A method and apparatus for satellite attitude determination based on multi-satellite sensors

Abstract

This invention discloses a satellite attitude determination method and apparatus based on multiple star sensors. Targeting satellites equipped with two or more star sensors, this invention fully utilizes the measurement information from each star sensor to determine the satellite's attitude. Simultaneously, this invention uses the satellite attitude information determined in the previous moment to predict the target satellite's attitude state in the next moment, and uses this prediction as the initial value for the target satellite's attitude filtering calculation in the next moment. Based on this, the attitude determination method provided by this invention not only has low computational complexity but also fully utilizes the measurement information from the star sensors, thereby effectively improving the accuracy of onboard attitude determination and making it suitable for widespread application and promotion in the field of satellite attitude determination.

Description

Technical Field

[0001] This invention belongs to the field of satellite attitude technology, specifically relating to a satellite attitude determination method and apparatus based on multi-satellite sensors. Background Technology

[0002] In recent years, with the continuous development of aerospace technology, the aerospace field has placed increasingly higher demands on the accuracy and stability of satellite attitude determination. Currently, star sensors, as the main attitude sensors used in the aerospace field, have advantages such as independent attitude determination, high measurement accuracy, and fast response speed. However, star sensors are susceptible to stray light such as sunlight and atmospheric radiation during their on-orbit operation, and the optical axis measurement accuracy of most star sensors is lower than their transverse axis measurement accuracy. Therefore, in order to ensure that the satellite can maintain high attitude determination accuracy throughout complex and diverse flight missions, multiple star sensors are often configured on-board simultaneously to measure the satellite's attitude.

[0003] In practical applications, most existing multi-satellite sensor attitude determination methods often struggle to fully utilize the measurement information from multiple satellite sensors to accurately determine satellite attitude when the optical axis and transverse axis measurement accuracies of the satellite sensors are inconsistent. This limits their applicability and makes them difficult to apply in real-world engineering projects. Therefore, how to effectively utilize the measurement information from multiple satellite sensors to determine satellite attitude in order to meet the requirements of high-precision onboard attitude control has become an urgent problem to be solved. Summary of the Invention

[0004] The purpose of this invention is to provide a satellite attitude determination method and apparatus based on multi-star sensors. It adopts a sequential processing approach to solve the problem that existing technologies struggle to fully utilize the measurement information from multiple star sensors for satellite attitude determination when the optical axis measurement accuracy and transverse axis measurement accuracy of star sensors are inconsistent.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] Firstly, a satellite attitude determination method based on multiple star sensors is provided, applicable to determining the attitude of a target satellite equipped with n star sensors, where n is a positive integer greater than 1, and the method includes:

[0007] The attitude state of the target satellite at time k-1 is estimated. Based on the attitude state of the target satellite at time k-1, and using the attitude dynamics equation and attitude kinematics equation of the target satellite, the attitude state of the target satellite is predicted in one step to obtain the attitude prediction value of the target satellite at time k, where k is a positive integer greater than or equal to 1.

[0008] For the i-th star sensor on the target satellite, obtain the attitude state quantity estimate and attitude estimation error variance matrix of the (i-1)-th star sensor at time k. When i is 1, the attitude state quantity estimate of the (i-1)-th star sensor at time k is the attitude prediction value of the target satellite at time k. The attitude estimation error variance matrix of the (i-1)-th star sensor at time k is the one-step prediction variance matrix of the target satellite at time k. The one-step prediction variance matrix is ​​calculated based on the attitude state quantity estimate of the target satellite at time k-1 and the attitude estimation error variance matrix of the n-th star sensor at time k-1.

[0009] Obtain the attitude measurement information of the i-th star sensor at time k, and calculate the attitude measurement value and filter gain matrix of the i-th star sensor at time k based on the attitude measurement information, the attitude state quantity estimate value and attitude estimation error variance matrix of the (i-1)-th star sensor at time k.

[0010] Based on the attitude measurement value and filter gain matrix of the i-th star sensor at time k, and the attitude state quantity estimate value of the (i-1)-th star sensor at time k, the attitude state quantity estimate value of the i-th star sensor at time k is calculated. The attitude state quantity estimate value of the i-th star sensor at time k includes the second attitude angle estimate value and the second attitude angular rate estimate value of the target satellite obtained when determining the attitude of the target satellite using the attitude measurement information of the i-th star sensor at time k.

[0011] The attitude estimation error variance matrix of the i-th star sensor at time k is calculated based on the filter gain matrix of the i-th star sensor at time k and the attitude estimation error variance matrix of the (i-1)-th star sensor at time k.

[0012] Increment i by 1, and re-acquire the attitude state quantity estimate and attitude estimation error variance matrix of the (i-1)th star sensor at time k, until i equals n. Then, take the attitude state quantity estimate of the nth star sensor at time k as the attitude state quantity estimate of the target satellite at time k, where the initial value of i is 1.

[0013] Based on the above disclosure, this invention targets satellites equipped with two or more star sensors. It employs a sequential processing approach to fully utilize the measurement information from each star sensor to determine the satellite's attitude. Specifically, it uses the attitude state quantity estimate and attitude estimation error variance matrix of the target satellite calculated based on the attitude measurement information from the previous star sensor as input. Then, it calculates the attitude state quantity estimate (i.e., the second attitude angle estimate and the second attitude angular rate estimate) of the target satellite at time k when the attitude measurement information from the next star sensor is used as input. This process is repeated until the final star sensor is used as the input. After the attitude measurement information of the instrument is used as the estimated attitude state quantity at the input, it can be used as the final estimated attitude state quantity of the target satellite at time k. At the same time, the present invention uses the estimated attitude state quantity at time k-1 and the attitude estimation error variance matrix of the last star sensor at time k-1, and combines it with the attitude dynamics and kinematic equations of the satellite to make a one-step prediction of the attitude state of the target satellite at time k, and uses the prediction result as the initial value for filtering calculation of the first star sensor at time k. Thus, by continuously processing in the above way, the estimated attitude state quantity of the target satellite at different times can be accurately determined.

[0014] Through the aforementioned design, this invention sequentially processes the measurement data of satellites equipped with two or more star sensors. Simultaneously, it uses the satellite attitude information determined in the previous moment to predict the target satellite's attitude state in the next moment, and uses this prediction as the initial value for the target satellite's attitude filtering calculation in the next moment. Based on this, the attitude determination method provided by this invention not only has low computational complexity but also fully utilizes the star sensor measurement information, thereby effectively improving the accuracy of onboard attitude determination and making it suitable for widespread application and promotion in the field of satellite attitude determination.

[0015] In one possible design, the attitude state quantity estimate of the target satellite at time k-1 is the attitude state quantity estimate of the nth star sensor at time k-1, and the attitude state quantity estimate of the nth star sensor at time k-1 includes: the third attitude angle estimate and the third attitude angular rate estimate of the target satellite obtained when determining the attitude of the target satellite using the attitude measurement information of the nth star sensor at time k-1;

[0016] Specifically, based on the estimated attitude state variables of the target satellite at time k-1, and using the attitude dynamics equations and attitude kinematics equations of the target satellite, a one-step prediction of the target satellite's attitude state is performed to obtain the predicted attitude value of the target satellite at time k, including:

[0017] Based on the estimated third attitude angle and the estimated third attitude angular rate, and using the attitude dynamics equation and attitude kinematics equation, the rate of change of attitude angle and the rate of change of attitude angular rate of the target satellite at time k-1 are calculated.

[0018] Based on the rate of change of the target satellite's attitude angle at time k-1 and the estimated value of the third attitude angle, the predicted value of the target satellite's attitude angle at time k is calculated; and

[0019] Based on the rate of change of the target satellite's attitude angular rate at time k-1 and the estimated value of the third attitude angular rate, the predicted value of the target satellite's attitude angular rate at time k is calculated.

[0020] The attitude prediction value of the target satellite at time k is formed by using the predicted attitude angle and attitude angular rate of the target satellite at time k.

[0021] In one possible design, the attitude state quantity estimate of the (i-1)th star sensor at time k includes: the first attitude angle estimate of the target satellite obtained when determining the attitude of the target satellite using the attitude measurement information of the (i-1)th star sensor at time k, wherein the attitude measurement information of the i-th star sensor at time k includes the satellite attitude angle measurement value, and the satellite attitude angle measurement value includes a quaternion used to characterize the satellite attitude;

[0022] Specifically, based on the attitude measurement information, and the attitude state quantity estimate and attitude estimation error variance matrix of the (i-1)th star sensor at time k, the attitude measurement value and filter gain matrix of the i-th star sensor at time k are calculated, including:

[0023] Calculate the difference between the measured satellite attitude angle and the first estimated attitude angle, and use the difference as the attitude measurement value of the i-th star sensor at time k.

