A Method for On-Orbit Calibration of a Two-Dimensional Turntable with Multi-Source Error Fusion

Abstract

The present invention relates to the field of aerospace technology, and particularly to an in-orbit calibration method for a two-dimensional turntable with multi-source error fusion. An in-orbit calibration method for a two-dimensional turntable with multi-source error fusion provided by an embodiment of the present invention includes: establishing an error model regarding the actual value of the camera optical axis, the errors of the entire link, and the measured value; defining a generalized error parameter based on the error model, and linearizing the error model according to the defined generalized error parameter to obtain a linear model; based on the initial value of the set error parameter, the linear model performs recursive operations through a recursive algorithm, and an error parameter estimation value is obtained through recursive operations in each sampling period. An embodiment of the present invention provides an in-orbit calibration method for a two-dimensional turntable with multi-source error fusion, which ensures the pointing accuracy of the camera optical axis during in-orbit operation.

Description

Technical Field

[0001] The present invention relates to the field of aerospace technology, and particularly relates to an on-orbit calibration method for a two-dimensional turntable with multi-source error fusion. Background Art

[0002] Due to its high precision and high agility, the two-dimensional turntable has been increasingly widely used in tasks such as rapid detection, tracking, and identification of space moving targets in the active and middle sections. A satellite equipped with a two-dimensional turntable can maintain the independence of the satellite attitude control while performing tracking tasks to meet the working requirements of other on-board payloads. To achieve precise tracking of the target, it is often required that the camera optical axis has a high pointing accuracy, and the system error links between the camera and the turntable, and between the turntable and the satellite coordinate system will directly affect this accuracy. Although the installation parameters are precisely measured and ground calibrated before the satellite is launched into orbit, during the launch process of the aircraft, both the turntable and the camera will withstand huge vibrations and impacts. At the same time, there are significant differences in gravity and other aspects between the on-orbit space environment and the ground environment, which will inevitably cause changes in the system structure parameters. Summary of the Invention

[0003] An embodiment of the present invention provides an on-orbit calibration method for a two-dimensional turntable with multi-source error fusion, which ensures the pointing accuracy of the camera optical axis during on-orbit operation.

[0004] An embodiment of the present invention provides an on-orbit calibration method for a two-dimensional turntable with multi-source error fusion, including:

[0005] Establish an error model regarding the actual value of the camera optical axis, the error of the entire link, and the measured value;

[0006] Define a generalized error parameter based on the error model, and linearize the error model according to the defined generalized error parameter to obtain a linear model;

[0007] Based on the set initial value of the error parameter, the linear model is recursively calculated through a recursive algorithm, and an error parameter estimation value is obtained through the recursive calculation in each sampling period.

[0008] In a possible design, the establishment of the error model regarding the pre-adjustment value, error value, and measured value of the camera optical axis includes:

[0009] Establish a pointing vector formula for the camera optical axis;

[0010] Decompose the image plane position error into a first azimuth error and a first pitch error, and obtain a plane transformation matrix according to the first azimuth error and the first pitch error;

[0011] Decompose the pointing error of the camera optical axis into a second azimuth error and a second pitch error, and obtain a camera optical axis transformation matrix according to the second azimuth error and the second pitch error;

[0012] Decompose the optical axis perpendicularity error into a third azimuth error and a third pitch error, and obtain a perpendicularity transformation matrix according to the third azimuth error and the third pitch error;

[0013] Establish a pitch transformation matrix according to the actual pitch angle value, the pitch axis measurement value, the pitch axis coding zero position error, the pitch axis encoder measurement error, the perpendicularity error of two pitch axis systems, and the rotation error of two pitch axis systems;

[0014] Establish an azimuth transformation matrix according to the actual azimuth angle value, the azimuth axis measurement value, the azimuth axis coding zero position error, the azimuth axis encoder measurement error, the perpendicularity error of two azimuth axis systems, and the rotation error of two azimuth axis systems;

[0015] Decompose the attitude error into a fourth azimuth error, a fourth pitch error, and a roll error, and obtain an attitude transformation matrix according to the fourth azimuth error, the fourth pitch error, and the roll error;

[0016] Obtain the error model according to the vector formula, the plane transformation matrix, the camera optical axis transformation matrix, the perpendicularity transformation matrix, the pitch transformation matrix, the azimuth transformation matrix, and the attitude transformation matrix.

