Directly mounted gyro and star sensor combined high stability space pointing system and method

Abstract

The present invention provides a high-stability space pointing system and method of a gyro and star sensor combination in a direct installation mode, which is used to solve the technical problems that the existing space pointing system of a gyro and star sensor combination based on a strapdown installation mode cannot directly sense the rotation angle of a two-dimensional turntable, resulting in its control stability being easily affected by the error of the rotation angle of the two-dimensional turntable, and the entire filtering process uses a maximum entropy filter based on a Cauchy kernel, which increases the calculation burden and causes a decrease in real-time performance. The present invention directly installs the gyro on the payload, installs the star sensor on the turntable base, and constructs a state model and a measurement model, adopts an event-driven filtering mechanism to respectively use Kalman filtering or maximum entropy filtering based on a Cauchy kernel for measurement update in different situations, effectively improves the accuracy of stable pointing of the two-dimensional turntable, can effectively handle non-Gaussian noise appearing in the measurement, and meets the requirements of the spacecraft for the robustness and stability of the space pointing system.

Description

Technical Field

[0001] The invention relates to a space pointing method, and in particular to a high-stability space pointing system and method of a gyro and star sensor combination in a direct installation mode. Background Art

[0002] In the field of aerospace, turntable structures have become a very important part of space tracking and aiming systems and tracking and detection systems because they can realize the pointing movement of payloads such as cameras and radars independently of spacecraft platforms such as satellites. Among them, the two-dimensional turntable is the most widely used turntable structure. It consists of two mutually perpendicular axis rotating platforms. Cameras, radars and other payloads are used to be fixedly mounted on an axis rotating platform for pointing movement. Due to the inevitable existence of control errors, installation errors and other factors in practical applications, there is a deviation between the actual pointing and the ideal pointing of the two-dimensional turntable, which affects the pointing control stability of the two-dimensional turntable. Therefore, high-precision pointing measurement of the two-dimensional turntable is an important prerequisite for achieving its high-stability control and thus improving the stability of the space tracking and aiming system or tracking and detection system.

[0003] At present, in space pointing applications, star sensors and gyroscopes are the most commonly used space pointing measurement devices. Although star sensors can provide high-precision attitude and direction information, their operating frequency is low and they are limited by time and environmental conditions. Although gyroscopes can continuously output angular velocity information at a high frequency and have good real-time performance, they have error drift and poor long-term attitude accuracy. Due to the good complementary properties of star sensors and gyroscopes, a space pointing system combining gyroscopes and star sensors has emerged in the industry. It uses the high-precision attitude and direction information obtained by star sensors to compensate for the drift of the gyroscope and obtain high-precision two-dimensional turntable pointing information.

[0004] However, the existing space pointing system of gyro and star sensor combination is mainly based on strapdown installation, that is, both the gyro and star sensor are installed on the turntable base of the two-dimensional turntable. In this mode, since the gyro and star sensor cannot directly sense the rotation angle of the two-dimensional turntable, the control stability of the two-dimensional turntable is very susceptible to the error of the two-dimensional turntable rotation angle. At the same time, in many applications, due to limited space and large size of the star sensor, it cannot be directly installed on the pitch axis of the two-dimensional turntable.

[0005] In addition, the data fusion of the existing gyro and star sensor combined space pointing system is currently mostly based on the Kalman filter algorithm or the maximum entropy filter algorithm. However, due to the influence of illumination and environment, it is easy for the space pointing system to generate non-Gaussian noise, resulting in a serious decline in the performance of the Kalman filter algorithm. As an emerging filtering theory, the maximum entropy filter algorithm uses the high-order moment of the signal instead of the second-order moment in the principle of minimum mean square error, so it shows excellent robustness when processing non-Gaussian noise. The existing filters using the maximum entropy filter algorithm mainly include the maximum entropy filter based on the Gaussian kernel and the maximum entropy filter based on the Cauchy kernel. In practical applications, if the quantity measurement is contaminated by multidimensional non-Gaussian noise (such as heavy-tailed noise), the maximum entropy filter based on the Gaussian kernel may collapse due to matrix singularity, resulting in a decrease in estimation accuracy. The maximum entropy filter based on the Cauchy kernel shows excellent performance in processing multidimensional non-Gaussian noise. However, most of the existing maximum entropy filters based on the Cauchy kernel use fixed-point iteration to update the state estimate, which involves a relatively large computational cost. Therefore, if the maximum entropy filter based on the Cauchy kernel is used in the entire filtering process of the gyro and star sensor combined pointing system, it will increase unnecessary calculation burden and lead to a decrease in real-time performance. Summary of the invention

[0006] The purpose of the present invention is to provide a high-stability space pointing system and method of a gyro and star sensor combination in a direct installation mode, in view of the fact that the existing space pointing system of a gyro and a star sensor combination based on a strapdown installation mode cannot directly sense the rotation angle of a two-dimensional turntable, resulting in that the control stability of the two-dimensional turntable is easily affected by the error of the rotation angle of the two-dimensional turntable, and that a maximum entropy filter based on a Cauchy kernel is used in the entire filtering process, which increases unnecessary calculation burden and leads to a decrease in real-time performance.