[0024] Obtain the observation matrix and observation noise variance matrix of the i-th star sensor, and calculate the filter gain matrix of the i-th star sensor at time k based on the observation matrix, the observation noise variance matrix and the attitude estimation error variance matrix of the (i-1)-th star sensor at time k.

[0025] In one possible design, based on the observation matrix, the observation noise variance matrix, and the attitude estimation error variance matrix of the (i-1)th star sensor at time k, the filter gain matrix of the i-th star sensor at time k is calculated, including:

[0026] Based on the observation matrix, the observation noise variance matrix, and the attitude estimation error variance matrix of the (i-1)th star sensor at time k, the filter gain matrix of the i-th star sensor at time k is calculated using the following formula (1).

[0027]

[0028] In the above formula (1), K k / STi H represents the filter gain matrix of the i-th star sensor at time k. STi Let R represent the observation matrix of the i-th star sensor. STi Let P represent the observation noise variance matrix of the i-th star sensor. i-1,k Let H represent the attitude estimation error variance matrix of the (i-1)th star sensor at time k, and let T represent the transpose operation, where H STi =[I3 0 3×3 ], I3 represents a 3x3 identity matrix, 0 3×3 Let P represent a 3x3 zero matrix, and when i is 1, P i-1,k Let be the one-step prediction variance matrix of the target satellite at time k.

[0029] In one possible design, the observation noise variance matrix R of the i-th star sensor STi It is represented in the body coordinate system of the target satellite, wherein the observation noise variance matrix of the i-th star sensor is obtained by the following method:

[0030] Obtain the measurement accuracy information of the i-th star sensor, wherein the measurement accuracy information includes the observation noise variance of the i-th star sensor in its optical axis direction and the observation noise variance in its horizontal axis direction;

[0031] Using the measurement accuracy information and the following formula (2), the observation noise variance matrix represented by the i-th star sensor in its body coordinate system is calculated;

[0032]

[0033] In the above formula (2), Let δ represent the observation noise variance matrix of the i-th star sensor in its body coordinate system. i γ represents the variance of the observation noise of the i-th star sensor along its horizontal axis. i Let $\mathbf{i}$ represent the observation noise variance of the $i$-th star sensor along its optical axis, and the optical axis of the $i$-th star sensor is $\mathbf{i}$ in its body coordinate system. STi Z STi axis;

[0034] Based on the observation noise variance matrix of the i-th star sensor in its body coordinate system, and using the following formula (3), the observation noise variance matrix of the i-th star sensor in the body coordinate system of the target satellite is calculated.

[0035]

[0036] In the above formula (3), The direction cosine matrix represents the body coordinate system of the i-th star sensor relative to the body coordinate system of the target satellite, and T represents the transpose operation.

[0037] In one possible design, the attitude state quantity estimate of the (i-1)th star sensor at time k includes: the first attitude angle estimate and the first attitude angular rate estimate of the target satellite obtained when determining the attitude of the target satellite using the attitude measurement information of the (i-1)th star sensor at time k; and the attitude prediction value of the target satellite at time k includes the attitude angle prediction value and the attitude angular rate prediction value of the target satellite at time k.

[0038] Specifically, based on the attitude measurement value and filter gain matrix of the i-th star sensor at time k, and the attitude state quantity estimate value of the (i-1)-th star sensor at time k, the attitude state quantity estimate value of the i-th star sensor at time k is calculated, including:

[0039] Based on the first attitude angular rate estimate, the first attitude angle estimate, the attitude measurement value of the i-th star sensor at time k and the filter gain matrix, and according to the following formula (4), the second attitude angle estimate and the second attitude angular rate estimate of the target satellite are calculated when the attitude measurement information of the i-th star sensor at time k is used to determine the attitude of the target satellite.

[0040]

[0041] In the above formula (4), This represents the estimated second attitude angle of the target satellite. This represents the first attitude angle estimate in the attitude state estimate of the (i-1)th star sensor at time k. This represents the estimated second attitude angular rate of the target satellite. This represents the first attitude angular rate estimate in the attitude state estimate of the (i-1)th star sensor at time k, where, when i is 1, Let be the predicted attitude angle of the target satellite at time k. The predicted attitude angular rate of the target satellite at time k;

[0042] Describes the first matrix. K k / STi Let Z represent the second matrix. k / STi Let || represent the attitude measurement value of the i-th star sensor at time k, where || represents the norm symbol. The order of the filter gain matrix of the i-th star sensor at time k is 6×3, and the first matrix is ​​composed of the first three rows of the filter gain matrix of the i-th star sensor at time k, and the second matrix is ​​composed of the last three rows of the filter gain matrix of the i-th star sensor at time k.

[0043] In one possible design, based on the filter gain matrix of the i-th star sensor at time k and the attitude estimation error variance matrix of the (i-1)-th star sensor at time k, the attitude estimation error variance matrix of the i-th star sensor at time k is calculated, including:

[0044] Obtain the observation matrix and observation noise variance matrix of the i-th star sensor;

[0045] Based on the observation matrix, the observation noise variance matrix, the filter gain matrix of the i-th star sensor at time k, and the attitude estimation error variance matrix of the (i-1)-th star sensor at time k, the attitude estimation error variance matrix of the i-th star sensor at time k is calculated according to the following formula (5).

[0046] P i,k = (I3-K) k / STi H STi )P i-1,k (I3-K k / STi H STi ) T +K k / STi R STi (K k / STi ) T (5)

[0047] In the above formula (5), P i,k Ii represents the attitude estimation error variance matrix of the i-th star sensor at time k, I3 represents the 3rd order identity matrix, and Ki represents the position of the star sensor. k / STi H represents the filter gain matrix of the i-th star sensor at time k. STi Let R represent the observation matrix of the i-th star sensor. STi Let P represent the observation noise variance matrix of the i-th star sensor. i-1,kLet P represent the attitude estimation error variance matrix of the (i-1)th star sensor at time k, where T represents the transpose operation, and when i is 1, P i-1,k Let be the one-step prediction variance matrix of the target satellite at time k.

[0048] In one possible design, the estimated attitude state variables of the target satellite at time k-1 include: the estimated third attitude angular rate of the target satellite;

[0049] Specifically, based on the estimated attitude state variables of the target satellite at time k-1 and the attitude estimation error variance matrix of the nth star sensor at time k-1, the one-step prediction variance matrix of the target satellite at time k is calculated, including:

[0050] Based on the estimated third attitude angular rate, and according to the following formula (6), the state transition matrix of the target satellite at time k is calculated;

[0051]

[0052] In the above formula (6), Φ k,k-1 This represents the state transition matrix of the target satellite at time k. The third attitude angular rate estimate is represented by J, the moment of inertia matrix of the target satellite is represented by h, the angular momentum of the momentum wheel mounted on the target satellite is represented by I3, and the third-order identity matrix is ​​represented by 0. 3×3 I represents a 3rd-order zero matrix, I6 represents a 6th-order identity matrix, ΔT represents the cycle time of the filter during target satellite attitude estimation, and (·) × Represents the cross product matrix corresponding to the vectors;

[0053] Based on the attitude estimation error variance matrix of the nth star sensor at time k-1 and the state transition matrix, the one-step prediction variance matrix of the target satellite at time k is calculated according to the following formula (7);

[0054]

[0055] In the above formula (7), P k,k-1 P represents the one-step prediction variance matrix of the target satellite at time k. n,k-1 Let Q represent the variance matrix of the attitude estimation error of the nth star sensor at time k-1. k Let T represent the system process noise variance matrix, where T is the transpose operation.

[0056] Secondly, a satellite attitude determination device based on multiple star sensors is provided, characterized in that it is applied to determining the attitude of a target satellite equipped with n star sensors, where n is a positive integer greater than 1, and the device comprises:

[0057] The attitude prediction unit is used to obtain the estimated value of the attitude state variables of the target satellite at time k-1, and based on the estimated value of the attitude state variables of the target satellite at time k-1, and using the attitude dynamics equation and attitude kinematics equation of the target satellite, to perform one-step prediction of the attitude state of the target satellite, and obtain the attitude prediction value of the target satellite at time k, where k is a positive integer greater than or equal to 1.

