A Method for Analyzing Satellite Capture Errors Using Photoelectric Theodolites Based on Residual Correlation Analysis

Abstract

This invention discloses a method for analyzing satellite imagery errors using an electro-optical theodolite based on residual correlation analysis. The method includes establishing a measurement residual model to obtain the azimuth and elevation angle measurement residuals; constructing an atmospheric refraction correction error model based on elevation angle measurement residual data from multiple electro-optical theodolites at different stations, performing linear fitting to obtain the atmospheric refraction correction coefficient, and correcting the elevation angle measurement residual data; performing cross-correlation calculations on the azimuth and elevation angle measurement residuals corrected for atmospheric refraction to obtain the maximum normalized cross-correlation factor; if the cross-correlation factor is less than 0.6, the vertical axis tilt angle correction error is considered not a major error factor in the measurement residuals; if the cross-correlation factor is greater than or equal to 0.6, the vertical axis tilt angle correction error is considered a major error factor in the measurement residuals. This method, by systematically separating error factors, can be extended to analyze other error factors, demonstrating strong operability and wide applicability in practical data analysis.

Description

Technical Field

[0001] This invention relates to a method for analyzing the shooting error of a photoelectric theodolite based on residual correlation analysis. It is applicable to analyzing whether the main factor causing the static angle measurement error of the photoelectric theodolite to exceed the tolerance is the vertical axis tilt angle correction error, and belongs to the field of target range optical measurement. Background Technology

[0002] The target range uses the intersection of angle measurement data from an electro-optical theodolite to obtain the external ballistic parameters of aerial targets. Therefore, the angle measurement accuracy of the electro-optical theodolite is a very important indicator. Typically, the static angle measurement error of the electro-optical theodolite is calculated using nighttime satellite imagery. Before the actual satellite imagery, the electro-optical theodolite needs to be leveled, and parameters such as the vertical axis tilt angle, aiming error, and zero-position error need to be measured to calculate the angle measurement data of the electro-optical theodolite relative to the celestial body. The measurement residuals are calculated based on the theoretical azimuth and elevation angles of the celestial body relative to the electro-optical theodolite and the theodolite's measurements. The total static angle measurement error, systematic error, and random error of the electro-optical theodolite are all statistical quantities based on the measurement residuals.

[0003] Currently, there is considerable research on satellite imaging procedures, calculation of theoretical values ​​for celestial bodies, and calculation of theodolite angle measurement accuracy, and the relevant theories are relatively mature. However, there is a lack of research on error backtracking analysis methods after accuracy verification results exceed tolerances. That is, after satellite imaging calculations reveal that the theodolite's static angle measurement accuracy exceeds tolerances, it is necessary to identify the specific error factors that caused the deviation. This lack of research results in a lack of theoretical guidance for the accuracy analysis and adjustment of equipment that exceeds tolerances. Summary of the Invention

[0004] The purpose of this invention is to propose a satellite imaging error analysis method for photoelectric theodolites based on residual correlation analysis. This method is specifically designed for photoelectric theodolites with excessive static angle measurement accuracy. It constructs a measurement residual model and uses data from different stations to correct the pitch angle residual for atmospheric refraction differences, obtaining the cross-correlation curves of the azimuth and pitch angle residuals. Based on the characteristics of these curves, a criterion is established to determine whether the main factor causing the error is an incorrect correction of the vertical axis tilt angle. This method is highly operable and widely applicable, and can also be extended to analyze the influence of other error factors. It has strong guiding significance for practical error factor analysis and equipment adjustment.

[0005] To achieve the above objectives, the technical solution of the present invention is as follows:

[0006] A method for analyzing satellite imagery errors using photoelectric theodolites based on residual correlation analysis is proposed. This method establishes a measurement residual model based on azimuth and elevation angle measurements from multiple photoelectric theodolites at different stations for multiple satellite images, obtaining azimuth and elevation angle measurement residual data respectively. An atmospheric refraction correction error model is constructed based on the elevation angle measurement residual data obtained from multiple photoelectric theodolites at different stations. This model is then linearly fitted to the acquired elevation angle residual data for multiple satellite images to obtain the atmospheric refraction correction coefficient, which is used to correct the elevation angle measurement residual data. Cross-correlation calculations are performed on the azimuth and elevation angle measurement residuals corrected for atmospheric refraction to obtain the maximum normalized cross-correlation factor. If the cross-correlation factor is less than a set threshold, the vertical axis tilt angle correction error is considered not a major error factor in the measurement residuals; if the cross-correlation factor is greater than the set threshold, the vertical axis tilt angle correction error is considered a major error factor in the measurement residuals.