[0007] In order to achieve the above purpose, the technical solution provided by the present invention is:

[0008] A high-stability space pointing system combining a gyro and a star sensor in a directly mounted manner, which is special in that it includes a two-dimensional turntable, a payload, a gyro and a star sensor;

[0009] The two-dimensional turntable includes a turntable base, an azimuth axis connected to the turntable base for vertical rotation, a turntable frame connected to the upper end of the azimuth axis, and a pitch axis connected to the inside of the turntable frame for horizontal rotation;

[0010] The load is fixedly mounted on the pitch axis for performing spatial pointing movement;

[0011] The gyro is mounted on the payload, and the star sensor is mounted on the turntable base, and is used to compensate for the drift of the gyro through the high-precision attitude and direction information obtained by the star sensor;

[0012] At the same time, the present invention also provides a high-stability space pointing method for a gyro and star sensor combination in a direct installation manner, which is special in that it includes the following steps:

[0013] Step 1, constructing the above-mentioned high-stability space pointing system of the combination of gyro and star sensor in the direct installation mode;

[0014] Step 2, calculating the gyro attitude conversion matrix according to the gyro output, and then obtaining the platform attitude error angle; using the platform attitude error angle and the gyro device error as state quantities to perform equation combination to obtain a state model;

[0015] Step 3, taking the attitude conversion matrix of the gyro, the attitude conversion matrix of the turntable base obtained by the star sensor measurement, the rotation angle of the azimuth axis and the rotation angle of the pitch axis as the quantity measurement; and then establishing the measurement model according to the relationship between the quantity measurement and the platform attitude error angle;

[0016] Step 4, initializing the filter, inputting the state quantity and quantity measurement of the high-stability space pointing system combined with the gyro and the star sensor into the filter, and the filter uses Kalman filtering based on the state model to perform time update on the high-stability space pointing system combined with the gyro and the star sensor to obtain prior information;

[0017] Step 5, according to the prior information, the filter uses an event-driven filtering mechanism based on the measurement model to measure and update the high-stability space pointing system of the gyro and star sensor combination, specifically: determine whether the measurement contains non-Gaussian noise, if not, it means that the measurement is normal, use Kalman filtering to update the measurement, and calculate the state estimation value and the state estimation error covariance matrix; if so, determine whether the prior information obtained in step 4 is accurate, if accurate, directly use the prior information as the state estimation value and the state estimation error covariance matrix, otherwise, use the maximum entropy filter based on the Cauchy kernel to measure and update, and calculate the state estimation value and the state estimation error covariance matrix;

[0018] Step 6, correct the gyro attitude according to the state estimation value obtained in step 5 to obtain the corrected gyro attitude; then calculate the two-dimensional turntable control value according to the corrected gyro attitude, and then update the rotation angle of the azimuth axis and the rotation angle of the pitch axis in real time to achieve high-stability spatial pointing of the two-dimensional turntable.

[0019] Further, in step 2, the device error of the gyroscope includes a zero bias error of the gyroscope and an installation error of the gyroscope;

[0020] The state model is: k =F k / k-1 X k-1 +Γ k / k-1 Wk-1 ;

[0021] Among them, X k is the system state vector in discrete form at time k, F k / k-1 is the state transfer matrix, X k-1 is the system state vector in discrete form at time k-1, Γ k / k-1 is the noise driving matrix, is the platform attitude error angle vector at time k-1, is the zero bias error vector of the gyro at time k-1, is the installation error vector of the gyro at time k-1, is the gyroscope's attitude transformation matrix, 0 3×3 is a 3×3 dimensional zero matrix, I 3×3 is a 3×3 dimensional identity matrix, W k-1 is the discretized system state noise.

[0022] Furthermore, in step 3, the measurement model is: Z k =H k X k +V k ;

[0023] Among them, Z k is the quantity measured at time k, H k is the measurement matrix at time k, V k is the measurement noise at time k.

[0024] Furthermore, step 4 is specifically as follows:

[0025] Step b1, initializing the filter according to the following formula;

[0026]

[0027] Among them, X0 is the state vector at the initial moment, is the initial state estimation of the filter, P0 is the error covariance matrix of the initial state estimation of the filter;

[0028] Step b2, updating the time;

[0029] According to the state estimation value and state estimation error covariance matrix at time k-1, the one-step state prediction value and one-step state prediction error covariance matrix at time k are calculated. The calculation formulas are:

[0030]

[0031]

[0032] in, and P k / k-1 are the one-step state prediction value and one-step state prediction error covariance matrix at time k, and P k-1 are the state estimation value and state estimation error covariance matrix at time k-1, Q k-1 is the system state noise variance matrix.