[0058] The attitude calculation unit, for the i-th star sensor on the target satellite, is used to obtain the attitude state quantity estimate and attitude estimation error variance matrix of the (i-1)-th star sensor at time k. When i is 1, the attitude state quantity estimate of the (i-1)-th star sensor at time k is the attitude prediction value of the target satellite at time k. The attitude estimation error variance matrix of the (i-1)-th star sensor at time k is the one-step prediction variance matrix of the target satellite at time k. The one-step prediction variance matrix is ​​calculated based on the attitude state quantity estimate of the target satellite at time k-1 and the attitude estimation error variance matrix of the n-th star sensor at time k-1.

[0059] The attitude calculation unit is used to obtain the attitude measurement information of the i-th star sensor at time k, and calculate the attitude measurement value and filter gain matrix of the i-th star sensor at time k based on the attitude measurement information, the attitude state quantity estimate value and attitude estimation error variance matrix of the (i-1)-th star sensor at time k.

[0060] The attitude calculation unit is used to calculate the attitude state quantity estimate of the i-th star sensor at time k based on the attitude measurement value and filter gain matrix of the i-th star sensor at time k, and the attitude state quantity estimate value of the (i-1)-th star sensor at time k. The attitude state quantity estimate value of the i-th star sensor at time k includes the second attitude angle estimate value and the second attitude angular rate estimate value of the target satellite obtained when determining the attitude of the target satellite using the attitude measurement information of the i-th star sensor at time k.

[0061] The attitude calculation unit is used to calculate the attitude estimation error variance matrix of the i-th star sensor at time k based on the filter gain matrix of the i-th star sensor at time k and the attitude estimation error variance matrix of the (i-1)-th star sensor at time k.

[0062] The attitude update unit is used to increment i by 1 and reacquire the attitude state quantity estimate and attitude estimation error variance matrix of the (i-1)th star sensor at time k until i equals n. Then, the attitude state quantity estimate of the nth star sensor at time k is used as the attitude state quantity estimate of the target satellite at time k, where the initial value of i is 1.

[0063] Thirdly, another satellite attitude determination device based on a multi-satellite sensor is provided. Taking the device as an electronic device as an example, it includes a memory, a processor, and a transceiver that are connected in sequence. The memory is used to store a computer program, the transceiver is used to send and receive messages, and the processor is used to read the computer program and execute the satellite attitude determination method based on a multi-satellite sensor as described in the first aspect or any possible design in the first aspect.

[0064] Fourthly, a storage medium is provided, on which instructions are stored, which, when executed on a computer, perform the satellite attitude determination method based on a multi-satellite sensor as described in the first aspect or any possible design of the first aspect.

[0065] Fifthly, a computer program product containing instructions is provided, which, when executed on a computer, causes the computer to perform the satellite attitude determination method based on a multi-satellite sensor as described in the first aspect or any possible design of the first aspect.

[0066] Beneficial effects:

[0067] (1) This invention is designed for satellites equipped with two or more star sensors. It performs sequential processing on the data measured by the star sensors. At the same time, this invention uses the satellite attitude information determined in the previous moment to predict the attitude state of the target satellite in the next moment and uses it as the initial value for the attitude filtering calculation of the target satellite in the next moment. In addition, this invention provides a method for converting the observation noise variance matrix in case of inconsistent optical axis measurement accuracy and horizontal axis measurement accuracy of the star sensors. It converts the measurement information of different star sensors into the satellite body coordinate system for attitude determination calculation. Based on this, the attitude determination method provided by this invention not only has a small amount of computation, but also makes full use of the measurement information of the star sensors. As a result, it can effectively improve the accuracy of on-board attitude determination, and thus adapt to the wide application and promotion in the field of satellite attitude determination. Attached Figure Description

[0068] Figure 1 This is a flowchart illustrating the steps of the satellite attitude determination method based on multi-satellite sensors provided in an embodiment of the present invention.

[0069] Figure 2This is a schematic diagram of the structure of a satellite attitude determination device based on a multi-satellite sensor provided in an embodiment of the present invention;

[0070] Figure 3 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0071] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the present invention will be briefly introduced below in conjunction with the accompanying drawings and descriptions of the embodiments or the prior art. Obviously, the following description of the structure of the accompanying drawings is only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. It should be noted that the description of these embodiments is for the purpose of helping to understand the present invention, but does not constitute a limitation of the present invention.

[0072] It should be understood that although the terms first, second, etc., may be used herein to describe various units, these units should not be limited by these terms. These terms are only used to distinguish one unit from another. For example, a first unit may be referred to as a second unit, and similarly, a second unit may be referred to as a first unit, without departing from the scope of the exemplary embodiments of the invention.

[0073] It should be understood that the term "and / or" that may appear in this document is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can mean: A exists alone, B exists alone, and A and B exist simultaneously. The term " / and" that may appear in this document describes another relationship between related objects, indicating that two relationships can exist. For example, A / and B can mean: A exists alone, and A and B exist alone. In addition, the character " / " that may appear in this document generally indicates that the related objects before and after it are in an "or" relationship.

[0074] Example:

[0075] See Figure 1As shown, the satellite attitude determination method based on multiple star sensors provided in this embodiment is applied to the determination of the attitude of a target satellite equipped with n star sensors (in this embodiment, n is a positive integer greater than 1). In specific implementation, this method uses a sequential processing approach to process the measurement data of each star sensor. At the same time, this method uses the satellite attitude information determined in the previous moment to predict the attitude state of the target satellite in the next moment, and uses it as the initial value for the attitude filtering calculation of the target satellite in the next moment. Therefore, the attitude determination method provided by this invention not only has a small computational load, but also can make full use of the measurement information of each star sensor, thereby effectively improving the accuracy of onboard attitude determination, and thus adapting to the wide application and promotion in the field of satellite attitude determination. In this embodiment, the method can be run on an onboard computer, but is not limited to the steps S1 to S6 below.

[0076] In this embodiment, the principle of the method is first explained. In practical applications, this method involves two calculation processes for attitude determination. The first is to use the estimated attitude state variables of the target satellite at the previous time step (k-1), and the attitude estimation error variance matrix of the nth star sensor at the previous time step, combined with the target satellite's attitude dynamics and kinematic equations, to perform a one-step prediction of the target satellite's attitude state at the next time step (k), obtaining the predicted attitude value and one-step prediction variance matrix for the next time step. The second calculation process involves using the aforementioned predicted attitude value and one-step prediction variance matrix as the initial data for filtering calculations by the first star sensor at the next time step, combined with its measurement data (i.e., attitude measurement information). The system uses the measurement data from the first star sensor to obtain the estimated attitude state variables and the variance matrix of the attitude estimation error of the target satellite when determining the satellite's attitude using the measurement data from the first star sensor. Then, based on the data calculated using the measurement data from the first star sensor as input, the system determines the attitude of the target satellite when the measurement data from the next star sensor is used as input. This process is repeated until the estimated attitude state variables corresponding to the measurement data from the nth star sensor are calculated. This estimated value is then used as the final estimated attitude state variables of the target satellite at time k. Thus, based on the aforementioned principle, the estimated attitude state variables of the target satellite at different times can be calculated, thereby achieving accurate determination of its attitude.

[0077] In practical applications, the specific process of determining the aforementioned attitude will be explained in conjunction with the following steps S1 to S6.

[0078] S1. Obtain the attitude state quantity estimate of the target satellite at time k-1. Based on the attitude state quantity estimate of the target satellite at time k-1, and using the attitude dynamics equation and attitude kinematics equation of the target satellite, perform a one-step prediction of the attitude state of the target satellite to obtain the attitude prediction value of the target satellite at time k, where k is a positive integer greater than or equal to 1. In this embodiment, the above is a one-step prediction process, and the attitude state quantity estimate of the target satellite at time k-1 is also used as an example. The attitude state quantity estimate of the target satellite at time k-1 is the attitude state quantity estimate of the nth star sensor at time k-1. The attitude state quantity estimate of the nth star sensor at time k-1 may include, but is not limited to, the third attitude angle estimate and the third attitude angular rate estimate of the target satellite obtained when determining the attitude of the target satellite using the attitude measurement information of the nth star sensor at time k-1.

[0079] After obtaining the predicted attitude value of the target satellite at time k, the attitude parameters of the target satellite at time k can be determined. The determination process is shown in steps S2 to S6 below.