[0007] A further provision of the scheme is that the set threshold is 0.6.

[0008] The solution further includes: establishing the measurement residual model includes:

[0009] First, determine the azimuth angle A of multiple photoelectric theodolites at different stations for the j-th frame of the i-th star. ij and pitch angle E ij Formula 1 for calculating the measured value.

[0010]

[0011] in:

[0012] A ij The azimuth angle measurement for the i-th star in the j-th frame;

[0013] E ij The azimuth angle measurement for the i-th star in the j-th frame;

[0014] A” ij Let be the encoder azimuth angle of the j-th frame for the i-th star;

[0015] E” ij Let i be the encoder pitch angle of the j-th frame of the i-th star;

[0016] Δa ij Let i be the azimuth angle of the j-th frame for the i-th star;

[0017] Δe ij Let i be the pitch angle of the j-th frame of the i-th star, representing the miss distance.

[0018] c represents the collimation error;

[0019] b is the horizontal axis tilt angle;

[0020] I is the tilt angle of the vertical axis;

[0021] g is the azimuth orientation difference;

[0022] h represents a zero positional difference;

[0023] a H The azimuth angle is the tilt angle of the vertical axis;

[0024] ΔP ij This is the correction value for atmospheric refractive error;

[0025] Second, based on Formula 1, establish Formula 2 for the measurement residual model. Using Formula 2, obtain the azimuth and elevation measurement residual data respectively.

[0026]

[0027] in:

[0028] A ij Let be the azimuth angle of the i-th star in the j-th frame;

[0029] E ij Let be the pitch angle of the i-th star in the j-th frame;

[0030] and These are the theoretical values ​​for the azimuth and elevation angles of the celestial body, respectively.

[0031] The scheme further includes: The atmospheric refractive error correction model is constructed by: using the azimuth and elevation angle measurement residual data obtained from multiple photoelectric theodolites at different stations, constructing a vertical axis tilt angle correction error model. This model consists of formulas 3 and 4. Formula 3 is the correction error formula for the azimuth measurement residual caused by the vertical axis tilt angle correction error, and formula 4 is the correction error formula for the elevation angle measurement residual caused by the vertical axis tilt angle correction error. Additionally, formula 6, the atmospheric refractive error correction model formula, is obtained based on atmospheric refractive error correction value formula 5.

[0032] ΔI sin(a H -A” ij )tan E” ij Formula 3

[0033] ΔI cos(a H -A” ij ) Formula 4

[0034]

[0035] Δkcot(E” ij ) Formula 6

[0036] in:

[0037] ΔI=I-I0

[0038] I0 is the true value of the vertical axis tilt angle;

[0039] P0 is the atmospheric pressure at the station;

[0040] T0 is the atmospheric temperature at the station.

[0041] The solution further involves: linearly fitting the elevation angle refractive error correction data of the acquired multi-star images using the atmospheric refractive error correction model to obtain the atmospheric refractive error correction coefficients and correct the elevation angle measurement residual data.

[0042] For the residual data of each station, cot(E”) ij () is the horizontal axis, and the pitch angle residual ΔE is the vertical axis. ij Plot the graph on the vertical axis and perform a straight line fit to obtain the fitting coefficient Δk. m Calculate the average of the fitting coefficients of the photoelectric theodolites at all different stations to obtain the atmospheric refraction correction coefficient Δk'; then, the elevation angle measurement residual ΔE′ after atmospheric refraction correction is obtained. ij Formula 7:

[0043] ΔE′ ij =ΔE ij -Δk'cot(E” ij ) Formula 7

[0044] And according to Formula 7, Formula 8 is used to calculate the cross-correlation coefficient of the azimuth and elevation measurement residuals of multiple star frames;

[0045]

[0046] By cross-correlation calculation of the elevation angle measurement residuals after correction for azimuth and atmospheric refraction using Formula 8, the normalized cross-correlation curves Corr for the azimuth and elevation directions of multiple star frames are obtained.