[0017] In a possible design, the vector formula is as follows:

[0018]

[0019] is the current actual pointing vector of the camera optical axis, is the initial vector of the camera optical axis, is the transformation matrix, and the transformation matrix , represents the transformation matrix between coordinate systems, b0 is the star system, b is the actual star system, A0 is the turntable azimuth coordinate system, A is the azimuth motion coordinate system, B0 is the pitch frame coordinate system, B is the pitch motion coordinate system, P0 is the ideal optical axis pointing coordinate system, P is the actual optical axis pointing coordinate system, and Cam is the actual pointing system in the image plane coordinate system, I is the J2000 satellite inertial system.

[0020] In a possible design, the plane transformation matrix is as follows:

[0021]

[0022] Among them, represents the transformation matrix obtained by rotating an angle n around the m axis, and are the first azimuth error and the first pitch error, respectively;

[0023] The camera optical axis transformation matrix is as follows:

[0024]

[0025] wherein, represents the transformation matrix obtained after rotating an angle n around the m axis, and are the second azimuth error and the second pitch error, respectively;

[0026] The perpendicularity transformation matrix is as follows:

[0027]

[0028] wherein, represents the transformation matrix obtained after rotating an angle n around the m axis, and are the third azimuth error and the third pitch error, respectively;

[0029] The pitch transformation matrix is as follows:

[0030]

[0031] wherein, represents the transformation matrix obtained after rotating an angle n around the m axis, is the actual value of the pitch angle, where is the measured value of the pitch axis, is the zero position error of the pitch axis encoder, is the encoder measurement error, 、 are the perpendicularity errors of the pitch axis system, 、 are the rotational errors of the pitch axis;

[0032] The azimuth transformation matrix is as follows:

[0033]

[0034] In the formula, represents the transformation matrix obtained after rotating an angle n around the m axis, is the actual value of the azimuth angle, is the measured value of the azimuth axis, is the rotational error of the azimuth axis, wherein is the zero position error of the azimuth angle, is the encoder measurement error, 、 are the perpendicularity errors of the azimuth axis system, , is the azimuth axis rotation error;

[0035] The attitude transformation matrix is as follows:

[0036]

[0037] where, represents the transformation matrix obtained after rotating by angle n around the m axis, and the fourth azimuth error, the fourth pitch error, and the roll error are respectively , and .

[0038] In a possible design, the error model is as follows:

[0039]

[0040]

[0041] where, is the measured value of the camera optical axis, represents the i-th element of, i = 1, 2, 3.

[0042] In a possible design, the generalized error parameters are as follows:

[0043] .

[0044] In a possible design, the linear model is as follows:

[0045]

[0046]

[0047]

[0048] where, is a recursive matrix composed only of the measured angles of the turntable.

[0049] In a possible design, based on the set initial values of the error parameters, the linear model performs recursive operations through a recursive algorithm, and an error parameter estimate value is obtained through recursive operations in each sampling period, including:

[0050] Define variables:

[0051]

[0052] , is the measured value of the camera optical axis, denoted by and denote the measured value y in the k-th sampling period and the recursive matrix , and the error parameters for each sampling period are calculated using the following recursive algorithm:

[0053]

[0054] where is the estimated value of the error parameter θ, and the initial value of the error parameter is determined according to the system ground precise measurement parameters combined with experiments , , c and are adjustable constants.