[0033] Furthermore, in step 5, the measurement update is performed using the maximum entropy filter based on the Cauchy kernel as follows:

[0034] Step a1, set iteration variable t = 1, The state estimate of the t+1 iteration is calculated by the following formula

[0035]

[0036]

[0037]

[0038]

[0039] in, is the state estimate of the first iteration, is the estimated value of the state at the tth iteration;

[0040] express The i-th element of , i=1,2…,n+m, σ is the kernel bandwidth, where e refers to and The one-step state prediction error covariance matrix P at time k is k / k-1 and the measurement noise variance matrix R k Cholesky decomposition of ;

[0041] Step a2: The estimated state value of the t+1 iteration The state estimate of the previous iteration Compare and determine whether the following conditions are met:

[0042] ε is the judgment threshold;

[0043] If satisfied, the iteration process terminates, otherwise, the iteration continues;

[0044] Step a3: Calculate the state estimation error covariance matrix P by the following formula: k :

[0045]

[0046] Where I is the identity matrix.

[0047] Furthermore, in step 5, the measurement update using Kalman filtering is specifically as follows:

[0048]

[0049]

[0050] P k =(IK k H k ) k / k-1

[0051] Among them, K k is the filter gain, is the state estimate, P k is the state estimation error covariance matrix.

[0052] Compared with the prior art, the present invention has the following beneficial effects:

[0053] 1. The present invention provides a high-stability space pointing system that combines a gyro and a star sensor in a directly installed manner. The gyro is directly installed on the load of the pitch axis of a two-dimensional turntable, and the star sensor is installed on the turntable base of the two-dimensional turntable. The rotation angle of the two-dimensional turntable can be directly sensed, and the influence of the rotation angle error of the two-dimensional turntable on the control stability accuracy of the two-dimensional turntable is effectively avoided.

[0054] 2. The present invention provides a high-stability space pointing method of a gyro and star sensor combination in a direct installation mode, in which the gyro is directly installed on the load of the pitch axis of a two-dimensional turntable, and the star sensor is installed on the turntable base of the two-dimensional turntable. A state model and a measurement model are constructed at the same time, and an event-driven filtering mechanism is adopted to perform measurement updates by using Kalman filtering or maximum entropy filtering based on Cauchy kernel in different situations. The method solves the problems of poor long-term attitude accuracy, low operating frequency, limitation by time and environmental conditions, low control stability accuracy and poor robustness of the system to non-Gaussian noise caused by a single pointing mode and a traditional combination mode, effectively improves the accuracy of the stable pointing of the two-dimensional turntable, can effectively handle the non-Gaussian noise appearing in the measurement, and meets the requirements of spacecraft for the robustness and stability of the space pointing system. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1It is a structural schematic diagram of an embodiment of a high-stability space pointing system of a gyro and star sensor combination in a direct installation mode of the present invention;

[0056] Figure 2 It is a schematic diagram of the principle of an embodiment of a high-stability space pointing method of a gyro and star sensor combination in a direct installation mode of the present invention;

[0057] Figure 3 The azimuth pointing error curves of the turntable obtained by using Kalman Filter, MCF, MCFCK and ED-MCFCK filtering respectively under non-Gaussian noise (α stable noise);

[0058] Figure 4 The turntable pitch angle pointing error curves obtained by using Kalman Filter, MCF, MCFCK and ED-MCFCK filtering respectively under non-Gaussian noise (α stable noise);

[0059] Figure 5 This is a comparison chart of the computational efficiency obtained by using Kalman Filter, MCF, MCFCK and ED-MCFCK filtering respectively under non-Gaussian noise (α-stable noise).

[0060] The specific reference numerals are as follows:

[0061] 1-Turntable base; 2-azimuth axis; 3-turntable frame; 4-pitch axis; 5-load; 6-gyroscope; 7-star sensor. DETAILED DESCRIPTION

[0062] In order to make the advantages and features of the present invention more clear, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0063] like Figure 1 As shown, a high-stability space pointing system of a gyro and star sensor combination in a direct installation mode includes a two-dimensional turntable, a load 5, a gyro 6 and a star sensor 7. The two-dimensional turntable includes a turntable base 1, an azimuth axis 2 connected to the turntable base 1 for vertical rotation, a turntable frame 3 connected to the upper end of the azimuth axis 2, and a pitch axis 4 connected to the inside of the turntable frame 3 for horizontal rotation. The load 5 is fixedly mounted on the pitch axis 4 for performing space pointing movement. In this embodiment, the load 5 is a camera. The gyro 6 is mounted on the camera, and the star sensor 7 is mounted on the turntable base 1. The high-precision attitude and direction information obtained by the star sensor 7 compensates the drift of the gyro 6 to obtain high-precision pointing information. In order to directly sense the rotation angle of the two-dimensional turntable, the present invention innovatively adopts a direct installation method, that is, the gyro 6 is directly mounted on the camera, which effectively avoids the influence of the rotation angle error of the two-dimensional turntable on the control stability accuracy of the two-dimensional turntable.

