Satellite solar array corner estimation method

Abstract

The application discloses a satellite solar cell array rotation angle estimation method, which comprises the following steps: step 1, establishing an earth inertial coordinate system, a satellite body coordinate system and a solar cell array coordinate system, and defining a satellite solar cell array rotation angle; step 2, establishing a state equation of an augmented state composed of a sun vector, the solar cell array rotation angle and a gyro constant drift noise; step 3, calculating an augmented state quantity estimation value by using an extended Kalman filter; and step 4, calculating a satellite solar cell array rotation angle estimation value. The method fuses gyro angular velocity and sun sensor vector data, constructs a nonlinear dynamic model containing a sun vector, a rotation angle and a gyro bias, and designs an EKF algorithm to estimate the solar cell array rotation angle in real time, thereby solving the strong dependence of a traditional scheme on a star sensor and a mechanical sensor, and significantly improving the autonomous recovery capability and energy guarantee reliability of a satellite in an extreme fault scene.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of spacecraft attitude control and fault recovery, and relates to a satellite solar cell array rotation angle estimation method, in particular to a method for estimating the rotation angle of a solar cell array by using extended Kalman filtering in the case of failure of an angle sensor and a star sensor. BACKGROUND

[0002] In deep space exploration missions, satellites are exposed to extreme space environments for a long time, which can easily cause on-board equipment failures. If the satellite cannot recover power supply after an in-orbit anomaly, the entire satellite energy supply will be interrupted, causing irreversible damage. For satellites equipped with motor-driven solar cell arrays, accurately obtaining the rotation angle of the solar cell array relative to the satellite body is a core prerequisite for realizing the sun orientation of the solar cell array and recovering power supply.

[0003] The rotation angle of the solar cell array can usually be directly measured by an angle sensor (potentiometer, encoder). The potentiometer reflects the angle through resistance changes, but is prone to measurement failure due to short circuits or mechanical wear. Although the encoder has high accuracy, it cannot directly obtain the absolute rotation angle of the solar cell array relative to the body after the satellite power supply is restarted. In addition, the rotation angle of the solar cell array can also be indirectly measured by a star sensor installed on the satellite body and a sun sensor installed on the solar cell array. However, the star sensor may not be able to provide reliable attitude data due to the loss of stored ephemeris information after the satellite is in an abnormal attitude (such as tumbling) or the power supply is restarted. SUMMARY

[0004] In view of the energy crisis caused by satellite in-orbit anomalies (such as attitude loss of control, star sensor failure, angle sensor failure, etc.), the application provides a satellite solar cell array rotation angle estimation method that does not rely on a star sensor and an angle sensor. This method fuses gyroscope angular velocity and sun sensor vector data to construct a nonlinear dynamic model containing a sun vector, a rotation angle, and a gyroscope bias, and designs an extended Kalman filter (EKF) algorithm to estimate the solar cell array rotation angle in real time. This method solves the strong dependence of traditional solutions on star sensors and mechanical sensors, realizes the estimation of the solar cell array rotation angle under extreme faults, and significantly improves the autonomous recovery capability and energy security reliability of the satellite under extreme fault scenarios.

[0005] The purpose of the application is achieved by the following technical solutions:

[0006] A satellite solar cell array rotation angle estimation method, comprising the following steps:

[0007] Step 1: Establishing an Earth Inertial Coordinate System , a satellite body coordinate system , and a solar cell array coordinate system , and defining a satellite solar cell array rotation angle ;

[0008] Step 2: Establish the system state equation composed of the sun vector, the solar array rotation angle and the gyro constant drift noise:

[0009]

[0010] In the formula, 、 is the state quantity matrix of the system at the moment; 、 is the system input matrix; g(·) is the system state nonlinear transition function matrix; is the system noise matrix; is the measurement matrix; is the measurement noise matrix; is the measurement value.

[0011] Step 3: Calculate the system state quantity estimation value by using the extended Kalman filter ;

[0012] Step 4: Calculate the solar array rotation angle estimation value of the satellite :

[0013]

[0014] In the formula, is the conversion matrix.

[0015] Compared with the prior art, the present application has the following advantages:

[0016] 1) The present application completely gets rid of the dependence on star sensors, angle sensors and ephemeris data.