[0047] The scheme further states that the maximum normalized cross-correlation factor is: according to the measurement residual model, the azimuth and pitch residuals that appear in pairs due to the vertical axis tilt angle correction error, and respectively conform to the sine and cosine variation laws; therefore, when the main factor of the measurement residual is the vertical axis tilt angle correction error, the cross-correlation curve of the azimuth and pitch residuals should conform to the characteristics of the cross-correlation curve of the sin function and the -cos function; the characteristic is that the correlation is 0 at 0, the correlation is positive and negative maxima at ±90° phase, and the cross-correlation curve is rotationally symmetrical about the zero point; the maximum normalized cross-correlation factor is defined based on the above characteristics.

[0048] The main advantage of this invention lies in establishing a method for analyzing error factors related to the excessive static angle measurement error of photoelectric theodolites. Firstly, based on the correction formula for atmospheric refraction, an atmospheric refraction correction error model is established. Then, using the elevation angle residual data from photoelectric theodolites at different stations, a linear fitting method is employed to correct the elevation angle measurement residual, eliminating the problem of large correction errors caused by the dependence of atmospheric refraction in the elevation direction on empirical formulas, which affects the characterization of other error factors. Next, utilizing the characteristic that azimuth and elevation angles caused by vertical axis tilt angle errors appear in pairs and exhibit sine and cosine variations with the azimuth angle, respectively, a normalized cross-correlation curve for the azimuth and elevation angle residuals is constructed. If the vertical axis tilt angle correction is incorrect, the normalized cross-correlation curve will exhibit a correlation of 0 at 0°, positive and negative maxima at ±90° phase, and rotational symmetry about the zero point. Finally, based on the above characteristics, the maximum normalized cross-correlation factor is defined as M. ef And set if M ef If M is less than 0.6, then the vertical axis tilt angle correction error is considered not to be a major error factor in the measurement residual; if M ef If the error is greater than or equal to 0.6, then the vertical axis tilt angle correction error is considered to be the main error factor in the measurement residual. This method can be extended to analyze other error factors by peeling away each error factor individually. It is highly operable and widely applicable in practical data analysis.

[0049] The present invention will now be described in detail with reference to the accompanying drawings and embodiments. Attached Figure Description

[0050] Figure 1 This is a flowchart of the method of the present invention;

[0051] Figure 2 A schematic diagram of the normalized cross-correlation curves of the azimuth and pitch angle residuals, with the vertical axis tilt angle correction error as the main out-of-tolerance factor. Detailed Implementation

[0052] A method for analyzing satellite imaging errors using an electro-optical theodolite based on residual correlation analysis is proposed for electro-optical theodolites with out-of-tolerance static angle measurement accuracy. This method belongs to post-processing of electro-optical theodolites and can be applied to the accuracy assessment of static satellite imaging in the field. It analyzes the impact of vertical axis tilt angle correction error on the accuracy assessment results. Figure 1 and Figure 2 As shown, the error analysis method includes:

[0053] A measurement residual model was established based on the azimuth and elevation angle measurements of multiple satellite images taken by photoelectric theodolites from multiple stations, yielding azimuth and elevation angle measurement residual data. An atmospheric refraction correction error model was constructed based on the elevation angle measurement residual data obtained from the photoelectric theodolites at multiple stations. This model was then used to linearly fit the acquired elevation angle residual data of the multiple satellite images, obtaining the atmospheric refraction correction coefficient and correcting the elevation angle measurement residual data. Cross-correlation calculations were performed on the azimuth and elevation angle measurement residuals corrected for atmospheric refraction, yielding the maximum normalized cross-correlation factor. If the cross-correlation factor was less than a set threshold, the vertical axis tilt angle correction error was considered not a major error factor in the measurement residuals; if the cross-correlation factor was greater than the set threshold, the vertical axis tilt angle correction error was considered a major error factor in the measurement residuals. The set threshold was 0.6.