[0080] S2. For the i-th star sensor on the target satellite, obtain the attitude state quantity estimate and attitude estimation error variance matrix of the (i-1)-th star sensor at time k. When i is 1, the attitude state quantity estimate of the (i-1)-th star sensor at time k is the predicted attitude value of the target satellite at time k. The attitude estimation error variance matrix of the (i-1)-th star sensor at time k is the one-step prediction variance matrix of the target satellite at time k, and the one-step prediction variance matrix is ​​calculated based on the attitude state quantity estimate of the target satellite at time k-1 and the attitude estimation error variance matrix of the n-th star sensor at time k-1. In this embodiment, this is equivalent to using the attitude data of the target satellite calculated based on the measurement data of the previous star sensor, and combining... The measurement data of the next star sensor is combined to calculate the estimated attitude state variables of the target satellite (i.e., the estimated attitude angle and attitude angular rate of the target satellite) when the attitude measurement information of the next star sensor is used as input. This process is repeated until the estimated attitude state variables calculated with the measurement data of the nth star sensor as input are obtained. Then, the estimated attitude state variables of the target satellite at time k can be obtained. Optionally, for example, the estimated attitude state variables of the (i-1)th star sensor at time k may include, but are not limited to, the estimated first attitude angle and the estimated first attitude angular rate of the target satellite obtained when the attitude measurement information of the (i-1)th star sensor at time k is used to determine the attitude of the target satellite. The specific calculation process of the prediction variance matrix in the aforementioned step is described in detail below.

[0081] After obtaining the attitude state quantity estimate and attitude estimation error variance matrix of the (i-1)th star sensor at time k, the attitude parameters of the target satellite can be determined when the attitude measurement information of the i-th star sensor is used as input. The specific determination process can be, but is not limited to, the steps S3 and S4 below.

[0082] S3. Obtain the attitude measurement information of the i-th star sensor at time k, and calculate the attitude measurement value and filter gain matrix of the i-th star sensor at time k based on the attitude measurement information, the attitude state quantity estimate value and attitude estimation error variance matrix of the (i-1)-th star sensor at time k. In this embodiment, the aforementioned attitude measurement information may include, but is not limited to, satellite attitude angle measurement values, and the satellite attitude angle measurement values ​​include quaternions or Euler angles used to characterize the satellite attitude. In this embodiment, quaternions are used as an example.

[0083] In practical implementation, for example, the satellite attitude angle measurement value is the attitude angle of the target satellite directly measured by the i-th star sensor, which can be, but is not limited to, expressed as: Q bi =[q0 q1 q2 q3] T In the formula, Q bi This represents the attitude quaternion of the target satellite's body coordinate system relative to the inertial coordinate system, while q0, q1, q2, and q3 are all quaternions Q. bi The component is T, and T represents the transpose operation.

[0084] Optionally, for example, the attitude measurement value and filter gain matrix of the i-th star sensor at time k can be calculated using, but not limited to, the following steps S31 to S32.

[0085] S31. Calculate the difference between the measured value of the satellite attitude angle and the estimated value of the first attitude angle, and use the difference as the attitude measurement value of the i-th star sensor at time k. In specific applications, the estimated value of the first attitude angle is actually a quaternion containing 4 elements. Therefore, the vector part of the deviation between the two quaternions is taken as the attitude measurement value of the i-th star sensor at time k.

[0086] After obtaining the attitude measurement values, it is also necessary to calculate the filter gain matrix of the i-th star sensor at time k. The calculation process is shown in step S32 below.

[0087] S32. Obtain the observation matrix and observation noise variance matrix of the i-th star sensor, and calculate the filter gain matrix of the i-th star sensor at time k based on the observation matrix, the observation noise variance matrix and the attitude estimation error variance matrix of the (i-1)-th star sensor at time k. In this embodiment, the filter gain matrix of the i-th star sensor at time k can be calculated by, but is not limited to, the following formula (1).

[0088]

[0089] In the above formula (1), K k / STi H represents the filter gain matrix of the i-th star sensor at time k. STi Let R represent the observation matrix of the i-th star sensor. STi Let P represent the observation noise variance matrix of the i-th star sensor. i-1,k Let H represent the attitude estimation error variance matrix of the (i-1)th star sensor at time k, and let T represent the transpose operation, where H STi =[I3 0 3×3 ], I3 represents a 3x3 identity matrix, 0 3×3 Let P represent a 3x3 zero matrix, and when i is 1, P i-1,k Let be the one-step prediction variance matrix of the target satellite at time k.

[0090] Furthermore, R STi Essentially, it is the observation noise variance matrix of the i-th star sensor represented in the satellite's body coordinate system, where the observation noise variance matrix of the i-th star sensor represented in its body coordinate system (i.e., the star sensor's own coordinate system) is... Generally, it can be calculated based on the measurement accuracy information of the i-th star sensor (which may include, but is not limited to, the observation noise variance of the i-th star sensor in its optical axis direction and its horizontal axis direction); wherein, for star sensors with differences in measurement accuracy in the optical axis / horizontal axis direction, its optical axis is set to O. STi Z STi The shaft, based on its measurement accuracy information, can be calculated using the following formula (2).

[0091]

[0092] In the above formula (2), Let δ represent the observation noise variance matrix of the i-th star sensor in its body coordinate system. i γ represents the variance of the observation noise of the i-th star sensor along its horizontal axis. iThis represents the observation noise variance of the i-th star sensor along its optical axis (where the optical axis of the i-th star sensor is O in its body coordinate system). STi Z STi (axis), therefore, R STi and The following relationship is satisfied, that is, R is calculated based on the observation noise variance matrix represented in the body coordinate system of the i-th star sensor, and using the following formula (3). STi :

[0093]

[0094] In the above formula (12), The direction cosine matrix of the i-th star sensor's body coordinate system relative to the target satellite's body coordinate system is determined by the star sensor's installation direction, and T represents the transpose operation. In this embodiment, the direction cosine matrix of the i-th star sensor's body coordinate system relative to the target satellite's body coordinate system, as well as the observation noise variance of the i-th star sensor in its horizontal and optical axis directions, are pre-stored in the onboard computer so that, when determining the target satellite's attitude, the observation noise variance matrix of the i-th star sensor in the satellite's body coordinate system can be calculated based on the aforementioned data.

[0095] Therefore, the filter gain matrix of the i-th star sensor at time k can be calculated using the aforementioned formulas (1), (2) and (3). Meanwhile, this embodiment provides a method for converting the observation noise variance matrix to address the inconsistency between the optical axis measurement accuracy and the horizontal axis measurement accuracy of the star sensor. This method converts the measurement information of different star sensors into the satellite body coordinate system for attitude determination calculation, thereby making full use of the star sensor measurement data and improving the attitude determination accuracy.

[0096] After calculating the attitude measurement value and filter gain matrix of the i-th star sensor at time k based on the aforementioned steps S31 to S32, the attitude state quantity estimate value of the i-th star sensor at time k can be calculated based on the attitude measurement value, filter gain matrix, and attitude state quantity estimate value of the (i-1)-th star sensor at time k.

[0097] Optionally, for example, the calculation process for determining the attitude of the target satellite using the attitude measurement information of the i-th star sensor can be, but is not limited to, as shown in step S4 below.

[0098] S4. Based on the attitude measurement value and filter gain matrix of the i-th star sensor at time k, and the attitude state quantity estimate value of the (i-1)-th star sensor at time k, calculate the attitude state quantity estimate value of the i-th star sensor at time k. The attitude state quantity estimate value of the i-th star sensor at time k includes the second attitude angle estimate value and the second attitude angular rate estimate value of the target satellite obtained when determining the attitude of the target satellite using the attitude measurement information of the i-th star sensor at time k. In specific implementation, for example, but not limited to, the second attitude angle estimate value and the second attitude angular rate estimate value can be calculated according to the following formula (2).

[0099]

[0100] In the above formula (4), This represents the estimated second attitude angle of the target satellite. This represents the first attitude angle estimate in the attitude state estimate of the (i-1)th star sensor at time k. This represents the estimated second attitude angular rate of the target satellite. This represents the first attitude angular rate estimate in the attitude state estimate of the (i-1)th star sensor at time k, where, when i is 1, Let be the predicted attitude angle of the target satellite at time k. The predicted attitude angular rate of the target satellite at time k;

[0101] Describes the first matrix. K k / STi Let Z represent the second matrix. k / STi Let || represent the attitude measurement value of the i-th star sensor at time k, where || represents the norm symbol. The order of the filter gain matrix of the i-th star sensor at time k is 6×3, and the first matrix is ​​composed of the first three rows of the filter gain matrix of the i-th star sensor at time k, and the second matrix is ​​composed of the last three rows of the filter gain matrix of the i-th star sensor at time k.