[0064] Based on the above-mentioned high-stability space pointing system of the combination of gyro and star sensor in direct installation mode, the present invention provides a high-stability space pointing method of the combination of gyro and star sensor in direct installation mode, which specifically includes the following steps:

[0065] Step 1: Build a high-stability space pointing system combining a gyro and a star sensor using the above direct installation method.

[0066] Step 2: Establish the state model of the high-stability space pointing system composed of gyroscope and star sensor.

[0067] Select the inertial coordinate system I as the navigation coordinate system, then the angular position relationship between the inertial coordinate system I and the gyro coordinate system P can be expressed by the attitude transformation matrix. The differential equation expression of the attitude transformation matrix is ​​as follows:

[0068]

[0069] in, is the attitude conversion matrix of gyroscope 6, for The differential matrix of is the output of gyro 6, for The antisymmetric matrix of .

[0070] Considering the error, there is an inertial coordinate system I′, then the corresponding attitude transformation matrix of gyro 6 is Since there is a platform attitude error angle between the inertial coordinate system I′ and the inertial coordinate system I, there is a relationship:

[0071]

[0072] in, is the transformation matrix from inertial coordinate system I to inertial coordinate system I′, I is the unit matrix, φ I is the platform attitude error angle, (φ I ×) is φ I The antisymmetric matrix of .

[0073] Platform attitude error angle φ I The differential equation is:

[0074]

[0075] in, is the platform attitude error angle φ I The differential value of P is the zero bias error of gyroscope 6.

[0076] It can be seen that the platform attitude error angle φ affected by gyro 6 I and zero bias error ε PThe attitude update of gyro 6 diverges over time. Therefore, we can use the attitude transformation matrix output by star sensor 7 Perform filter estimation and correction.

[0077] The state quantity X of the high-stability space pointing system composed of gyroscope and star sensor is defined as:

[0078]

[0079] Among them, η P is the installation error of gyroscope 6.

[0080] According to equations (3) and (4), the state model is established as:

[0081]

[0082] Among them, w P is the system state noise, 0 3×3 is a 3×3 dimensional zero matrix, 0 3×1 is a 3×1 dimensional zero matrix.

[0083] Discretizing equation (5), we can get the following discretized state model:

[0084]

[0085] Among them, X k is the system state vector in discrete form at time k, is the platform attitude error angle vector at time k, is the zero bias error vector of gyro 6 at time k, is the installation error vector of gyro 6 at time k, is the platform attitude error angle vector at time k-1, is the zero bias error vector of gyro 6 at time k-1, is the installation error vector of gyro 6 at time k-1, is the state transfer matrix, is the system state vector in discrete form at time k-1, is the noise driving matrix, I 3×3 is a 3×3 dimensional identity matrix, W k-1 is the discretized system state noise.

[0086] make Then we have:

[0087] X k =F k / k-1 X k-1 +Γ k / k-1 W k-1 (7)

[0088] Step 3: Establish a measurement model of a high-stability space pointing system combining a gyroscope and a star sensor.

[0089] In the direct installation mode of the present invention, there is an installation deflection angle between the gyro 6 and the star sensor 7. Therefore, the error matrix M constructed according to the installation deflection angle between the gyro 6 and the star sensor 7 is: Zb for:

[0090]

[0091] in, is the updated attitude transformation matrix of gyroscope 6, P i is the gyro coordinate system obtained in each calculation, i=1,2…; is the attitude conversion matrix output by the star sensor 7; is the conversion matrix from the star sensor 7 to the turntable base 1; is the transformation matrix from the azimuth axis 2 to the turntable base 1, which is based on the rotation angle θ of the azimuth axis 2 α calculate; is the transformation matrix from the pitch axis 4 to the azimuth axis 2, which is based on the rotation angle θ of the pitch axis 4 f calculate.

[0092] In practical applications, the installation deflection angle should be calibrated and compensated in advance. Therefore, it can be considered that the star sensor coordinate system B is consistent with the turntable base coordinate system G, and the pitch axis coordinate system E is consistent with the gyro coordinate system P. It can be obtained that:

[0093]

[0094] in, From the pitch axis coordinate system E to the calculated gyro coordinate system P i The transformation matrix, From the gyro coordinate system P to the calculated gyro coordinate system P i The transformation matrix, φ P is the gyro coordinate system P and the calculated gyro coordinate system P i The gyro attitude error angle, They are respectively P Components in the x, y and z directions.

[0095] According to the definition of antisymmetric matrix, we can get:

[0096]

[0097] Therefore, substituting formula (10) into formula (9) yields

[0098]

[0099] According to the error matrix M Zb Calculate the quantity measurement Z at time k k :

[0100]

[0101] Among them, M ij is the error matrix M Zb The value of the i-th row and j-th column, i=1,2,3; j=1,2,3.