[0054] The establishment of the measurement residual model includes:

[0055] First, determine the azimuth angle A of multiple photoelectric theodolites at different stations for the j-th frame of the i-th star. ij and pitch angle E ij Formula 1 for calculating the measured value (which is a known technique),

[0056]

[0057] in:

[0058] A ij The azimuth angle measurement for the i-th star in the j-th frame;

[0059] E ij The azimuth angle measurement for the i-th star in the j-th frame;

[0060] A” ij Let be the encoder azimuth angle of the j-th frame for the i-th star;

[0061] E” ij Let i be the encoder pitch angle of the j-th frame of the i-th star;

[0062] Δa ij Let i be the azimuth angle of the j-th frame for the i-th star;

[0063] Δe ij Let i be the pitch angle of the j-th frame of the i-th star, representing the miss distance.

[0064] c represents the collimation error;

[0065] b is the horizontal axis tilt angle;

[0066] I is the tilt angle of the vertical axis;

[0067] g is the azimuth orientation difference;

[0068] h represents a zero positional difference;

[0069] a H The azimuth angle is the tilt angle of the vertical axis;

[0070] ΔP ij This is the atmospheric refractive error correction value, obtained from empirical formula 5;

[0071] Second, based on Formula 1, establish Formula 2 for the measurement residual model (a known technique). From Formula 2, obtain the azimuth and elevation measurement residual data respectively.

[0072]

[0073] in:

[0074] A ij Let be the azimuth angle of the i-th star in the j-th frame;

[0075] E ij Let be the pitch angle of the i-th star in the j-th frame;

[0076] and These are the theoretical values ​​for the azimuth and elevation angles of the celestial body, respectively.

[0077] The atmospheric refractive error correction model is constructed as follows: Based on the azimuth and elevation angle measurement residual data obtained from multiple photoelectric theodolites at different stations, a vertical axis tilt angle correction error model is constructed. This model consists of formulas 3 and 4. Formula 3 is the correction error formula for the azimuth measurement residual caused by the vertical axis tilt angle correction error, and formula 4 is the correction error formula for the elevation angle measurement residual caused by the vertical axis tilt angle correction error. Formula 6, the atmospheric refractive error correction model formula, is obtained from atmospheric refractive error correction value formula 5.

[0078] The total angle measurement error, systematic error, and random error of an optical theodolite are all based on the measurement residual ΔA. ij and ΔE ij The statistics. Ideally, the measurement residuals should be a random sequence with a mean of 0. However, as can be seen from formula (1), errors in shaft system error calculation, encoder error calculation, and atmospheric refraction correction can all lead to errors in the measurement of celestial angles, thus introducing non-randomness into the measurement residual sequence. The vertical axis tilt angle correction error model and the atmospheric refraction correction error model are established below respectively:

[0079] 1) Vertical axis tilt angle correction error model

[0080] Assuming the true value of the vertical axis tilt angle is I0, but the actual measured value of the vertical axis tilt angle used for error correction in formula (1) is I, then the correction error caused by the vertical axis tilt angle correction error to the azimuth measurement residual is:

[0081] ΔI sin(a H -A” ij )tan E” ij Formula 3

[0082] Where, ΔI = I - I0;

[0083] The correction error that the vertical axis tilt angle correction error brings to the pitch angle measurement residual is:

[0084] ΔI cos(a H -A” ij ) Formula 4

[0085] Formulas (3) and (4) are the error models for correcting the vertical axis tilt angle.

[0086] It can be seen that the vertical axis tilt angle correction error will bring correction errors to the azimuth and elevation angle measurement residuals that conform to the sine and cosine variation law, and the two appear in pairs.

[0087] 2) Atmospheric refractive error correction model

[0088] The atmospheric refractive error correction value is usually calculated using an empirical formula (a well-known technique), which is:

[0089]

[0090] in,

[0091] P0 is the atmospheric pressure at the station;

[0092] T0 is the atmospheric temperature at the station.

[0093] It can be seen that the atmospheric refractive error correction value is a number directly proportional to the cotangent of the pitch angle. However, the proportionality coefficient in the above formula is a statistical empirical value, which differs from the actual situation. Therefore, assuming that this proportionality coefficient has an error amount Δk, the atmospheric refractive error correction error caused by this error coefficient is:

[0094] Δk cot(E” ij ) Formula 6

[0095] This is the atmospheric refractive error correction model. It can be seen that the atmospheric refractive error correction is related to cot(E). ijLinear correlation. This error is usually large, which obscures the cosine variation of the pitch angle residual caused by the vertical axis tilt angle correction error with the azimuth angle, making it difficult to analyze the impact of the vertical axis tilt angle on the measurement residual.