[0102] Therefore, by using the aforementioned formula (4), the second attitude angle estimate and the second attitude angular rate estimate of the target satellite can be calculated when the attitude measurement information of the i-th star sensor at time k is used to determine the attitude of the target satellite. Then, in order to facilitate the subsequent attitude determination calculation of the target satellite using the attitude measurement information of the (i+1)-th star sensor, it is also necessary to calculate the attitude estimation error variance matrix of the i-th star sensor at time k. The calculation process can be, but is not limited to, the following step S5.

[0103] S5. Calculate the attitude estimation error variance matrix of the i-th star sensor at time k based on the filter gain matrix of the i-th star sensor at time k and the attitude estimation error variance matrix of the (i-1)-th star sensor at time k. In this embodiment, for example, but not limited to, the attitude estimation error variance matrix of the i-th star sensor at time k can be calculated based on the filter gain matrix of the i-th star sensor at time k, combined with the observation matrix and noise variance matrix of the i-th star sensor. Optionally, but not limited to, the following formula (5) can be used to calculate it.

[0104] P i,k = (I3-K) k / STi H STi )P i-1,k (I3-K k / STi H STi ) T +K k / STi R STi (K k / STi ) T (5)

[0105] In the above formula (5), P i,k Ii represents the attitude estimation error variance matrix of the i-th star sensor at time k, I3 represents the 3rd order identity matrix, and Ki represents the position of the star sensor. k / STi H represents the filter gain matrix of the i-th star sensor at time k. STi Let R represent the observation matrix of the i-th star sensor. STi Let P represent the observation noise variance matrix of the i-th star sensor. i-1,k Let P represent the attitude estimation error variance matrix of the (i-1)th star sensor at time k, where T represents the transpose operation, and when i is 1, P i-1,k Let be the one-step prediction variance matrix of the target satellite at time k.

[0106] Thus, based on the aforementioned formula (5), the attitude estimation error variance matrix of the i-th star sensor at time k can be calculated. Then, the attitude state quantity estimate and attitude estimation error variance matrix of the i-th star sensor at time k can be used as the initial values ​​for calculating the attitude determination of the target satellite using the attitude measurement information of the (i+1)-th star sensor. This process is then repeated until the attitude state quantity estimate and attitude estimation error variance matrix of the n-th star sensor at time k are calculated. Finally, the attitude state quantity estimate of the target satellite at time k can be obtained. Specifically, the sequential calculation process is shown in step S6 below.

[0107] S6. Increment i by 1, and re-acquire the attitude state quantity estimate and attitude estimation error variance matrix of the (i-1)th star sensor at time k, until i equals n. Then, take the attitude state quantity estimate of the nth star sensor at time k as the attitude state quantity estimate of the target satellite at time k, where the initial value of i is 1. In this embodiment, this is equivalent to taking the second attitude angle estimate and the second attitude angular rate estimate of the nth star sensor at time k as the final attitude angle estimate and attitude angular rate estimate of the target satellite at time k.

[0108] The following example illustrates the sequential processing described in steps S1 to S6:

[0109] Assuming n is 2, firstly, for the first star sensor, it acquires the attitude prediction value and one-step prediction variance matrix of the target satellite at time k. The aforementioned attitude prediction value and one-step prediction variance matrix are calculated based on the estimated attitude state variables of the target satellite at time k-1, and the attitude estimation error variance matrix of the nth star sensor at time k-1, combined with the attitude kinematic equation and dynamic equation of the target satellite.

[0110] Then, the attitude measurement information (i.e., satellite attitude angle measurement value) of the first star sensor at time k is calculated, and the deviation between it and the attitude angle prediction value in the attitude prediction value is obtained. The vector part of the deviation quaternion is used as the attitude measurement value of the first star sensor at time k. Then, the one-step prediction variance matrix, the observation matrix and the observation noise variance matrix of the first star sensor are substituted into the aforementioned formula (1) to calculate the filter gain matrix of the first star sensor at time k.

[0111] Next, substitute the aforementioned attitude angle prediction value, attitude angular rate prediction value, filter gain matrix of the first star sensor, and attitude measurement value into the aforementioned formula (4) to calculate the second attitude angle estimate and second attitude angular rate estimate of the target satellite obtained when using the attitude measurement information of the first star sensor to determine the attitude of the target satellite; then, substitute the filter gain matrix, observation matrix, observation noise variance matrix, and the aforementioned one-step prediction variance matrix of the first star sensor into the aforementioned formula (5) to calculate the attitude estimation error variance matrix of the first star sensor; in this way, the filtering calculation of the first star sensor can be completed, and when performing the filtering calculation of the next star sensor, the attitude state quantity estimate of the (i-1)th star sensor (i.e. the first star sensor) at time k is the second attitude angle estimate and second attitude angular rate estimate of the first star sensor.

[0112] Furthermore, the attitude state quantity estimate and attitude estimation error variance matrix of the first star sensor can be used as the initial values ​​for attitude determination calculation of the second star sensor. Specifically, the deviation between the attitude angle measurement value of the second star sensor and the second attitude angle estimate value of the first star sensor is calculated, and the vector part of the deviation quaternion is taken as the attitude measurement value of the second star sensor at time k. Then, the second attitude angle estimate value and the second attitude angular rate estimate value of the first star sensor, as well as the filter gain matrix and measurement value of the second star sensor, are substituted into the aforementioned formula (4) to calculate the second attitude angle estimate value and the second attitude angular rate estimate value of the target satellite obtained when using the attitude measurement information of the second star sensor to determine the attitude of the target satellite.

[0113] Similarly, by substituting the filter gain matrix, observation matrix, observation noise variance matrix of the second star sensor and the attitude estimation error variance matrix of the first star sensor into the aforementioned formula (5), the attitude estimation error variance matrix of the second star sensor can be calculated. At this time, the attitude determination of the target satellite at time k is completed, that is, the attitude state quantity estimate of the second star sensor is used as the final attitude state quantity estimate of the target satellite at time k and output.

[0114] Finally, based on the attitude estimation error variance matrix of the second star sensor at time k and the estimated attitude state of the target satellite at time k, the predicted attitude value and one-step prediction variance matrix of the target satellite at time k+1 can be calculated. In this way, by continuously calculating based on this principle, the estimated attitude state of the target satellite at different times can be obtained, thereby completing the accurate determination of the attitude of the target satellite at different times.

[0115] In one possible design, the second aspect of this embodiment discloses the specific calculation process of the attitude prediction value and the one-step prediction variance matrix in the first aspect of the embodiment, which may be, but is not limited to, the steps shown below.

[0116] In this embodiment, it has been explained above that the attitude state quantity estimate of the target satellite at time k-1 is the attitude state quantity estimate of the nth star sensor at time k-1. The attitude state quantity estimate of the nth star sensor at time k-1 may include, but is not limited to, the third attitude angle estimate and the third attitude angular rate estimate of the target satellite obtained when determining the attitude of the target satellite using the attitude measurement information of the nth star sensor at time k-1. Thus, the one-step prediction variance matrix of the target satellite at time k is calculated based on the attitude state quantity estimate of the target satellite at time k-1 and the attitude estimation error variance matrix of the nth star sensor at time k-1, which may include, but is not limited to, steps S01 and S02 as described below.

[0117] S01. Based on the estimated third attitude angular rate, and according to the following formula (6), calculate the state transition matrix of the target satellite at time k.

[0118]

[0119] In the above formula (6), Φ k,k-1 This represents the state transition matrix of the target satellite at time k. The third attitude angular rate estimate is represented by J, the moment of inertia matrix of the target satellite is represented by h, the angular momentum of the momentum wheel mounted on the target satellite is represented by I3, and the third-order identity matrix is ​​represented by 0. 3×3 I represents a 3rd-order zero matrix, I6 represents a 6th-order identity matrix, ΔT represents the cycle time of the filter during target satellite attitude estimation, and (·) × The cross product matrix represents the vector; of course, the aforementioned moment of inertia matrix, angular momentum, and filter period are all preset in the onboard computer.

[0120] After obtaining the state transition matrix of the target satellite at time k, its one-step prediction variance matrix at time k can be calculated, as shown in step S02 below.