[0102] according to The measurement model can be established as:

[0103]

[0104] Among them, V k is the measurement noise at time k,

[0105] Let the measurement matrix at time k be Then we have:

[0106] Z k =H k X k +V k (14)

[0107] Step 4: Obtain prior information.

[0108] Initialize the filter, input the state and quantity measurements of the high-stability space pointing system combined with gyroscopes and star sensors into the filter, and the filter uses Kalman filtering based on the state model to update the high-stability space pointing system combined with gyroscopes and star sensors in time to obtain prior information. The prior information includes the one-step state prediction value of the system and the one-step state prediction error covariance matrix. The specific process is as follows:

[0109] (1) Filter initialization

[0110]

[0111] X0 is the state vector at the initial moment, is the initial state estimate of the filter, P0 is the error covariance matrix of the initial state estimate of the filter, and E[·] represents the expectation.

[0112] (2) Time update

[0113] According to the state estimation value and state estimation error covariance matrix at time k-1, calculate the one-step state prediction value and one-step state prediction error covariance matrix at time k:

[0114]

[0115] in, and P k / k-1 are the one-step state prediction value and one-step state prediction error covariance matrix at time k, and P k-1 are the state estimation value and state estimation error covariance matrix at time k-1, Q k-1 is the system state noise variance matrix.

[0116] Step 5: The filter uses an event-driven filtering mechanism based on the measurement model to measure and update the high-stability space pointing system composed of the gyroscope and star sensor.

[0117] According to the Markov transform criterion, an event-driven filtering mechanism is established. First, the driving condition of the event-driven filter is related to the filter’s new information vector. The calculation formula is as follows:

[0118]

[0119] Under normal measurement conditions, the filter’s innovation vector It should obey Gaussian distribution, and its error covariance matrix P ZZ,k / k-1 The calculation formula is:

[0120]

[0121] Among them, R k is the measurement noise variance matrix.

[0122] Since the error covariance matrix P ZZ,k / k-1 is an orthogonal matrix, so we can construct the unitary matrix L k , the two satisfy the following relationship:

[0123]

[0124] in, YesP ZZ,k / k-1 The eigenvalue of i Indicates the number of eigenvalues.

[0125] So we can define Normalizing the new information vector to obtain the Markov transform

[0126]

[0127] The elements of are uncorrelated and follow a standard Gaussian distribution, so the event-driven condition for detecting non-Gaussian noise is constructed as:

[0128]

[0129] in, for The infinite norm of in for The i-th component of β and κ α Represent the minimum and maximum thresholds respectively.

[0130] τ k is the judgment condition, τ k =1 indicates that the measurement is normal and the measurement does not contain non-Gaussian noise. At this time, Kalman filtering (KF) is used to update the measurement and calculate the state estimation value and the state estimation error covariance matrix; τ k = 0 indicates that the measurement contains non-Gaussian noise. There are two cases. It means that the prior information is accurate enough and there is no need to update the quantity measurement. The one-step state prediction value and the one-step state prediction error covariance matrix obtained in step 4 can be directly used as the state estimation value and the state estimation error covariance matrix respectively. Case 2 is It indicates that the prior information is inaccurate, and the maximum entropy filter based on Cauchy kernel is used for measurement update to calculate the state estimation value and the state estimation error covariance matrix.

[0131] The process of measuring updates using Kalman filtering is as follows:

[0132]

[0133] P k =(IK k H k ) k / k-1 (25)

[0134] Among them, K k is the filter gain, is the state estimate, P k is the state estimation error covariance matrix.

[0135] The focus of the present invention is how to update the measurement when the measurement contains non-Gaussian noise and the prior information is inaccurate. The present invention designs a new measurement update method based on the maximum entropy criterion, which is as follows:

[0136] First, the following equation can be established based on the state model obtained in step 2 and the measurement model obtained in step 3:

[0137]

[0138] in, And satisfy:

[0139]

[0140] Among them, B k yes Cholesky decomposition, multiply both sides of equation (26) by We can get:

[0141] Y k =M k X k +E k (28)

[0142] in,

[0143] Therefore, the entropy cost function J can be established as:

[0144]

[0145] Where L = n + m, indicating Y k The dimensions of X are n and m. k and Z k The dimension of Indicates E k The i-th element of Represents Y k The i-th component of Indicates M k The weight of the i-th row, σ is the kernel bandwidth, or

[0146] The optimal state estimation can be obtained as follows:

[0147]

[0148] After simplification, we can get:

[0149]

[0150] in, And satisfy:

[0151]

[0152] in, Representation vector The state component of Represents vector Z k The measurement component, i = 1, 2…m, m is Z k Dimension. Expanding formula (31) and combining it with the matrix inversion lemma, we can obtain:

[0153]

[0154] Among them, the filter gain satisfy:

[0155]

[0156] in, and The one-step state prediction error covariance matrix P at time k is k / k-1 and the measurement noise variance matrix R k Cholesky decomposition of .