[0096] The atmospheric refractive error correction model formula 6 is used to linearly fit the elevation angle refractive error correction data of the acquired multi-star images to obtain the atmospheric refractive error correction coefficient and correct the elevation angle measurement residual.

[0097] For the residual data of each station, cot(E) i ' j (') is the horizontal axis, and the pitch angle residual ΔE is the vertical axis. ij Plot the graph on the vertical axis and perform a straight line fit to obtain the fitting coefficient Δk. m Calculate the average of the fitting coefficients of the photoelectric theodolites at all different stations to obtain the atmospheric refraction correction coefficient Δk'; then, the elevation angle measurement residual ΔE after atmospheric refraction correction is obtained. i ′ j Formula 7:

[0098] ΔE i ′ j =ΔE ij -Δk'cot(E i ' j ') Formula 7

[0099] Based on Formula 7, Formula 8 is used to calculate the cross-correlation coefficients of the azimuth and elevation measurement residuals for multiple star frames.

[0100]

[0101] The results are obtained by cross-correlation calculation of the elevation angle measurement residuals after correction for azimuth and atmospheric refraction using Formula 8, as shown below. Figure 2 The normalized cross-correlation curves (Corr) for the azimuth and pitch directions of the multi-star image frame are shown.

[0102] The maximum normalized cross-correlation factor (using M) eff (This is represented as follows): According to the measurement residual model, the azimuth and pitch residuals, which appear in pairs due to the vertical axis tilt angle correction error, respectively conform to sine and cosine variation laws. Therefore, when the main factor of the measurement residual is the vertical axis tilt angle correction error, the cross-correlation curves of the azimuth and pitch residuals should conform to the characteristics of the cross-correlation curves of the sin and cosine functions. These characteristics are: the correlation is 0 at 0°, the correlation reaches positive and negative maxima at ±90° phase, and the cross-correlation curve is rotationally symmetric about the zero point. Based on these characteristics, the maximum normalized cross-correlation factor is defined as M. eff .

[0103] The contents not described in detail in the embodiments are existing technologies known to those skilled in the art.

[0104] The above-described embodiment of the electro-optical theodolite satellite imaging error analysis method based on residual correlation analysis establishes a set of error factor analysis methods for static angle measurement errors exceeding tolerances in electro-optical theodolites. First, based on the correction formula for atmospheric refraction difference, an atmospheric refraction difference correction error model is established. Then, using elevation angle residual data from electro-optical theodolites at different stations, a linear fitting method is used to correct the elevation angle measurement residuals, eliminating the problem of large correction errors caused by the dependence of atmospheric refraction difference in the elevation direction on empirical formulas, which affects the characterization of other error factors. Next, utilizing the characteristic that azimuth and elevation angles caused by vertical axis tilt angle errors appear in pairs and exhibit sine and cosine variations with azimuth angle, respectively, normalized cross-correlation curves for azimuth and elevation angle residuals are constructed. If the vertical axis tilt angle correction is incorrect, the normalized cross-correlation curve will exhibit a correlation of 0 at 0°, positive and negative maxima at ±90° phase, and rotational symmetry about zero. Finally, based on the above characteristics, the maximum normalized cross-correlation factor is defined as M. eff And set if M eff If M is less than 0.6, then the vertical axis tilt angle correction error is considered not to be a major error factor in the measurement residual; if M eff If the error is greater than or equal to 0.6, then the vertical axis tilt angle correction error is considered to be the main error factor in the measurement residual. This method can be extended to analyze other error factors by peeling away each error factor individually. It is highly operable and widely applicable in practical data analysis.

Claims

1. A method for analyzing photoelectric theodolite photographing errors based on residual correlation analysis, characterized in that, A measurement residual model was established based on the azimuth and elevation angle measurements of multiple satellite images taken by photoelectric theodolites from multiple stations, yielding azimuth and elevation angle measurement residual data. An atmospheric refraction correction error model was constructed based on the elevation angle measurement residual data obtained from the photoelectric theodolites at multiple stations. This model was then used to linearly fit the acquired elevation angle residual data of the multiple satellite images, obtaining the atmospheric refraction correction coefficient and correcting the elevation angle measurement residual data. Cross-correlation calculations were performed on the azimuth and elevation angle measurement residuals corrected for atmospheric refraction, yielding the maximum normalized cross-correlation factor. If the cross-correlation factor was less than a set threshold, the vertical axis tilt angle correction error was considered not a major error factor in the measurement residuals; if the cross-correlation factor was greater than the set threshold, the vertical axis tilt angle correction error was considered a major error factor in the measurement residuals.