[0121] S02. Based on the attitude estimation error variance matrix of the nth star sensor at time k-1 and the state transition matrix, the one-step prediction variance matrix of the target satellite at time k is calculated according to the following formula (7).

[0122]

[0123] In the above formula (7), P k,k-1 P represents the one-step prediction variance matrix of the target satellite at time k. n,k-1 Let Q represent the variance matrix of the attitude estimation error of the nth star sensor at time k-1. k Let T represent the system process noise variance matrix, where T is the transpose operation.

[0124] Thus, through the aforementioned steps S01 and S02, the one-step prediction variance matrix of the target satellite at time k can be calculated based on the estimated attitude angular rate of the target satellite at time k-1 and the attitude estimation error variance matrix of the nth star sensor at time k-1.

[0125] Then, by using the estimated attitude state of the target satellite at time k-1, the predicted attitude value of the target satellite at time k can be calculated. The calculation process can be, but is not limited to, the steps S03 to S06 below.

[0126] S03. Based on the estimated third attitude angle and the estimated third attitude angular rate, and using the attitude dynamics equation and attitude kinematics equation, calculate the rate of change of attitude angle and the rate of change of attitude angular rate of the target satellite at time k-1; in specific applications, the aforementioned rate of change of attitude angle and rate of change of attitude angular rate can be calculated using, but is not limited to, the following formula (8).

[0127]

[0128] In the above formula (8), This represents the rate of change of the target satellite's attitude angle at time k-1 (in quaternion form). This represents the estimated value of the third attitude angle (in quaternion form). This represents the rate of change of the target satellite's attitude angular rate at time k-1. This represents the estimated value of the third attitude angular rate. T represents the rate of change of the angular momentum of the target satellite's momentum wheel. MT T represents the control torque of the target satellite's magnetor. d This represents the external disturbance torque experienced by the target satellite. It is the matrix shown in the following formula (9).

[0129]

[0130] In the above formula (9), q 0,k-1 ,q 1,k-1 ,q 2,k-1 ,q 3,k-1 Then all are The amount.

[0131] According to the aforementioned formula (8), the attitude angle change rate and attitude angular rate change rate of the target satellite at time k-1 can be obtained; then, the attitude state is predicted in one step, and the predicted values ​​of the satellite attitude angle and attitude angular rate at the next time can be obtained. The calculation formula is shown in the following formula (10).

[0132] Based on the rate of change of the target satellite's attitude angle at time k-1 and the estimated value of the third attitude angle, S04 calculates the predicted value of the target satellite's attitude angle at time k.

[0133] Based on the rate of change of the target satellite's attitude angular rate at time k-1 and the estimated value of the third attitude angular rate, S05 calculates the predicted value of the target satellite's attitude angular rate at time k.

[0134] In this embodiment, for example, but not limited to, the following formula (10) can be used to calculate the predicted attitude angle and attitude rate of the target satellite at time k.

[0135]

[0136] In the above formula (10), This represents the predicted attitude angle of the target satellite at time k. This represents the predicted attitude angular rate of the target satellite at time k. This represents the rate of change of the target satellite's attitude angle at time k-1. This represents the rate of change of the target satellite's attitude angular rate at time k-1.

[0137] Thus, the predicted attitude angle and attitude angular rate of the target satellite at time k can be calculated using the aforementioned formula. Then, the predicted attitude of the target satellite at time k can be constructed using the two predicted values, as shown in step S06 below.

[0138] S06. Using the predicted attitude angle and attitude angular rate of the target satellite at time k, the predicted attitude value of the target satellite at time k is formed.

[0139] Therefore, through the aforementioned steps S01 to S06, the estimated attitude state of the target satellite at time k-1 and the attitude estimation error variance matrix of the nth star sensor at time k-1 can be used to achieve one-step prediction of the attitude state of the target satellite at time k, thereby obtaining its attitude prediction value and one-step prediction variance matrix at time k. Then, based on the aforementioned parameters, by executing the aforementioned steps S1 to S6, the attitude of the target satellite at different times can be accurately determined.

[0140] Therefore, through the satellite attitude determination method based on multiple star sensors described in detail in steps S1-S6 and S01-S06 above, this invention employs a sequential processing approach to process the measurement data of each star sensor. Simultaneously, this method uses the estimated attitude state variables determined in the previous moment to predict the target satellite's attitude state in the next moment, and uses these as the initial values ​​for attitude determination in the next moment. Thus, the attitude determination method provided by this invention, by adopting a sequential processing approach, not only has a low computational load but also fully utilizes the measurement information of each star sensor, thereby improving attitude determination accuracy. Furthermore, this invention addresses the inconsistency between the optical axis measurement accuracy and the transverse axis measurement accuracy of the star sensors by providing a method for converting the observation noise variance matrix, uniformly converting the measurement information of different star sensors to the satellite body coordinate system for attitude determination calculation. Based on this, the computational load for on-board attitude determination can be reduced. In summary, this invention is suitable for the accurate determination of the attitude of satellites equipped with multiple star sensors and is suitable for widespread application and promotion in the field of satellite attitude determination.

[0141] like Figure 2 As shown, the third aspect of this embodiment provides a hardware device for implementing the satellite attitude determination method based on multi-satellite sensors described in the first and second aspects of the embodiments, comprising:

[0142] The attitude prediction unit is used to obtain the estimated value of the attitude state variables of the target satellite at time k-1. Based on the estimated value of the attitude state variables of the target satellite at time k-1, and using the attitude dynamics equation and attitude kinematics equation of the target satellite, the unit performs a one-step prediction of the attitude state of the target satellite to obtain the attitude prediction value of the target satellite at time k, where k is a positive integer greater than or equal to 1.

[0143] The attitude calculation unit, for the i-th star sensor on the target satellite, is used to obtain the attitude state quantity estimate and attitude estimation error variance matrix of the (i-1)-th star sensor at time k. When i is 1, the attitude state quantity estimate of the (i-1)-th star sensor at time k is the attitude prediction value of the target satellite at time k. The attitude estimation error variance matrix of the (i-1)-th star sensor at time k is the one-step prediction variance matrix of the target satellite at time k. The one-step prediction variance matrix is ​​calculated based on the attitude state quantity estimate of the target satellite at time k-1 and the attitude estimation error variance matrix of the n-th star sensor at time k-1.

[0144] The attitude calculation unit is used to obtain the attitude measurement information of the i-th star sensor at time k, and calculate the attitude measurement value and filter gain matrix of the i-th star sensor at time k based on the attitude measurement information, the attitude state quantity estimate value and attitude estimation error variance matrix of the (i-1)-th star sensor at time k.

[0145] The attitude calculation unit is used to calculate the attitude state quantity estimate of the i-th star sensor at time k based on the attitude measurement value and filter gain matrix of the i-th star sensor at time k, and the attitude state quantity estimate value of the (i-1)-th star sensor at time k. The attitude state quantity estimate value of the i-th star sensor at time k includes the second attitude angle estimate value and the second attitude angular rate estimate value of the target satellite obtained when determining the attitude of the target satellite using the attitude measurement information of the i-th star sensor at time k.

[0146] The attitude calculation unit is used to calculate the attitude estimation error variance matrix of the i-th star sensor at time k based on the filter gain matrix of the i-th star sensor at time k and the attitude estimation error variance matrix of the (i-1)-th star sensor at time k.

[0147] The attitude update unit is used to increment i by 1 and reacquire the attitude state quantity estimate and attitude estimation error variance matrix of the (i-1)th star sensor at time k until i equals n. Then, the attitude state quantity estimate of the nth star sensor at time k is used as the attitude state quantity estimate of the target satellite at time k, where the initial value of i is 1.

[0148] The working process, working details and technical effects of the device provided in this embodiment can be found in the first and second aspects of the embodiment, and will not be repeated here.

[0149] like Figure 3 As shown, the fourth aspect of this embodiment provides another satellite attitude determination device based on a multi-satellite sensor. Taking the device as an electronic device as an example, it includes: a memory, a processor, and a transceiver that are connected in sequence. The memory is used to store a computer program, the transceiver is used to send and receive messages, and the processor is used to read the computer program and execute the satellite attitude determination method based on a multi-satellite sensor as described in the first and second aspects of the embodiments.