[0157] To estimate the state using equation (34), we first need to calculate the filter gain in equation (35) The calculation of the gain essentially depends on the state estimate, which involves equations (32) and (33). Therefore, the measurement update process of the maximum entropy filter based on the Cauchy kernel is as follows:

[0158] (1) Let iteration variable t = 1, The state estimate of the t+1 iteration is calculated by the following formula

[0159]

[0160] in, express The i-th element of , i=1,2…,n+m, σ is the kernel bandwidth, where e refers to

[0161] (2) The current state estimate The previous state estimate Compare and if the condition of formula (40) is met, the iteration process is terminated, otherwise the iteration continues.

[0162]

[0163] Among them, ε is the judgment threshold.

[0164] (3) Calculate the state estimation error covariance matrix according to the following formula:

[0165]

[0166] The optimal estimation of the designed state model and measurement model is performed through an event-driven filtering mechanism to obtain the optimal estimated value of the system state.

[0167] Step 6: Achieve highly stable spatial pointing of the two-dimensional turntable.

[0168] The gyro attitude is corrected according to the state estimation value obtained in step 5 to obtain a corrected high-precision gyro attitude; the two-dimensional turntable control amount is calculated according to the corrected high-precision gyro attitude, and then the rotation angle of the azimuth axis 2 and the rotation angle of the pitch axis 4 are updated in real time to achieve high-stability spatial pointing of the two-dimensional turntable. The specific steps are as follows:

[0169] According to the position of the spacecraft and the target satellite, the unit position vector u in the inertial coordinate system I is calculated. I , the calculation formula is:

[0170]

[0171] Among them, [x 本 ,y 本 ,z 本 ] and [x 目 ,y 目 ,z 目 ] are the position coordinates of the spacecraft and the target star respectively.

[0172] According to the optimal estimate of the system obtained in step 5, and the attitude conversion matrix of Gyro 6 It can be calculated that:

[0173]

[0174] Further, according to formula (9) and formula (10), we can calculate Update value of Then, the attitude conversion matrix of gyroscope 6 is updated, and the updated attitude conversion matrix of gyroscope 6 is obtained.

[0175]

[0176] According to the attitude transformation matrix updated by gyroscope 6 Calculate the target vector u in the gyro coordinate system P P , the calculation formula is:

[0177]

[0178] The miss distance in the gyro coordinate system P is calculated by the following formula. The miss distance includes the error angle of the azimuth axis 2 rotation angle: Error angle with pitch axis 4

[0179]

[0180] in, are the target vector u P Three components in the gyro coordinate system.

[0181] because For small angles, the closed-loop control can also be directly approximated as:

[0182]

[0183] The calculated miss distance is then converted into a two-dimensional turntable control amount:

[0184]

[0185] Among them, θ f is the rotation angle of the pitch axis 4.

[0186] According to the two-dimensional turntable control amount, calculate the rotation angle θ of the azimuth axis 2 at the next moment α and the rotation angle θ of the pitch axis 4 f :

[0187]

[0188] Thereby, highly stable spatial pointing of the two-dimensional turntable can be achieved.

[0189] like Figure 2 The figure is a schematic diagram of the principle of a high-stability space pointing method of a gyro and star sensor combination in a direct installation mode of the present invention. The principle is as follows: the attitude of the gyro 6 is updated to obtain the attitude conversion matrix after the gyro 6 is updated Then obtain the rotation angle θ of the current azimuth axis 2 α and the rotation angle θ of the pitch axis 4 f . At the same time, obtain the attitude conversion matrix output by star sensor 7 Combined with the current rotation angle θ of axis 2 α , the rotation angle θ of the pitch axis 4 f And the updated attitude transformation matrix of Gyro 6 Construct error matrix M Zb , and then obtain the quantity measurement; the state quantity and quantity measurement of the high-stability space pointing system composed of gyroscopes and star sensors are input into the filter, and the filter uses Kalman filtering based on the state model to update the high-stability space pointing system composed of gyroscopes and star sensors in time to obtain prior information; then according to the prior information, the filter uses an event-driven filtering mechanism based on the measurement model to measure and update the high-stability space pointing system composed of gyroscopes and star sensors, so as to iteratively update the attitude of gyroscope 6 and realize feedback correction of gyroscope attitude. Finally, the two-dimensional turntable control quantity is calculated using the corrected high-precision gyroscope attitude, and then the rotation angle θ of the azimuth axis 2 is calculated. α and the rotation angle θ of the pitch axis 4f Real-time updates are performed to achieve highly stable spatial pointing of the two-dimensional turntable.

[0190] The effects of the present invention are described below through simulation verification.