2. The error analysis method of claim 1, wherein, The set threshold is 0.

6.

3. The error analysis method according to claim 1, characterized in that, The establishment of the measurement residual model includes: One, determine the azimuth angle A of the i-th star and the j-th frame for the photoelectric theodolite of multiple different stations ij And the elevation angle E ij The calculation formula is 1, Official 1 in: A ij Azimuth measurement value for the i-th star in the j-th frame; E ij the azimuth measurement value for the i-th star in the j-th frame; Let be the encoder azimuth angle of the j-th frame for the i-th star; Let i be the encoder pitch angle of the j-th frame of the i-th star; Let i be the azimuth angle of the j-th frame for the i-th star; Let i be the pitch angle of the j-th frame of the i-th star, representing the miss distance. For collimation error; The tilt angle of the horizontal axis; The tilt angle of the vertical axis; This refers to the azimuth orientation difference; The difference is zero. The azimuth angle is the tilt angle of the vertical axis; This is the correction value for atmospheric refractive error; Second, based on Formula 1, establish Formula 2 for the measurement residual model. Using Formula 2, obtain the measurement residual data for azimuth and elevation angles respectively. Official 2 in: A ij Azimuth of the i-th star on the j-th frame; E ij Elevation angle for the i-th star in the j-th frame; and These are the theoretical values ​​for the azimuth and elevation angles of the celestial body, respectively.

4. The error analysis method according to claim 1, characterized in that, The atmospheric refractive error correction model is constructed as follows: Based on the residual data of azimuth and elevation angle measurements obtained from multiple photoelectric theodolites at different stations, a vertical axis tilt angle correction error model is constructed. The vertical axis tilt angle correction error model consists of Formula 3 and Formula 4. Formula 3 is the correction error formula for the vertical axis tilt angle correction error to the azimuth angle measurement residual, and Formula 4 is the correction error formula for the vertical axis tilt angle correction error to the elevation angle measurement residual. And the atmospheric refractive error correction model formula 6 obtained from formula 5, Official 3 Official 4 Official 5 Official 6 in: ； I0 is the true value of the vertical axis tilt angle; P0 is the atmospheric pressure at the station; T0 is the atmospheric temperature at the station.

5. The error analysis method according to claim 4, characterized in that, The process involves linearly fitting the elevation angle refractive error correction data of the acquired multi-star images using an atmospheric refractive error correction model to obtain the atmospheric refractive error correction coefficients and correct the elevation angle measurement residual data. For the residual data of each station, in Using the horizontal axis as the pitch angle residual Plot the graph on the vertical axis and perform a straight line fit to obtain the fitting coefficients. ; The average of the fitting coefficients of the photoelectric theodolites at all different stations is calculated to obtain the atmospheric refractive difference correction coefficient. The pitch angle measurement residual after atmospheric refraction correction is as follows: Formula 7: Official 7 And based on Formula 7, Formula 8 is used to calculate the azimuth and elevation directions of the multi-star image frame to measure the residuals. Cross-correlation coefficient; Official 8 By cross-correlation calculations using Formula 8 on the elevation angle measurement residuals corrected for azimuth and atmospheric refraction, normalized cross-correlation curves for azimuth and elevation directions of multiple star frames are obtained. .

6. The error analysis method according to claim 1, characterized in that, The maximum normalized cross-correlation factor is: according to the measurement residual model, the azimuth and pitch residuals that appear in pairs due to the vertical axis tilt angle correction error, and respectively conform to the sine and cosine variation laws; therefore, when the main factor of the measurement residual is the vertical axis tilt angle correction error, the cross-correlation curve of the azimuth and pitch residuals should conform to the characteristics of the cross-correlation curve of the sin function and the -cos function. The characteristic is that the correlation is 0 at 0, the correlation is positive and negative maxima at ±90° phase, and the cross-correlation curve is rotationally symmetric about the zero point; based on the above characteristics, the maximum normalized cross-correlation factor is defined.

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