[0017] 2) The algorithm complexity of the present application is low, and the present application can be run in real time on a satellite embedded processor. BRIEF DESCRIPTION OF DRAWINGS

[0018] Figure 1 is a specific flowchart of the satellite solar array rotation angle estimation method;

[0019] Figure 2 is a schematic diagram of the earth inertial coordinate system, the satellite body coordinate system and the solar array coordinate system;

[0020] Figure 3 is a schematic diagram of the solar array rotation angle;

[0021] Figure 4 is a general scheme diagram of the simulation experiment;

[0022] Figure 5 is a gyro combined measurement angular velocity curve diagram; ​

[0023] Figure 6 Measuring the sun vector curve for the sun sensor;

[0024] Figure 7 Satellite solar array rotation angle estimation result curve. DETAILED DESCRIPTION

[0025] The technical solutions of the present application are further described below in conjunction with the drawings, but are not limited thereto, and any modification or equivalent replacement to the technical solutions of the present application without departing from the spirit and scope of the present application shall be encompassed in the protection scope of the present application.

[0026] The present application provides a satellite solar array rotation angle estimation method, as shown in the accompanying drawings, the method comprises the following steps: Figure 1

[0027] Step 1: as shown in Figure 2 and Figure 3 , establish the earth inertial coordinate system , the satellite body coordinate system and the solar array coordinate system , and define the satellite solar array rotation angle , wherein:

[0028] The earth inertial coordinate system : the coordinate system does not rotate with the earth rotation, the origin is located at the center of mass of the earth. The plane is located on the equator, the axis points to the spring, the axis points to the geographical north pole of the earth, and the axis is established by the right-hand rule.

[0029] The satellite body coordinate system : the coordinate origin of the coordinate system is located at the center of mass of the satellite, the axis, the axis and the axis are the nominal principal axes of inertia.

[0030] The solar array coordinate system : the coordinate system is fixed with the solar array, the origin is located at the connection point of the solar array and the satellite, the axis points to the normal direction of the solar array plane, the axis is the driving axis of the solar array, the axis and the axis and the axis form a right-hand coordinate system.

[0031] The satellite solar array rotation angle ​Assume the drive axis of the satellite's solar array is perpendicular to the satellite's coordinate system. Axis coincidence (for the drive axis of the satellite's solar array and the coordinate system of the satellite body) In the case of misaligned axes, since the installation method of the satellite solar array is known, the situation considered in this invention can be obtained through a coordinate transformation. Therefore, the satellite solar array's coordinates around the satellite body coordinate system... The axis rotates, and the satellite solar array rotates at an angle of _____. .

[0032] Step 2: Establish the system state equation composed of the solar vector, solar array rotation angle, and gyroscope drift noise. The formula is as follows:

[0033] (1)

[0034] In the formula, , They are respectively , The state matrix of the system at any given time; g is the system input matrix; g(·) is the system state nonlinear transition function matrix; For system noise array; For measurement array; To measure the noise array; These are measured values.

[0035] The derivation of the state equations is as follows:

[0036] Assuming the satellite solar array rotation angle Keep it unchanged throughout the process. This can be considered a constant value. This takes into account the rotation of the solar cell array around its axis. We can obtain:

[0037] (2)

[0038] In the formula, For the coordinate system of the solar cell array The solar vector below; For the satellite body coordinate system To the solar cell array coordinate system The rotation matrix, due to It is considered a constant, therefore It can also be viewed as a constant matrix; Represents the satellite's body coordinate system The solar vector below.

[0039] according to From equation (2), we can obtain:

[0040] (3)

[0041] Taking the derivative of equation (3) gives:

[0042] (4)

[0043] In the inertial system, the vector The transformation equation between the inertial system and the rotating system (the satellite body coordinate system) is:

[0044] (5)

[0045] where is the angular velocity of the satellite body coordinate system relative to the Earth inertial coordinate system , which can be measured by the gyro combination installed on the satellite, From the following equation:

[0046]

[0047] Assume that the sun vector in the Earth inertial coordinate system does not change during the process of angle estimation, i.e.:

[0048] (6)

[0049] Then equation (5) is further simplified as:

[0050] (7)

[0051] Substituting equations (4) and (5) into equation (7) gives:

[0052] (8)

[0053] Multiplying the matrix on both sides of equation (11) gives:

[0054] (9)

[0055] According to , equation (9) is further simplified as:

[0056] (10)

[0057] Considering the constant drift of the gyroscope , equation (10) is simplified as:

[0058] (11)

[0059] The following functions are defined:

[0060] (12)

[0061] where:

[0062]

[0063] Equation (11) is further simplified as:

[0064] (13)

[0065] The discrete state equation of the sun vector in the sun-sail coordinate system at time k is given by:

[0066] (14)

[0067] where, is a 3-dimensional identity matrix, is the sampling time, , and are the satellite angular velocity, the satellite gyro constant drift, and the sun vector in the sun-sail coordinate system at time k-1, respectively, is the process noise, satisfying , is the variance matrix of the sun vector process noise . During the entire estimation process, the satellite sun-sail rotation angle is almost constant, so the state equation of is:

[0068] (15)

[0069] where, and are the satellite sun-sail rotation angles at times k and k-1, respectively, is the process noise, is the variance matrix of the satellite sun-sail rotation angle process noise .

[0070] The state equation of the satellite gyro constant drift can be expressed as:

[0071] (16)

[0072] where, and are the satellite gyro constant drifts at times k and k-1, respectively, is the process noise,​​ Variance matrix of constant process noise for satellite gyroscope .

[0073] Define the state and input as follows:

[0074]

[0075] The corresponding state equation is obtained as shown in equation (1).

[0076] In equation (1), the system state nonlinear transition function matrix is

[0077] ;

[0078] The system process noise is , and satisfies , is the system process noise variance matrix; since the sun vector in the solar array coordinate system is measurable, the measurement matrix , is a 3-row 6-column all-zero matrix; the measurement noise satisfies , is the measurement noise variance matrix.

[0079] Step 3: Calculate the system state quantity estimate value using extended Kalman filtering , the process is as follows:

[0080] Prediction:

[0081] (17)

[0082] In the formula, is the prediction value matrix of the system state quantity at time k; is the system state estimate value matrix at time k; is the prediction value of the system state covariance matrix; is the estimation value of the system state covariance matrix at time k; is the system noise variance matrix; is the Jacobian matrix of the nonlinear transition function relative to the system state at time k, the specific form is:

[0083]

[0084] is an intermediate variable.

[0085] Update: ​​​

[0086] (18)

[0087] wherein, is the filter gain coefficient at time k, is the system state estimation value matrix at time k, is the estimation value of the system state covariance matrix at time k, is the measurement noise covariance matrix, is the measurement value matrix.

[0088] Step 4: Calculate the estimated value of the satellite solar array rotation angle , the formula of which is as follows:

[0089] (19)

[0090] wherein, is the transformation matrix, .

[0091] Embodiment:

[0092] In this embodiment, the effectiveness of the satellite solar array rotation angle estimation method proposed in the present application is verified through simulation tests.

[0093] As Figure 4 is the overall scheme diagram of the simulation test. The satellite attitude dynamics and environmental disturbance torque are modeled, the initial attitude quaternion and initial angular velocity of the satellite are set, the satellite freely moves under the action of the environmental disturbance torque, and the attitude angular velocity of the satellite body is calculated. According to the set solar array rotation angle, the conversion relationship between the satellite body coordinate system and the solar array coordinate system (B) can be obtained, and the actual sun vector is calculated. The gyro combination measures the satellite body angular velocity , and the sun sensor installed on the solar array measures the sun vector . According to the measurement results of the simulated gyro combination and the sun sensor, the method proposed in the present application is used to estimate the solar array rotation angle. The estimated solar array angle is compared with the set value used to generate the simulation data to verify the effectiveness of the proposed method.

[0094] The satellite attitude dynamics equation is:

[0095]

[0096] wherein, J is the inertia matrix of the satellite, and T is the external disturbance torque on the satellite. When simulating the emergency recovery scenario of the out-of-control satellite, only the gravity gradient torque is considered as the external torque, which is calculated by the following formula: ​

[0097]

[0098] wherein, represents the earth gravitational constant, represents the position vector of the satellite, which is the vector from the mass center of the earth to the mass center of the satellite. is the velocity vector corresponding to the translational motion of the satellite. In the mathematical simulation, the position and velocity vectors of the satellite are calculated by using the two-body motion equation as follows:

[0099]

[0100] After the attitude angular velocity of the satellite is obtained, the measurement results of the gyro assembly and the sun sensor are further simulated.