[0055] The present invention has at least the following beneficial effects compared with the prior art:

[0056] Compared with the prior art, the technical method adopted in this application proposes an online autonomous calibration method for multi-source error fusion, fully explores the error dynamics characteristics of the entire camera-two-dimensional turntable-satellite link, fuses multi-source errors into the system's generalized parametric linearized errors, and uses the recursive gradient method to online identify the generalized error parameters. The entire algorithm design is simple, the parameter debugging workload is small, no additional data input is required, the calculation is simple, and this algorithm can be adapted to a large class of military and civilian satellite systems with similar on-orbit calibration requirements, and has strong engineering practicability. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the following drawings are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0058] Figure 1 is a turntable rotation angle curve diagram provided by an embodiment of the present invention;

[0059] Figure 2 is an online calibration result diagram of errors provided by an embodiment of the present invention;

[0060] Figure 3 is a comparison diagram of the online calibration result of errors and the true errors provided by an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0061] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0062] In the description of the embodiments of the present invention, unless otherwise clearly defined and limited, the terms "first" and "second" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance; unless otherwise specified or stated, the term "plurality" means two or more; the terms "connection", "fixation", etc. should all be understood in a broad sense. For example, "connection" can be a fixed connection, a detachable connection, an integral connection, or an electrical connection; it can be directly connected or indirectly connected through an intermediate medium. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0063] In the description of this specification, it should be understood that the orientation terms such as "upper" and "lower" described in the embodiments of the present invention are described from the angles shown in the accompanying drawings and should not be construed as limiting the embodiments of the present invention. In addition, in the context, it should also be understood that when it is mentioned that an element is connected "above" or "below" another element, it can not only be directly connected "above" or "below" another element, but also be indirectly connected "above" or "below" another element through an intermediate element.

[0064] The embodiments of the present invention provide a method for on-orbit calibration of a two-dimensional turntable with multi-source error fusion, including:

[0065] Establish an error model regarding the actual value of the camera optical axis, the errors of the full link, and the measured values;

[0066] Define generalized error parameters based on the error model, and linearize the error model according to the defined generalized error parameters to obtain a linear model;

[0067] Based on the initial values of the set error parameters, the linear model performs recursive operations through a recursive algorithm, and an error parameter estimation value is obtained through recursive operations in each sampling period.

[0068] Compared with the prior art, the technical method adopted in this application proposes an online autonomous calibration method for multi-source error fusion, fully explores the error dynamics characteristics of the entire camera-two-dimensional turntable-satellite link, fuses multi-source errors into the system's generalized parametric linearized error, and uses the recursive gradient method to online identify the generalized error parameters. The entire algorithm design is simple, with little workload for parameter debugging, no need to add additional data input, and simple calculations. This algorithm can be adapted to a large class of military and civilian satellite systems with similar on-orbit calibration requirements and has strong engineering practicability.

[0069] In some embodiments of the present invention, establishing the error model regarding the pre-adjustment value, error value, and measurement value of the camera optical axis includes:

[0070] Establish the pointing vector formula of the camera optical axis;

[0071] Decompose the image plane position error into the first azimuth error and the first pitch error, and obtain the plane transformation matrix according to the first azimuth error and the first pitch error;

[0072] Decompose the camera optical axis pointing error into the second azimuth error and the second pitch error, and obtain the camera optical axis transformation matrix according to the second azimuth error and the second pitch error;

[0073] Decompose the optical axis perpendicularity error into the third azimuth error and the third pitch error, and obtain the perpendicularity transformation matrix according to the third azimuth error and the third pitch error;

[0074] Establish the pitch transformation matrix according to the actual pitch value, pitch axis measurement value, pitch axis coding zero position error, pitch axis encoder measurement error, perpendicularity error of two pitch axis systems, and rotational error of two pitch axis systems;

[0075] Establish the azimuth transformation matrix according to the actual azimuth value, azimuth axis measurement value, azimuth axis coding zero position error, azimuth axis encoder measurement error, perpendicularity error of two azimuth axis systems, and rotational error of two azimuth axis systems;

[0076] Decompose the attitude error into the fourth azimuth error, the fourth pitch error, and the roll error, and obtain the attitude transformation matrix according to the fourth azimuth error, the fourth pitch error, and the roll error;

[0077] Obtain the error model according to the vector formula, the plane transformation matrix, the camera optical axis transformation matrix, the perpendicularity transformation matrix, the pitch transformation matrix, the azimuth transformation matrix, and the attitude transformation matrix.