[0191] The event-driven filtering mechanism (ED-MCFCK) of the present invention is comprehensively evaluated by computer simulation. In the simulation verification, the known data are the attitude reference of the spacecraft platform and the tracking vector between it and the target star. The zero bias error of gyro 6 is 0.1° / h, and the random walk of gyro 6 is The scale factor error of gyro 6 is 100PPM, the attitude angle error of gyro 6 is 5″, and the angle measurement error of star sensor 7 is 5″. The sampling frequency of gyro 6 is 20Hz, and the measurement frequency of star sensor 7 is 1Hz. The initial attitude of the spacecraft is (142.162°, -89.78°, 63.16°), and the simulation time is 3600s.

[0192] In the two time periods (1000s, 1500s) and (2500s, 3000s), α-stable noise is injected into the measurement. Among them, α-stable noise is a very important type of non-Gaussian random distribution, which is used to simulate the non-Gaussian noise encountered in the actual environment. The characteristic function of α-stable noise is given by the following formula

[0193]

[0194] in:

[0195]

[0196] The characteristic exponent β, symmetry parameter ζ, scale parameter α and location parameter δ in the α-stable noise are set to (1.8, 0, 1.2, 0) respectively, t represents the time, j is the imaginary unit, and j 2 =-1.

[0197] Figure 3 and Figure 4In the case of non-Gaussian noise (α-stable noise), the Kalman filter algorithm (KalmanFilter), the maximum entropy filter algorithm based on Gaussian kernel (MCF), the maximum entropy filter algorithm based on Cauchy kernel (MCFCK) and the event-driven filtering mechanism (ED-MCFCK) of the present invention are used to obtain the turntable azimuth pointing error and turntable pitch angle pointing error curves. From the analysis of the figure, it can be concluded that the Kalman Filter cannot effectively handle the measurement abnormality in the measurement failure stage (containing non-Gaussian noise), which directly affects the accuracy of the measurement update process in the filtering process, and then causes a significant decrease in pointing accuracy, and the turntable azimuth and pitch angle pointing errors fluctuate violently; due to the limitation of the Gaussian kernel function, the MCF is also unable to handle the measurement abnormality (containing non-Gaussian noise) with thicker tail noise, so the pointing error shows a divergent trend; on the contrary, the MCFCK and the ED-MCFCK of the present invention can effectively deal with this abnormality by virtue of the robustness of the Cauchy kernel function to abnormal measurement non-Gaussian noise, and maintain the stability of the turntable azimuth and turntable pitch angle pointing errors.

[0198] Figure 5 The calculation efficiency of Kalman Filter, MCF, MCFCK and ED-MCFCCK of the present invention is also compared. First, it can be seen that the calculation efficiency of Kalman Filter is the best under the condition of α stable noise measurement failure, which is also the main factor that KalmanFilter is widely used in engineering practice. Secondly, the calculation efficiency of MCF and MCFCK is obviously weaker than that of Kalman Filter. Compared with Kalman Filter, the filtering time of MCF increases by 149.29%, and the filtering time of MCFCK increases by 100.71%. Compared with Kalman Filter, the calculation efficiency of both is significantly reduced. The reason is that both will perform multiple iterative calculations in each filtering process to improve the robustness of the algorithm under abnormal measurement conditions. However, this processing method increases the amount of calculation under normal conditions, generates unnecessary calculation burden, and leads to poor real-time performance, which is not suitable for practical application. The ED-MCFCK proposed by the present invention adopts an event-driven mechanism when processing non-Gaussian noise, thereby effectively detecting measurement abnormalities (non-Gaussian noise) and processing them, so that the algorithm significantly improves the calculation efficiency compared with MCF and MCFCK. In addition, the computational efficiency of the ED-MCFCK of the present invention is 103.21% compared to the Kalman Filter, and the time taken by the two algorithms is relatively close. Therefore, the ED-MCFCK algorithm can show strong robustness and real-time performance when facing non-Gaussian noise measurement failure situations in actual engineering applications.

[0199] The above description is only used to illustrate the technical solution of the present invention rather than to limit it. For ordinary professional and technical personnel in the field, the specific technical solution recorded in the above embodiment can be modified, or some of the technical features therein can be replaced by equivalents, and these modifications or replacements do not make the essence of the corresponding technical solution deviate from the scope of the technical solution protected by the present invention.