[0101] In the simulation test, the satellite inertia matrix is kg·m 2 ; the initial position vector of the satellite is ; the initial velocity vector of the satellite is ; the initial angular velocity of the satellite is ; the constant drift of the gyro is ; the measurement noise of the gyro assembly is ; the rotation angle of the solar cell array is ; the initial sun vector is ; the simulated measurement results of the gyro assembly and the sun sensor are shown in Figure 5 and Figure 6 respectively. It is assumed that the initial system state is , is a 4-row 1-column matrix; the covariance matrix of the initial system state is ; the process noise covariance matrix is ; the measurement noise covariance of the sun sensor is ; the sampling time T s = 0.5 s; Figure 7 is the estimation result obtained by the satellite solar cell rotation angle estimation method proposed in the present application. It can be seen that the estimation value of the satellite solar cell array rotation angle can quickly converge to the vicinity of the true value and remain stable. Through the simulation, it can be seen that the present embodiment can not depend on the star sensor, and the estimation value can quickly converge to the vicinity of the true value of the satellite solar cell array rotation angle. The effectiveness and superiority of the satellite solar cell array rotation angle estimation method proposed in the present application are proved.

Claims

1. A method for estimating the rotation angle of a satellite solar array, characterized in that... The method includes the following steps: Step 1: Establish the Earth's inertial coordinate system Satellite coordinate system and solar cell array coordinate system And define the rotation angle of the satellite solar array. ; Step 2: Establish the system state equations consisting of the solar vector, solar cell array rotation angle, and gyroscope drift noise; The system state equation is: In the formula, , They are respectively , The state matrix of the system at any given time; g is the system input matrix; g(·) is the system state nonlinear transition function matrix; For system noise array; For measurement array; To measure the noise array; These are measured values; The system state nonlinear transition function matrix is: , It is a 3D identity matrix; the system process noise is , The noise of the solar vector process at time k-1. The noise during the rotation process of the satellite solar array at time k-1. Let the noise of the satellite gyroscope during constant drift be at time k-1, and satisfy the following conditions: , Let V be the system process noise variance matrix. Noise from solar vector processes The variance matrix, Noise during the rotation process of satellite solar array The variance matrix, Noise during the constant drift process of satellite gyroscopes The variance matrix; due to the coordinate system of the solar cell array The solar vector below Measurable, therefore measurement array , It is a 3x6 matrix with all zeros; the measurement noise satisfies , To measure the noise variance matrix; Step 3: Calculate the estimated system state variables using an extended Kalman filter. ; Step 4: Calculate the estimated rotation angle of the satellite solar array. .

2. The satellite solar array rotation angle estimation method according to claim 1, characterized in that... The Earth inertial coordinate system It does not rotate with the Earth's rotation; the origin... Located at the Earth's center of mass, The plane is located on the equator. The axis points towards the vernal equinox. The axis points to the Earth's geographic North Pole. The axes are established using the right-hand rule; the satellite body coordinate system origin of coordinates Located at the satellite's center of mass, axis, shaft and The axis is the nominal principal axis of inertia; the solar array coordinate system Fixed to the solar cell array, origin Located at the connection point between the solar array and the satellite, The axis points in the direction of the normal to the solar cell array. The axis is the drive axis for the solar cell array. shaft and shaft and The axes form a right-handed coordinate system; assuming the drive axes of the satellite's solar array are perpendicular to the satellite's body coordinate system. The axes coincide, and the satellite's solar array revolves around the satellite's coordinate system. The axis rotates, and the satellite solar array rotates at an angle of _____. .

3. The satellite solar array rotation angle estimation method according to claim 1, characterized in that... The specific steps of step 3 are as follows: predict: In the formula, Let be the matrix of predicted system state variables at time k; for The system state estimation matrix at any given time; The predicted value of the system state covariance matrix; for The estimated value of the system state covariance matrix at time t; Let V be the system noise variance matrix; for The Jacobian matrix of the nonlinear transfer function at time step relative to the system state; renew: In the formula, for The filter gain coefficient at time t. for The system state estimation matrix at time t, for The estimated value of the system state covariance matrix at time t. To measure the noise covariance matrix, This is a matrix of measurement values.

4. The satellite solar array rotation angle estimation method according to claim 1, characterized in that... The The formula is as follows: In the formula, For the transformation matrix, for The system state estimation matrix at time t.

5. The satellite solar array rotation angle estimation method according to claim 4, characterized in that... The .

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