametric quantities, i.e., unknown parameter quantities;

[0074] f(α i , β i ; p i ) is the theoretical calculated value of the azimuth angle considering parameter quantities, g(α i , β i ; p i ) is the theoretical calculated value of the pitch angle considering parameter quantities;

[0075] The parameter identification module is used to identify the parameters of the semi-parametric model by using the least squares iteration method, obtain the undetermined parameter pi, and obtain the first-stage estimated value pi* of pi;

[0076] The non-parametric quantity estimation module is used to substitute pi* into the semi-parametric model and estimate the non-parametric quantity by using the kernel estimation method to obtain the first-stage estimated value h αi * of the non-parametric quantity h αi * and the first-stage estimated value h βi * of the non-parametric quantity h βi *;

[0077] The pointing error correction model module is used to substitute the first-stage non-parametric errors h αi * and h βi * into the semi-parametric model, and use the least squares method again to obtain the second-stage estimated value i of the undetermined parameter p At the same time, substitute into the semi-parametric model to calculate and obtain and i.e., obtain the pointing error correction model;

[0078] The application module is used to accurately calculate the azimuth angle error δα i and the pitch angle error δβ i .

[0079] Embodiment III

[0080] This embodiment provides an electronic device, including:

[0081] At least one processor, at least one memory, and a communication interface; wherein,

[0082] The processor, the memory, and the communication interface communicate with each other;

[0083] The memory stores program instructions executable by the processor, and the processor invokes the program instructions to execute the method of Embodiment 1.

[0084] Embodiment 4

[0085] This embodiment of the present invention provides a non-transitory computer-readable storage medium, and the non-transitory computer-readable storage medium stores computer instructions, and the computer instructions cause the computer to execute the method of Embodiment 1.

Claims

1. A servo pointing error correction method based on the least squares estimation of a nonlinear semi-parametric model, characterized in that: include: Get a series of actual azimuth and elevation angle observations and Construct the azimuth and elevation error correction function f(α i , β i ) and g(α i , β i ), which includes, in addition to known parameters, unknown parameters that cannot be measured; Construct the azimuth error δα i and the pitch angle error δβ i The semi-parametric model, azimuth error δα i and the pitch angle error δβ i It can be expressed as: Among them, α i is the theoretical calculated value of azimuth angle, β i is the theoretical calculated value of the pitch angle, is the azimuth error correction value caused by the non-parametric quantity, is the pitch angle error correction value caused by the non-parameter quantity; f(α i ,β i ;p i ) is the theoretical calculated value of the azimuth considering the parameter quantity, g(α i ,β i ;p i ) is the theoretical calculated value of the pitch angle considering the parameter quantity; The least squares iteration method is used to identify the parameters of the semi-parametric model, and the undetermined parameter pi is obtained, and the first-stage estimated value pi* of pi is obtained; Substitute pi* into the semi-parametric model and use the kernel estimation method to estimate the non-parametric quantity. The obtained non-parametric quantity h αi The first-stage estimate of h αi * and non-parametric h βi The first-stage estimate of h βi *; The nonparametric error h of the first stage αi * and h βi *Substitute into the semi-parametric model and use the least squares method again to obtain the unknown parameter p i Second-stage estimates At the same time Substituting into the semi-parametric model, we can get and That is, the pointing error correction model is obtained; The pointing error correction model is used to accurately calculate the azimuth error δα i and the pitch angle error δβ i .

2. The servo pointing error correction method based on the least squares estimation of the nonlinear semi-parametric model according to claim 1 is characterized in that: The method of obtaining a series of actual azimuth angle observation values ​​and pitch angle observation values and Including: Building actual azimuth and elevation observation values and A testing device, the testing device comprising a laser, an optoelectronic servo platform and a receiving screen arranged along the optical path, the distance between the exit port of the optoelectronic servo platform and the receiving screen is Lmm, the receiving screen is fixed to a two-dimensional translation stage, and a right-handed receiving screen coordinate system O1-X1Y1Z1 is established; According to the calibrated zero position and coordinate system of the optoelectronic servo platform, a series of measurement points are tested to obtain a series of actual azimuth angle observation values ​​and pitch angle observation values. and 3. The servo pointing error correction method based on the least squares estimation of the nonlinear semi-parametric model according to claim 2 is characterized in that: The receiving screen adopts a large-array CCD.

