Attitude prediction type star tracking method

Abstract

The invention relates to an attitude prediction type star tracking method, and relates to the technical field of star sensors. The method comprises the following steps: obtaining historical angular velocity data; predicting the angular velocity of the next frame; predicting the attitude quaternion of the next frame; projecting a sky area fixed star to an image surface; performing window matching on the projection star and the observation star of the next frame; calculating the accurate attitude quaternion of the next frame; the target with the window matched successfully is used for attitude calculation, and the accurate attitude of the next frame is obtained; and repeating the steps to realize autonomous star tracking. According to the attitude prediction type star tracking method disclosed by the invention, the angular velocity of the next frame can be quickly and accurately predicted through polynomial fitting of historical angular velocity data, and the real-time performance and the accuracy are remarkably improved; the method can well adapt to high-angular-speed maneuver, and the tracking capability of the star sensor in a complex dynamic environment is enhanced; the method reduces the dependence on an external sensor, improves the independence and anti-interference capability of the system, simplifies the calculation process, and improves the overall calculation efficiency.

Description

Technical Field

[0001] The invention relates to the technical field of star sensors, and in particular to an attitude prediction star tracking method. Background Art

[0002] Star sensors are high-precision astronomical navigation devices, mainly used for spacecraft attitude measurement. By identifying and tracking stars in the sky, star sensors can provide information about the current attitude of the spacecraft, helping the navigation system to achieve precise positioning and stable control. In modern space missions, star sensors are widely used in attitude control and navigation of satellites, space shuttles and other manned or unmanned spacecraft.

[0003] The star sensor has two working modes: initial attitude capture and star tracking. When the star sensor is in a state of spatial loss, it will work in the initial attitude capture mode, which has high computational complexity and poor real-time performance. When the initial attitude capture is successful, it enters the star tracking mode. In the star tracking recognition mode, the star sensor can output real-time attitude information at a high data update rate. This high update frequency is particularly important for performing high-precision tasks, such as satellite communications, earth observation, deep space exploration, etc., and can significantly improve the accuracy and effectiveness of mission execution. The core work of the star sensor is usually performed in the star tracking recognition mode, which is the key to ensuring the long-term stable attitude of the spacecraft.

[0004] There are two main existing star tracking methods: one is to perform window matching by predicting the center of mass position of the star, which performs poorly during high angular velocity maneuvers; the other is to rely on other sensors to provide attitude or angular velocity information for tracking, which increases the star sensor's dependence on external platforms and limits its autonomous working capabilities.

[0005] In summary, it is particularly necessary to develop a star tracking method that can autonomously adapt to large angular velocity maneuvers in order to improve the reliability of star sensors in complex dynamic environments. Summary of the invention

[0006] The present invention aims to solve the technical problems that the star tracking method in the prior art performs poorly when maneuvering at a large angular velocity and the star sensor is overly dependent on an external platform, and provides an attitude prediction star tracking method.

[0007] In order to solve the above technical problems, the technical solutions of the present invention are as follows:

[0008] An attitude prediction star tracking method comprises the following steps:

[0009] Step 1: Obtain historical angular velocity data;

[0010] Extract the attitude quaternion of historical N frames, and use the quaternion differential equation to obtain the required historical N frames of angular velocity data through the correlation of time intervals;

[0011] Step 2: Fit the historical angular velocity with a second-order polynomial to predict the angular velocity of the next frame;

[0012] Perform polynomial fitting on the angular velocity data of the historical N frames to obtain the coefficients of the polynomial, and use the obtained polynomial expression to predict the angular velocity of the next frame;

[0013] Step 3: Predict the next frame posture quaternion;

[0014] Based on the attitude quaternion of the current frame and the angular velocity of the next frame predicted by polynomial fitting, the attitude quaternion of the next frame is predicted;

[0015] Step 4: Project the stars in the sky onto the image plane;

[0016] According to the predicted next frame attitude quaternion, the stars in the sky are projected onto the image plane;

[0017] Step 5: Window matching between the projected star and the next frame of observed star;

[0018] Step 6: Calculate the precise attitude quaternion of the next frame based on the successfully matched stars;

[0019] The target that successfully matches the window is used for posture calculation to obtain the precise posture of the next frame;

[0020] Step 7. Repeat steps 1 to 6 to achieve autonomous satellite tracking.