[0150] For specific examples, the memory may include, but is not limited to, random access memory (RAM), read-only memory (ROM), flash memory, first-in-first-out (FIFO) memory, and / or first-in-last-out (FILO) memory, etc.; specifically, the processor may include one or more processing cores, such as a 4-core processor, an 8-core processor, etc. The processor may be implemented using at least one hardware form of DSP (Digital Signal Processing), FPGA (Field-Programmable Gate Array), PLA (Programmable Logic Array). The processor may also include a main processor and a coprocessor. The main processor, also known as the CPU (Central Processing Unit), is used to process data in the wake-up state; the coprocessor is a low-power processor used to process data in the standby state.

[0151] In some embodiments, the processor may integrate a GPU (Graphics Processing Unit), which is responsible for rendering and drawing the content to be displayed on the screen. For example, the processor may not be limited to microprocessors of the STM32F105 series, reduced instruction set computer (RISC) microprocessors, x86 architecture processors, or processors with integrated neural network processing units (NPUs). The transceiver may be, but is not limited to, a Wi-Fi transceiver, a Bluetooth transceiver, a General Packet Radio Service (GPRS) transceiver, a ZigBee (a low-power LAN protocol based on the IEEE 802.15.4 standard) transceiver, a 3G transceiver, a 4G transceiver, and / or a 5G transceiver. Furthermore, the device may also include, but is not limited to, a power module, a display screen, and other necessary components.

[0152] The working process, working details and technical effects of the electronic device provided in this embodiment can be found in the first and second aspects of the embodiment, and will not be repeated here.

[0153] The fifth aspect of this embodiment provides a storage medium that stores instructions containing the satellite attitude determination method based on a multi-satellite sensor as described in the first and / or second aspects of the embodiments. That is, the storage medium stores instructions that, when executed on a computer, perform the satellite attitude determination method based on a multi-satellite sensor as described in the first and / or second aspects of the embodiments.

[0154] The storage medium refers to a carrier for storing data, which may include, but is not limited to, floppy disks, optical disks, hard disks, flash memory, USB flash drives, and / or memory sticks. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable devices.

[0155] The working process, working details and technical effects of the storage medium provided in this embodiment can be found in the first and second aspects of the embodiment, and will not be repeated here.

[0156] The sixth aspect of this embodiment provides a computer program product containing instructions that, when executed on a computer, cause the computer to perform the satellite attitude determination method based on a multi-satellite sensor as described in the first and / or second aspects of the embodiments, wherein the computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device.

[0157] Finally, it should be noted that the above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A satellite attitude determination method based on multi-satellite sensors, characterized in that, The method is applied to determine the attitude of a target satellite equipped with n star sensors, where n is a positive integer greater than 1, and the method includes: The attitude state of the target satellite at time k-1 is estimated. Based on the attitude state of the target satellite at time k-1, and using the attitude dynamics equation and attitude kinematics equation of the target satellite, the attitude state of the target satellite is predicted in one step to obtain the attitude prediction value of the target satellite at time k, where k is a positive integer greater than or equal to 1. For the i-th star sensor on the target satellite, obtain the attitude state quantity estimate and attitude estimation error variance matrix of the (i-1)-th star sensor at time k. When i is 1, the attitude state quantity estimate of the (i-1)-th star sensor at time k is the attitude prediction value of the target satellite at time k. The attitude estimation error variance matrix of the (i-1)-th star sensor at time k is the one-step prediction variance matrix of the target satellite at time k. The one-step prediction variance matrix is ​​calculated based on the attitude state quantity estimate of the target satellite at time k-1 and the attitude estimation error variance matrix of the n-th star sensor at time k-1. Obtain the attitude measurement information of the i-th star sensor at time k, and calculate the attitude measurement value and filter gain matrix of the i-th star sensor at time k based on the attitude measurement information, the attitude state quantity estimate value and attitude estimation error variance matrix of the (i-1)-th star sensor at time k. Based on the attitude measurement value and filter gain matrix of the i-th star sensor at time k, and the attitude state quantity estimate value of the (i-1)-th star sensor at time k, the attitude state quantity estimate value of the i-th star sensor at time k is calculated. The attitude state quantity estimate value of the i-th star sensor at time k includes the second attitude angle estimate value and the second attitude angular rate estimate value of the target satellite obtained when determining the attitude of the target satellite using the attitude measurement information of the i-th star sensor at time k. The attitude estimation error variance matrix of the i-th star sensor at time k is calculated based on the filter gain matrix of the i-th star sensor at time k and the attitude estimation error variance matrix of the (i-1)-th star sensor at time k. Increment i by 1, and re-acquire the attitude state quantity estimate and attitude estimation error variance matrix of the (i-1)th star sensor at time k, until i equals n. Then, take the attitude state quantity estimate of the nth star sensor at time k as the attitude state quantity estimate of the target satellite at time k, where the initial value of i is 1.

2. The method according to claim 1, characterized in that, The attitude state quantity estimate of the target satellite at time k-1 is the attitude state quantity estimate of the nth star sensor at time k-1, and the attitude state quantity estimate of the nth star sensor at time k-1 includes: the third attitude angle estimate and the third attitude angular rate estimate of the target satellite obtained when the attitude measurement information of the nth star sensor at time k-1 is used to determine the attitude of the target satellite. Specifically, based on the estimated attitude state variables of the target satellite at time k-1, and using the attitude dynamics equations and attitude kinematics equations of the target satellite, a one-step prediction of the target satellite's attitude state is performed to obtain the predicted attitude value of the target satellite at time k, including: Based on the estimated third attitude angle and the estimated third attitude angular rate, and using the attitude dynamics equation and attitude kinematics equation, the rate of change of attitude angle and the rate of change of attitude angular rate of the target satellite at time k-1 are calculated. Based on the rate of change of the target satellite's attitude angle at time k-1 and the estimated value of the third attitude angle, the predicted value of the target satellite's attitude angle at time k is calculated; and Based on the rate of change of the target satellite's attitude angular rate at time k-1 and the estimated value of the third attitude angular rate, the predicted value of the target satellite's attitude angular rate at time k is calculated. The attitude prediction value of the target satellite at time k is formed by using the predicted attitude angle and attitude angular rate of the target satellite at time k.

3. The method according to claim 1, characterized in that, The attitude state quantity estimate of the (i-1)th star sensor at time k includes: the first attitude angle estimate of the target satellite obtained when determining the attitude of the target satellite using the attitude measurement information of the (i-1)th star sensor at time k, wherein the attitude measurement information of the i-th star sensor at time k includes the satellite attitude angle measurement value, and the satellite attitude angle measurement value includes a quaternion used to characterize the satellite attitude. Specifically, based on the attitude measurement information, and the attitude state quantity estimate and attitude estimation error variance matrix of the (i-1)th star sensor at time k, the attitude measurement value and filter gain matrix of the i-th star sensor at time k are calculated, including: Calculate the difference between the measured satellite attitude angle and the first estimated attitude angle, and use the difference as the attitude measurement value of the i-th star sensor at time k. Obtain the observation matrix and observation noise variance matrix of the i-th star sensor, and calculate the filter gain matrix of the i-th star sensor at time k based on the observation matrix, the observation noise variance matrix and the attitude estimation error variance matrix of the (i-1)-th star sensor at time k.

4. The method according to claim 3, characterized in that, Based on the observation matrix, the observation noise variance matrix, and the attitude estimation error variance matrix of the (i-1)th star sensor at time k, the filter gain matrix of the i-th star sensor at time k is calculated, including: Based on the observation matrix, the observation noise variance matrix, and the attitude estimation error variance matrix of the (i-1)th star sensor at time k, the filter gain matrix of the i-th star sensor at time k is calculated using the following formula (1). In the above formula (1), K k / STi H represents the filter gain matrix of the i-th star sensor at time k. STi Let R represent the observation matrix of the i-th star sensor. STi Let P represent the observation noise variance matrix of the i-th star sensor. i-1,k Let H represent the attitude estimation error variance matrix of the (i-1)th star sensor at time k, and let T represent the transpose operation, where H STi =[I3 0 3×3 ], I3 represents a 3x3 identity matrix, 0 3×3 Let P represent a 3x3 zero matrix, and when i is 1, P i-1,k Let be the one-step prediction variance matrix of the target satellite at time k.