[0078] In some embodiments of the present invention, the vector formula is as follows:

[0079]

[0080] is the current actual pointing vector of the camera optical axis, is the initial vector of the camera optical axis, is the transformation matrix, and the transformation matrix , represents the transformation matrix between coordinate systems. b0 is the celestial coordinate system, b is the actual celestial coordinate system, A0 is the azimuth coordinate system of the turntable, A is the azimuth motion coordinate system, B0 is the pitch frame coordinate system, B is the pitch motion coordinate system, P0 is the ideal optical axis pointing coordinate system, P is the actual optical axis pointing coordinate system, and Cam is the actual pointing system in the image plane coordinate system. I is the J2000 satellite inertial system.

[0081] In this embodiment, it can be assumed that the initial pointing of the camera optical axis is , and the above vector formula is the actual pointing vector of the sensor after azimuth and pitch rotation under the influence of system errors.

[0082] In this embodiment, the specific directions of the respective coordinate axes in each coordinate system are as follows:

[0083] (1) Celestial coordinate system (b0), including: The axis is along the longitudinal axis of the satellite structure and points in the satellite flight direction. The axis is perpendicular to the longitudinal axis and points to the center of the earth. The axis is in the same plane as the axis, axis, and forms a right-handed system with them; the actual celestial coordinate system (b system), whose axis coincides with the actual pointing of the longitudinal axis of the satellite structure.

[0084] (2) Turntable azimuth coordinate system (A0), The axis coincides with the actual pointing of the azimuth axis, The axis is along the zero position direction of the azimuth encoder; the azimuth motion coordinate system (A system), which is fixedly connected to the azimuth frame and is used to describe the motion of the azimuth axis, The axis is along the instantaneous axis direction of the azimuth encoder.

[0085] (3) Turntable pitch coordinate system, including: pitch frame coordinate system (B0 system), The axis coincides with the actual pointing of the pitch axis after azimuth angle rotation, and the axis is along the zero position direction of the pitch encoder; the pitch motion coordinate system (B system), which is fixedly connected to the pitch frame and is used to describe the motion of the pitch axis, and the axis is along the instantaneous axis direction of the pitch encoder.

[0086] (4) Optical axis coordinate system, including: ideal optical axis pointing coordinate system (P0 system), The axis coincides with the ideal pointing of the optical axis after azimuth and pitch rotation and coincides with the F system in the absence of optical axis perpendicularity error. The actual optical axis pointing coordinate system (P system), whose The axis coincides with the actual pointing direction of the camera optical axis.

[0087] (5) Image plane coordinate system, including: actual pointing system (Cam system), The axis points to the actual target and coincides with the optical axis coordinate system in the absence of image plane position error.

[0088] In some embodiments of the present invention, the plane transformation matrix is as follows:

[0089]

[0090] Wherein, Represents the transformation matrix obtained after rotating by an angle n around the m axis, And Are the first azimuth error and the first pitch error respectively;

[0091] The camera optical axis transformation matrix is as follows:

[0092]

[0093] Wherein, Represents the transformation matrix obtained after rotating by an angle n around the m axis, And Are the second azimuth error and the second pitch error respectively;

[0094] Since the turntable adopts a two-degree-of-freedom structure, there is only an optical axis perpendicularity error between the camera optical axis system and the turntable pitch axis system. The perpendicularity transformation matrix is as follows:

[0095]

[0096] Wherein, Represents the transformation matrix obtained after rotating by an angle n around the m axis, And Are the third azimuth error and the third pitch error respectively;

[0097] The pitch transformation matrix is as follows:

[0098]

[0099] Wherein, Represents the transformation matrix obtained after rotating by an angle n around the m axis, Is the actual value of the pitch angle, where Is the measured value of the pitch axis, Is the zero position error of the pitch axis encoder, Is the encoder measurement error, 、 Are the perpendicularity errors of the pitch axis system, 、 is the pitching axis rotation error;

[0100] The azimuth transformation matrix is as follows:

[0101]

[0102] In the formula, represents the transformation matrix obtained after rotating an angle n around the m axis, is the actual value of the azimuth angle, is the measured value of the azimuth axis, is the rotation error of the azimuth axis, where is the azimuth angle zero position error, is the encoder measurement error, , is the perpendicularity error of the azimuth axis system, , is the pitching axis rotation error;

[0103] Since there is an error between the actual attitude of the satellite and the theoretical attitude, there is also a pointing deviation between the actual initial pointing of the camera and the ideal initial pointing, and there is an azimuth error , pitching error and roll error , and the attitude transformation matrix is as follows:

[0104] Among them, represents the transformation matrix obtained after rotating an angle n around the m axis, and the fourth azimuth error, the fourth pitching error, and the roll error are respectively , and .

[0105] In some embodiments of the present invention, the error model is as follows:

[0106]

[0107]

[0108] Among them, is the measured value of the camera optical axis, represents the i-th element of, i = 1, 2, 3.

[0109] In some embodiments of the present invention, the generalized error parameters are as follows:

[0110] .

[0111] In some embodiments of the present invention, the linear model is as follows:

[0112]

[0113]

[0114]

[0115] Among them, is a recursive matrix composed only of the angles measured by the turntable.

[0116] In some embodiments of the present invention, based on the set initial value of the error parameter, the linear model performs recursive operations through a recursive algorithm, and an estimated value of the error parameter is obtained through recursive operations in each sampling period, including:

[0117] Define variables:

[0118]

[0119] , is the measured value of the camera optical axis, and and represent the measured value y and the recursive matrix in the k-th sampling period. The error parameter of each sampling period is calculated using the following recursive algorithm:

[0120] Among them, is the estimated value of the error parameter θ. The initial value of the error parameter is determined according to the system ground precise measurement parameters in combination with experiments. , , c and are adjustable constants.

[0121] To more clearly illustrate the effect of the present application, simulation verification is carried out according to the method provided by the present application. The initial mode of the satellite is set to the normal earth-facing mode, that is, the three axes of the satellite body are in a zero attitude with respect to the earth. The angular curve of the turntable is as Figure 1 shown, and the online calibration structure is as Figures 2 to 3 shown. It can be seen from the figure that after the recursive error online identification of the present application, the estimated value can be made close to the true error.