[0021] In the above technical solution, step one is specifically as follows:

[0022] A quaternion Q is defined as follows:

[0023] Q=(q w ,q v )=q0+q1i+q2j+q3k=q w +q v

[0024] Where: q w =q0, which is the real part of the quaternion Q; q v =q1i+q2j+q3k, is the imaginary part of the quaternion Q, i, j, k are the imaginary units;

[0025] The quaternion differential equation is:

[0026]

[0027] in, Represents quaternion from QN-1 To Q N Change, Q represents Q N-1 The quaternion when ω b From Q N-1 To Q N The angular velocity of is:

[0028]

[0029] Use the above formula to calculate the angular velocity data of historical N frames:

[0030] ω b (1),ω b (3),ω b (3),…,ω b (N).

[0031] In the above technical solution, step 2 is specifically as follows:

[0032] Step 2.1 uses the least squares method to perform polynomial fitting on the angular velocity data of the historical N frames; taking the second-order polynomial fitting as an example, the second-order polynomial function expression is:

[0033] f(x)=ax 2 +bx+c

[0034] Using the least squares method for fitting, the sum of squared errors is expressed as:

[0035]

[0036] Let S error Minimum, then:

[0037]

[0038] Among them, x i ∈[1,N] represents the second-order polynomial independent variable, ω b (i) represents the historical N frames of angular velocity measurement values.

[0039] From the above formula, the coefficient matrix of the second-order polynomial is:

[0040]

[0041] Use the above formula to calculate the angular velocity of the three axes respectively Perform fitting;

[0042] Step 2.2: Based on the polynomial expression obtained in step 2.1, predict the three-axis angular velocity of the next frame:

[0043]

[0044] Among them, x N+1is the value of the second-order polynomial independent variable, which is used to calculate the three-axis angular velocity of the next frame through the fitted function.

[0045] In the above technical solution, step three is specifically as follows:

[0046] The quaternion differential equation is expressed as:

[0047]

[0048] From the quaternion Q at time N N Predict the quaternion Q at time N+1 N+1 It is expressed as:

[0049]

[0050] Among them, Q N+1 is the predicted quaternion at the next moment, I is the identity matrix, Q N Represents the current quaternion, ω b (N+1) indicates the predicted N To Q N+1 The three-axis angular velocity of dt is the time.

[0051] In the above technical solution, step 4 is specifically as follows:

[0052] Step 4.1 Convert the attitude quaternion to a rotation matrix:

[0053]

[0054] The predicted N+1 time quaternion Q N+1 Use the above formula to transform into rotation matrix R N+1 ;

[0055] Step 4.2 Project the star onto the image plane; given a star, the star vector of the star in the inertial system is are the coordinate values ​​of the X-axis, Y-axis, and Z-axis in the inertial system respectively; the vector converted to the star sensor coordinate system is are the coordinate values ​​on the X-axis, Y-axis, and Z-axis in the star sensor coordinate system respectively;

[0056] but:

[0057] V i ′=R N+1 ·V i

[0058] The phase coordinates of the projected star are:

[0059]

[0060] Among them, X0 and Y0 represent the camera principal point, f represents the camera angular distance, p represents the pixel size, and X i and Y i The star vector V i The coordinate value projected onto the image plane.

[0061] In the above technical solution, step five is specifically as follows:

[0062] Set a window matching threshold win T , when observing target Target_X j and Target_Y j With the projected star satisfied:

[0063] |Target_X j -X i | <win T and|Target_Y j -Y i | <win T

[0064] The star matching is considered successful.

[0065] In the above technical solution, step six is ​​specifically: use the target with successful window matching for attitude solution to obtain the precise attitude quaternion Q at time N+1 N+1 .