5. The method according to claim 4, characterized in that, The observation noise variance matrix R of the i-th star sensor STi It is represented in the body coordinate system of the target satellite, wherein the observation noise variance matrix of the i-th star sensor is obtained by the following method: Obtain the measurement accuracy information of the i-th star sensor, wherein the measurement accuracy information includes the observation noise variance of the i-th star sensor in its optical axis direction and the observation noise variance in its horizontal axis direction; Using the measurement accuracy information and the following formula (2), the observation noise variance matrix represented by the i-th star sensor in its body coordinate system is calculated; In the above formula (2), Let δ represent the observation noise variance matrix of the i-th star sensor in its body coordinate system. i γ represents the variance of the observation noise of the i-th star sensor along its horizontal axis. i Let $\mathbf{i}$ represent the observation noise variance of the $i$-th star sensor along its optical axis, and the optical axis of the $i$-th star sensor is $\mathbf{i}$ in its body coordinate system. STi Z STi axis; Based on the observation noise variance matrix of the i-th star sensor in its body coordinate system, and using the following formula (3), the observation noise variance matrix of the i-th star sensor in the body coordinate system of the target satellite is calculated. In the above formula (3), The direction cosine matrix represents the body coordinate system of the i-th star sensor relative to the body coordinate system of the target satellite, and T represents the transpose operation.

6. The method according to claim 1, characterized in that, The attitude state quantity estimate of the (i-1)th star sensor at time k includes: the first attitude angle estimate and the first attitude angular rate estimate of the target satellite obtained when determining the attitude of the target satellite using the attitude measurement information of the (i-1)th star sensor at time k; and the attitude prediction value of the target satellite at time k includes the attitude angle prediction value and the attitude angular rate prediction value of the target satellite at time k. Specifically, based on the attitude measurement value and filter gain matrix of the i-th star sensor at time k, and the attitude state quantity estimate value of the (i-1)-th star sensor at time k, the attitude state quantity estimate value of the i-th star sensor at time k is calculated, including: Based on the first attitude angular rate estimate, the first attitude angle estimate, the attitude measurement value of the i-th star sensor at time k and the filter gain matrix, and according to the following formula (4), the second attitude angle estimate and the second attitude angular rate estimate of the target satellite are calculated when the attitude measurement information of the i-th star sensor at time k is used to determine the attitude of the target satellite. In the above formula (4), This represents the estimated second attitude angle of the target satellite. This represents the first attitude angle estimate in the attitude state estimate of the (i-1)th star sensor at time k. This represents the estimated second attitude angular rate of the target satellite. This represents the first attitude angular rate estimate in the attitude state estimate of the (i-1)th star sensor at time k, where, when i is 1, Let be the predicted attitude angle of the target satellite at time k. The predicted attitude angular rate of the target satellite at time k; Describes the first matrix. K k / STi Let Z represent the second matrix. k / STi Let || represent the attitude measurement value of the i-th star sensor at time k, where || represents the norm symbol. The order of the filter gain matrix of the i-th star sensor at time k is 6×3, and the first matrix is ​​composed of the first three rows of the filter gain matrix of the i-th star sensor at time k, and the second matrix is ​​composed of the last three rows of the filter gain matrix of the i-th star sensor at time k.

7. The method according to claim 1, characterized in that, Based on the filter gain matrix of the i-th star sensor at time k and the attitude estimation error variance matrix of the (i-1)-th star sensor at time k, the attitude estimation error variance matrix of the i-th star sensor at time k is calculated, including: Obtain the observation matrix and observation noise variance matrix of the i-th star sensor; Based on the observation matrix, the observation noise variance matrix, the filter gain matrix of the i-th star sensor at time k, and the attitude estimation error variance matrix of the (i-1)-th star sensor at time k, the attitude estimation error variance matrix of the i-th star sensor at time k is calculated according to the following formula (5). P i,k =(I3-K k / STi H STi )P i-1,k (I3-K k / STi H STi ) T +K k / STi R STi (K k / STi ) T (5) In the above formula (5), P i,k Ii represents the attitude estimation error variance matrix of the i-th star sensor at time k, I3 represents the 3rd order identity matrix, and Ki represents the position of the star sensor. k / STi H represents the filter gain matrix of the i-th star sensor at time k. STi Let R represent the observation matrix of the i-th star sensor. STi Let P represent the observation noise variance matrix of the i-th star sensor. i-1,k Let P represent the attitude estimation error variance matrix of the (i-1)th star sensor at time k, where T represents the transpose operation, and when i is 1, P i-1,k Let be the one-step prediction variance matrix of the target satellite at time k.

8. The method according to claim 1, characterized in that, The estimated attitude state of the target satellite at time k-1 includes: the estimated third attitude angular rate of the target satellite; Specifically, based on the estimated attitude state variables of the target satellite at time k-1 and the attitude estimation error variance matrix of the nth star sensor at time k-1, the one-step prediction variance matrix of the target satellite at time k is calculated, including: Based on the estimated third attitude angular rate, and according to the following formula (6), the state transition matrix of the target satellite at time k is calculated; In the above formula (6), Φ k,k-1 This represents the state transition matrix of the target satellite at time k. The third attitude angular rate estimate is represented by J, the moment of inertia matrix of the target satellite is represented by h, the angular momentum of the momentum wheel mounted on the target satellite is represented by I3, and the third-order identity matrix is ​​represented by 0. 3×3 I represents a 3rd-order zero matrix, I6 represents a 6th-order identity matrix, ΔT represents the cycle time of the filter during target satellite attitude estimation, and (·) × Represents the cross product matrix corresponding to the vectors; Based on the attitude estimation error variance matrix of the nth star sensor at time k-1 and the state transition matrix, the one-step prediction variance matrix of the target satellite at time k is calculated according to the following formula (7); In the above formula (7), P k,k-1 P represents the one-step prediction variance matrix of the target satellite at time k. n,k-1 Let Q represent the variance matrix of the attitude estimation error of the nth star sensor at time k-1. k Let T represent the system process noise variance matrix, where T is the transpose operation.

9. A satellite attitude determination device based on multi-satellite sensors, characterized in that, An apparatus for determining the attitude of a target satellite equipped with n star sensors, where n is a positive integer greater than 1, and the apparatus comprises: The attitude prediction unit is used to obtain the estimated value of the attitude state variables of the target satellite at time k-1, and based on the estimated value of the attitude state variables of the target satellite at time k-1, and using the attitude dynamics equation and attitude kinematics equation of the target satellite, to perform one-step prediction of the attitude state of the target satellite, and obtain the attitude prediction value of the target satellite at time k, where k is a positive integer greater than or equal to 1. The attitude calculation unit, for the i-th star sensor on the target satellite, is used to obtain the attitude state quantity estimate and attitude estimation error variance matrix of the (i-1)-th star sensor at time k. When i is 1, the attitude state quantity estimate of the (i-1)-th star sensor at time k is the attitude prediction value of the target satellite at time k. The attitude estimation error variance matrix of the (i-1)-th star sensor at time k is the one-step prediction variance matrix of the target satellite at time k. The one-step prediction variance matrix is ​​calculated based on the attitude state quantity estimate of the target satellite at time k-1 and the attitude estimation error variance matrix of the n-th star sensor at time k-1. The attitude calculation unit is used to obtain the attitude measurement information of the i-th star sensor at time k, and calculate the attitude measurement value and filter gain matrix of the i-th star sensor at time k based on the attitude measurement information, the attitude state quantity estimate value and attitude estimation error variance matrix of the (i-1)-th star sensor at time k. The attitude calculation unit is used to calculate the attitude state quantity estimate of the i-th star sensor at time k based on the attitude measurement value and filter gain matrix of the i-th star sensor at time k, and the attitude state quantity estimate value of the (i-1)-th star sensor at time k. The attitude state quantity estimate value of the i-th star sensor at time k includes the second attitude angle estimate value and the second attitude angular rate estimate value of the target satellite obtained when determining the attitude of the target satellite using the attitude measurement information of the i-th star sensor at time k. The attitude calculation unit is used to calculate the attitude estimation error variance matrix of the i-th star sensor at time k based on the filter gain matrix of the i-th star sensor at time k and the attitude estimation error variance matrix of the (i-1)-th star sensor at time k. The attitude update unit is used to increment i by 1 and reacquire the attitude state quantity estimate and attitude estimation error variance matrix of the (i-1)th star sensor at time k until i equals n. Then, the attitude state quantity estimate of the nth star sensor at time k is used as the attitude state quantity estimate of the target satellite at time k, where the initial value of i is 1.

10. A satellite attitude determination device based on multi-satellite sensors, characterized in that, include: A memory, a processor, and a transceiver are sequentially connected in communication, wherein the memory is used to store computer programs, the transceiver is used to send and receive messages, and the processor is used to read the computer programs and execute the satellite attitude determination method based on a multi-satellite sensor as described in any one of claims 1 to 8.

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