[0122] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A two-dimensional turntable on-orbit calibration method with multi-source error fusion, characterized in that: include: Establish an error model about the actual value of the camera optical axis, the error of the entire link, and the measured value, including: Establish the pointing vector formula of the camera optical axis; Decompose the image plane position error into the first orientation error and the first pitch error ,according to and Get the plane transformation matrix; Decompose the camera optical axis pointing error into the second orientation error and the second pitch error ,according to and Get the camera optical axis transformation matrix; Decompose the optical axis perpendicularity error into the third position error and the third pitch error ,according to and Get the verticality transformation matrix; According to the actual value of the pitch angle, the pitch axis measurement value, the pitch axis encoding zero position error, the pitch axis encoder measurement error, and the verticality error of the two pitch axis systems and , rotation error of the two pitch axis systems and , establish the pitch transformation matrix; According to the actual value of azimuth angle, measured value of azimuth axis, and rotation error of azimuth axis , azimuth axis encoder zero position error, azimuth axis encoder measurement error, two azimuth axis perpendicularity error and , and the rotation errors of the two azimuth axes and , establish the orientation transformation matrix; Decompose the attitude error into the fourth orientation error , the fourth pitch error and roll error , obtaining an attitude transformation matrix according to the fourth azimuth error, the fourth pitch error and the roll error; The error model is obtained according to the vector formula, the plane transformation matrix, the camera optical axis transformation matrix, the verticality transformation matrix, the pitch transformation matrix, the azimuth transformation matrix and the attitude transformation matrix; Defining generalized error parameters based on the error model, and linearizing the error model according to the defined generalized error parameters to obtain a linear model; Based on the set initial value of the error parameter, the linear model performs recursive operation through a recursive algorithm, and obtains an error parameter estimation value through recursive operation in each sampling period; The generalized error parameter is as follows: 。 2. The calibration method according to claim 1, characterized in that: The vector formula is as follows: is the actual pointing vector of the camera optical axis. is the initial vector of the camera optical axis, is the transformation matrix, the transformation matrix , It represents the transformation matrix between coordinate systems, b0 is the star system, b is the actual star system, A0 is the turntable azimuth coordinate system, A is the azimuth motion coordinate system, B0 is the pitch frame coordinate system, B is the pitch motion coordinate system, P0 is the ideal optical axis pointing coordinate system, P is the actual optical axis pointing coordinate system, Cam is the actual pointing system in the image plane coordinate system, I It is the inertial system of J2000 satellite.

3. The calibration method according to claim 2, characterized in that: The plane transformation matrix is ​​as follows: in, Represents the transformation matrix obtained after rotating around the m axis by angle n. and are the first azimuth error and the first pitch error respectively; The camera optical axis transformation matrix is ​​as follows: in, Represents the transformation matrix obtained after rotating around the m axis by angle n. and are the second azimuth error and the second pitch error respectively; The verticality transformation matrix is ​​as follows: in, Represents the transformation matrix obtained after rotating around the m axis by angle n. and They are the third position error and the third pitch error respectively; The pitch transformation matrix is ​​as follows: in, Represents the transformation matrix obtained after rotating around the m axis by angle n. is the actual value of the pitch angle, where is the pitch axis measurement value, is the zero position error of the pitch axis encoder, is the encoder measurement error, , is the verticality error of the pitch axis system, , is the pitch axis rotation error; The orientation transformation matrix is ​​as follows: In the formula, Represents the transformation matrix obtained after rotating around the m axis by angle n. is the actual value of the azimuth angle, is the azimuth axis measurement value, is the azimuth axis rotation error, where Azimuth zero error, is the encoder measurement error, , is the verticality error of the azimuth axis system, , is the azimuth axis rotation error; The posture transformation matrix is ​​as follows: in, represents the transformation matrix obtained after rotating around the m-axis by an angle n, and the fourth azimuth error, the fourth pitch error and the roll error are respectively , and .

4. The calibration method according to claim 1, characterized in that: The error model is as follows: in, is the camera optical axis measurement value, express The i-th dimension element of , i=1, 2, 3.

5. The calibration method according to claim 1, characterized in that: The linear model is as follows: in, is a recursive matrix consisting only of the turntable measurement angles.

6. The calibration method according to claim 5, characterized in that: Based on the set initial value of the error parameter, the linear model performs recursive calculations through a recursive algorithm, and obtains an error parameter estimation value through recursive calculations in each sampling period, including: Define variables: , is the camera optical axis measurement value, and Represents the measured value y and the recursive matrix φ of the kth sampling period, and uses the following recursive algorithm to calculate the error parameters of each sampling period: in, is the estimated value of the error parameter θ, the initial value of which is determined based on the system ground precision measurement parameters combined with experiments, , , c and α are adjustable constants.

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