[0066] The present invention has the following beneficial effects:

[0067] The attitude prediction star tracking method of the present invention, firstly, can quickly and accurately predict the angular velocity of the next frame by fitting the historical angular velocity data with a polynomial, significantly improving the real-time performance and accuracy; secondly, it can well adapt to large angular velocity maneuvers, enhancing the tracking capability of the star sensor in a complex dynamic environment; in addition, it reduces the dependence on external sensors, improves the independence and anti-interference capability of the system, simplifies the calculation process, and improves the overall calculation efficiency. The above advantages of the attitude prediction star tracking method of the present invention will enable it to further promote the application and development of star sensors in modern aerospace missions. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0069] Figure 1 The figure is a schematic diagram of the steps of the attitude prediction star tracking method of the present invention. DETAILED DESCRIPTION

[0070] The inventive concept of the present invention is:

[0071] The attitude prediction star tracking method of the present invention realizes autonomous tracking mainly through the following steps: first, a polynomial fitting method is used to predict the angular velocity of the next frame based on the historical angular velocity data, and then the attitude of the next frame is calculated in combination with the attitude quaternion of the current frame. Then, the predicted attitude is used to project the star body in the sky onto the image plane, and the star position is matched by the projection coordinates and the target measurement coordinates. Finally, the matching result is used to calculate and update the attitude to complete the tracking of the next frame. This method significantly improves the real-time performance and accuracy of the star sensor under rapid maneuvering conditions and has good adaptability.

[0072] The present invention is described in detail below with reference to the accompanying drawings.

[0073] like Figure 1 As shown, the attitude prediction star tracking method of the present invention is implemented by the following steps:

[0074] Step 1: Obtain historical angular velocity data.

[0075] Extract the attitude quaternion of the current frame and the previous N frames, and use the quaternion differential equation to obtain the required angular velocity data of the previous N frames through the correlation of time intervals. The current frame and the previous N frames in the above content are historical N frames. It should be noted that if you want to obtain N frames of angular velocity data, then you need N+1 frames of attitude quaternion data (each two adjacent frames of attitude quaternion can calculate an angular velocity value), so what is extracted here is the attitude quaternion of "previous N frames + current frame".

[0076] A quaternion Q can be defined as follows:

[0077] Q=(q w ,q v )=q0+q1i+q2j+q3k=q w +q v (1)

[0078] Where: q w =q0, which is the real part of the quaternion Q; q v =q1i+q2j+q3k, is the imaginary part of the quaternion Q, i, j, k are the imaginary units.

[0079] The first form of the quaternion differential equation is:

[0080]

[0081] in, Represents quaternion from Q N-1 To Q N Change, Q represents Q N-1 The quaternion when ω b From Q N-1 To Q NThe three-axis angular velocity of . Then:

[0082]

[0083] Use formula (3) to calculate the angular velocity data of historical N frames:

[0084] ω b (1),ω b (3),ω b (3),…,ω b (N) (4)

[0085] Step 2: Fit the historical angular velocity with a second-order polynomial to predict the angular velocity of the next frame.

[0086] The least square method is used to perform polynomial fitting on the angular velocity data of the historical N frames to obtain the coefficients of the polynomial, and the obtained polynomial expression is used to predict the angular velocity of the next frame.

[0087] Step 2.1 uses the least squares method to perform polynomial fitting on the angular velocity data of the historical N frames. Taking the second-order polynomial fitting as an example, the second-order polynomial function expression is:

[0088] f(x)=ax 2 +bx+c (5)

[0089] Using the least squares method for fitting, the sum of squared errors is expressed as:

[0090]

[0091] Let S error Minimum, then:

[0092]

[0093] Among them, x i ∈[1,N] represents the second-order polynomial independent variable, ω b (i) represents the historical N frames of angular velocity measurement values.

[0094] According to formula (7), the coefficient matrix of the second-order polynomial is:

[0095]

[0096] Use formula (8) to calculate the angular velocity of the three axes Perform the fitting.