4. The servo pointing error correction method based on the least squares estimation of the nonlinear semi-parametric model according to claim 1 is characterized in that: The undetermined parameter quantity pi includes: laser incident angle X, laser incident angle Y, distance between the photoelectric servo platform and the receiving screen, scanning coordinate system rotation, photoelectric servo platform X-direction tilt error, and photoelectric servo platform Y-direction tilt error.

5. The servo pointing error correction method based on the least squares estimation of the nonlinear semi-parametric model according to claim 1 is characterized in that: Substituting pi* into the semi-parametric model, using the kernel estimation method to estimate the non-parametric quantity, the obtained non-parametric quantity h αi The first-stage estimate of h αi * and non-parametric h βi The first-stage estimate of h βi *, specifically including: i * Substituting into the semiparametric model, we can get According to the above formula, we can get: in The kernel estimation method is used to estimate the non-parametric quantity. K is the selected kernel function. Considering the distribution of the measured data, the Gaussian kernel function is used here. H is the window width, which is a constant related to n. The mean square error is used to measure the accuracy of the kernel estimation. When the mean square error is the smallest, the non-parametric quantity h can be obtained. αi The first-stage estimate of h αi * and non-parametric h βi The first-stage estimate of h βi *.

6. The servo pointing error correction device based on the least squares estimation of the nonlinear semi-parametric model according to claim 5, characterized in that: The device comprises: Acquisition module, used to obtain a series of actual azimuth observation values ​​and pitch angle observation values and Construct a model module to construct the azimuth and elevation error correction function f(α i , β i ) and g(α i , β i ), which includes, in addition to known parameters, unknown parameters that cannot be measured; Used to construct the azimuth error δα i and the pitch angle error δβ i The semi-parametric model, azimuth error δα i and the pitch angle error δβ i It can be expressed as: Among them, α i is the calculated value of azimuth, β i is the calculated value of the pitch angle, is the azimuth error correction value caused by the non-parametric quantity, is the pitch angle error correction value caused by the non-parameter quantity; f(α i ,β i ;p i ) is the theoretical calculated value of the azimuth considering the parameter quantity, g(α i ,β i ;p i ) is the theoretical calculated value of the pitch angle considering the parameter quantity; A parameter identification module is used to perform parameter identification of the semi-parametric model using a least squares iteration method to obtain an undetermined parameter pi and a first-stage estimated value pi* of pi; The non-parametric quantity estimation module is used to substitute pi* into the semi-parametric model and estimate the non-parametric quantity using the kernel estimation method. The obtained non-parametric quantity h αi The first-stage estimate of h αi * and non-parametric h βi The first-stage estimate of h βi *; The pointing error correction model module is used to convert the non-parametric error h αi * and h βi *Substitute into the semi-parametric model and use the least squares method again to obtain the unknown parameter p i Second-stage estimates At the same time Substituting into the semi-parametric model, we can get and That is, the pointing error correction model is obtained; Application module for accurate calculation of azimuth error δα i and the pitch angle error δβ i .

7. An electronic device, characterized in that: include: At least one processor, at least one memory and a communication interface; wherein, The processor, memory and communication interface communicate with each other; The memory stores program instructions that can be executed by the processor, and the processor calls the program instructions to execute the method according to any one of claims 1 to 5.

8. A non-transitory computer-readable storage medium, characterized in that: The non-transitory computer-readable storage medium stores computer instructions, which cause a computer to execute the method of any one of claims 1 to 5.

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