Claims

1. A high-stability space pointing method for a combination of a gyro and a star sensor in a direct installation mode, characterized in that: The following steps are involved: Step 1, building a space pointing system; the space pointing system comprises a two-dimensional turntable, a load (5), a gyroscope (6) and a star sensor (7); the two-dimensional turntable comprises a turntable base (1), an azimuth axis (2) vertically connected to the turntable base (1), a turntable frame (3) connected to the upper end of the azimuth axis (2) and a pitch axis (4) horizontally connected to the inside of the turntable frame (3); the load (5) is fixedly mounted on the pitch axis (4) for performing space pointing movement; the gyroscope (6) is mounted on the load (5), and the star sensor (7) is mounted on the turntable base (1); Step 2, calculating the attitude conversion matrix of the gyroscope (6) according to the output of the gyroscope (6), and then obtaining the attitude error angle of the platform; using the attitude error angle of the platform and the device error of the gyroscope (6) as state quantities to perform equation combination to obtain a state model; Step 3, taking the attitude conversion matrix of the gyroscope (6), the attitude conversion matrix of the turntable base (1) measured by the star sensor (7), the rotation angle of the azimuth axis (2) and the rotation angle of the pitch axis (4) as quantitative measurements; and then establishing a measurement model according to the relationship between the quantitative measurements and the platform attitude error angle; Step 4, initializing the filter, inputting the state quantity and quantity measurement of the high-stability space pointing system combined with the gyro and the star sensor into the filter, and the filter uses Kalman filtering based on the state model to perform time update on the high-stability space pointing system combined with the gyro and the star sensor to obtain prior information; Step 5, according to the prior information, the filter uses an event-driven filtering mechanism based on the measurement model to measure and update the high-stability space pointing system of the gyro and star sensor combination, specifically: determine whether the measurement contains non-Gaussian noise, if not, it means that the measurement is normal, use Kalman filtering to update the measurement, and calculate the state estimation value and the state estimation error covariance matrix; if so, determine whether the prior information obtained in step 4 is accurate, if accurate, directly use the prior information as the state estimation value and the state estimation error covariance matrix, otherwise, use the maximum entropy filter based on the Cauchy kernel to measure and update, and calculate the state estimation value and the state estimation error covariance matrix; The measurement update using the maximum entropy filter based on the Cauchy kernel is specifically as follows: Step a1, set iteration variable t = 1, The state estimate of the t+1 iteration is calculated by the following formula in, is the state estimate of the first iteration, is the estimated value of the state at the tth iteration, is the one-step state prediction value at time k, Z k is the quantity measured at time k, H k is the measurement matrix at time k; express The i-th element of , i=1,2…,n+m, σ is the kernel bandwidth, where e refers to and The one-step state prediction error covariance matrix P at time k is k / k-1 and the measurement noise variance matrix R k Cholesky decomposition of ; Step a2: The estimated state value of the t+1 iteration The state estimate of the previous iteration Compare and determine whether the following conditions are met: ε is the judgment threshold; If satisfied, the iteration process terminates, otherwise, the iteration continues; Step a3: Calculate the state estimation error covariance matrix P by the following formula: k : Where I is the identity matrix, P k / k-1 is the one-step state prediction error covariance matrix at time k; The measurement update using Kalman filtering is specifically as follows: P k =(I-K k H k )P k / k-1 Among them, K k is the filter gain, is the state estimate, P k is the state estimation error covariance matrix; Step 6, correcting the gyro attitude according to the state estimation value obtained in step 5 to obtain a corrected gyro attitude; then calculating the two-dimensional turntable control amount according to the corrected gyro attitude, and then updating the rotation angle of the azimuth axis (2) and the rotation angle of the pitch axis (4) in real time, thereby realizing high-stability spatial pointing of the two-dimensional turntable.

2. The high-stability space pointing method of the gyro and star sensor combination in a direct installation mode according to claim 1, characterized in that: In step 2, the device error of the gyroscope (6) includes a zero bias error of the gyroscope (6) and an installation error of the gyroscope (6); The state model is: k =F k / k-1 X k-1 +Γ k / k-1 W k-1 ; Among them, X k is the system state vector in discrete form at time k, F k / k-1 is the state transfer matrix, X k-1 is the system state vector in discrete form at time k-1, Γ k / k-1 is the noise driving matrix, is the platform attitude error angle vector at time k-1, is the zero bias error vector of the gyro (6) at time k-1, is the installation error vector of the gyro (6) at time k-1, is the attitude transformation matrix of the gyroscope (6), 0 3×3 is a 3×3 dimensional zero matrix, I 3×3 is a 3×3 dimensional identity matrix, W k-1 is the discretized system state noise.

3. The high-stability space pointing method of the gyro and star sensor combination in a direct installation mode according to claim 2 is characterized in that: In step 3, the measurement model is: Z k =H k X k +V k ; Among them, Z k is the quantity measured at time k, H k is the measurement matrix at time k, V k is the measurement noise at time k.

4. The high-stability space pointing method of the gyro and star sensor combination in a direct installation mode according to claim 3 is characterized in that: Step 4 is as follows: Step b1, initializing the filter according to the following formula; Among them, X0 is the state vector at the initial moment, is the initial state estimation of the filter, P0 is the error covariance matrix of the initial state estimation of the filter, and E[·] represents the expectation; Step b2, updating the time; According to the state estimation value and state estimation error covariance matrix at time k-1, the one-step state prediction value and one-step state prediction error covariance matrix at time k are calculated. The calculation formulas are: in, and P k / k-1 are the one-step state prediction value and one-step state prediction error covariance matrix at time k, and P k-1 are the state estimation value and state estimation error covariance matrix at time k-1, Q k-1 is the system state noise variance matrix.

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