[0097] Step 2.2: Based on the polynomial expression obtained in step 2.1, predict the three-axis angular velocity of the next frame:

[0098]

[0099] Among them, x N+1 is the value of the second-order polynomial independent variable, which is used to calculate the three-axis angular velocity of the next frame through the fitted function.

[0100] Step 3: Predict the next frame posture quaternion.

[0101] Based on the attitude quaternion of the current frame and the angular velocity of the next frame predicted by polynomial fitting, the attitude quaternion of the next frame is predicted.

[0102] The second form of the quaternion differential equation is:

[0103]

[0104] From the quaternion Q at time N N Predict the quaternion Q at time N+1 N+1 It can be expressed as:

[0105]

[0106] Among them, Q N+1 is the predicted quaternion at the next moment, I is the identity matrix, Q N Represents the current quaternion, ω b (N+1) indicates the predicted N To Q N+1 is the angular velocity, and dt is the time.

[0107] Step 4: Project the stars in the sky onto the image plane.

[0108] Based on the predicted attitude quaternion of the next frame, the stars in the sky are projected onto the image plane.

[0109] Step 4.1 Convert the attitude quaternion to a rotation matrix:

[0110]

[0111] The predicted quaternion Q at the N+1 moment N+1 Use formula (12) to transform into rotation matrix R N+1 .

[0112] Step 4.2 Project the star onto the image plane; given a star, the star vector of the star in the inertial system is are the coordinate values ​​of the X-axis, Y-axis, and Z-axis in the inertial system respectively; the vector converted to the star sensor coordinate system is are the coordinate values ​​on the X-axis, Y-axis, and Z-axis in the star sensor coordinate system respectively;

[0113] but:

[0114] V i ′=R N+1 ·Vi (13)

[0115] The phase coordinates of the projected star are:

[0116]

[0117] Among them, X0 and Y0 represent the camera principal point, f represents the camera angular distance, p represents the pixel size, and X i and Y i is the star vector V i The coordinate value projected onto the image plane.

[0118] Step 5: Window matching between the projected star and the next frame of observed star.

[0119] When matching the projected star with the next frame observation target, set a window matching threshold win T In this example, win T =5, when the observed target Target_X j and Target_Y j With the projected star satisfied:

[0120] |Target_X j -X i | <win T and|Target_Y j -Y i | <win T (16)

[0121] The star matching is considered successful.

[0122] Step 6: Calculate the precise attitude quaternion of the next frame based on the successfully matched stars.

[0123] The target that successfully matches the window is used for attitude calculation to obtain the precise attitude quaternion Q at time N+1 N+1 .

[0124] Step 7. Repeat steps 1 to 6 to achieve autonomous satellite tracking.

[0125] The attitude prediction star tracking method of the present invention, firstly, can quickly and accurately predict the angular velocity of the next frame by fitting the historical angular velocity data with a polynomial, significantly improving the real-time performance and accuracy; secondly, it can well adapt to large angular velocity maneuvers, enhancing the tracking capability of the star sensor in a complex dynamic environment; in addition, it reduces the dependence on external sensors, improves the independence and anti-interference capability of the system, simplifies the calculation process, and improves the overall calculation efficiency. The above advantages of the attitude prediction star tracking method of the present invention will enable it to further promote the application and development of star sensors in modern aerospace missions.

[0126] Obviously, the above embodiments are merely examples for the purpose of clear explanation, and are not intended to limit the implementation methods. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the implementation methods here. The obvious changes or modifications derived therefrom are still within the scope of protection of the invention.

Claims

1. An attitude prediction star tracking method, characterized in that: The following steps are involved: Step 1: Obtain historical angular velocity data; Extract the attitude quaternion of the historical N frames, and use the quaternion differential equation to obtain the required historical N frames of angular velocity data through the correlation of time intervals; Step 2: Fit the historical angular velocity with a second-order polynomial to predict the angular velocity of the next frame; Perform polynomial fitting on the angular velocity data of the historical N frames to obtain the coefficients of the polynomial, and use the obtained polynomial expression to predict the angular velocity of the next frame; Step 3: Predict the next frame posture quaternion; Based on the attitude quaternion of the current frame and the angular velocity of the next frame predicted by polynomial fitting, the attitude quaternion of the next frame is predicted; Step 4: Project the stars in the sky onto the image plane; According to the predicted next frame attitude quaternion, the stars in the sky are projected onto the image plane; Step 5: Window matching between the projected star and the next frame of observed star; Step 6: Calculate the precise attitude quaternion of the next frame based on the successfully matched stars; The target that successfully matches the window is used for posture calculation to obtain the precise posture of the next frame; Step 7. Repeat steps 1 to 6 to achieve autonomous satellite tracking.

2. The attitude prediction star tracking method according to claim 1, characterized in that: Step 1 is as follows: A quaternion Q is defined as follows: Q=(q w ,q v )=q0+q1i+q2j+q3k=q w +q v Where: q w =q0, which is the real part of the quaternion Q; q v =q1i+q2j+q3k, is the imaginary part of the quaternion Q, i, j, k are the imaginary units; The quaternion differential equation is: in, Represents quaternion from Q N-1 To Q N Change, Q represents Q N-1 The quaternion when ω b From Q N-1 To Q N The angular velocity of is: Use the above formula to calculate the angular velocity data of historical N frames: oh b (1),ω b (3),ω b (3),…,ω b (N).

3. The attitude prediction star tracking method according to claim 1, characterized in that: Step 2 is as follows: Step 2.1 uses the least squares method to perform polynomial fitting on the angular velocity data of the historical N frames; taking the second-order polynomial fitting as an example, the second-order polynomial function expression is: f(x)=ax 2 +bx+c Using the least squares method for fitting, the sum of squared errors is expressed as: Let S error Minimum, then: Among them, x i ∈[1,N] represents the second-order polynomial independent variable, ω b (i) represents the historical N frames of angular velocity measurement values. From the above formula, the coefficient matrix of the second-order polynomial is: Use the above formula to calculate the angular velocity of the three axes respectively Perform fitting; Step 2.2: Based on the polynomial expression obtained in step 2.1, predict the three-axis angular velocity of the next frame: Among them, x N+1 is the value of the second-order polynomial independent variable, which is used to calculate the three-axis angular velocity of the next frame through the fitted function.

4. The attitude prediction star tracking method according to claim 1, characterized in that: Step three is as follows: The quaternion differential equation is expressed as: From the quaternion Q at time N N Predict the quaternion Q at time N+1 N+1 It is expressed as: Among them, Q N+1 is the predicted quaternion at the next moment, I is the identity matrix, Q N Represents the current quaternion, ω b (N+1) indicates the predicted N To Q N+1 The three-axis angular velocity of dt is the time.

5. The attitude prediction star tracking method according to claim 1, characterized in that: Step 4 is as follows: Step 4.1 Convert the attitude quaternion to a rotation matrix: The predicted N+1 time quaternion Q N+1 Use the above formula to transform into rotation matrix R N+1 ; Step 4.2 Project the star onto the image plane; given a star, the star vector of the star in the inertial system is are the coordinate values ​​of the X-axis, Y-axis, and Z-axis in the inertial system respectively; the vector converted to the star sensor coordinate system is are the coordinate values ​​on the X-axis, Y-axis, and Z-axis in the star sensor coordinate system respectively; but: V i ′=R N+1 ·V i The phase coordinates of the projected star are: Among them, X0 and Y0 represent the camera principal point, f represents the camera angular distance, p represents the pixel size, and X i and Y i The star vector V i The coordinate value projected onto the image plane.

6. The attitude prediction star tracking method according to claim 1, characterized in that: Step 5 is as follows: Set a window matching threshold win T , when observing target Target_X j and Target_Y j With the projected star satisfied: |Target_X j -X i |<win T 且|Target_Y j -Y i |<win T The star matching is considered successful.

7. The attitude prediction star tracking method according to claim 1, characterized in that: Step 6 is as follows: Use the successfully matched window target for attitude calculation to obtain the precise attitude quaternion Q at time N+1 N+1 .

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