Method for calculating passive sensing of spatial non-cooperative target state by laser warning device

Abstract

The application discloses a kind of laser warning device passive sensing space non-cooperative target state calculation methods, first establish the relative motion state model of our satellite and enemy satellite and laser warning device observation model, then obtain observation angle information, according to the initial relative state quantity and initial relative state quantity error estimation value of our spacecraft and enemy satellite according to observation angle information, according to the relative state information between our satellite and enemy satellite is obtained according to the relative motion state model of our satellite and enemy satellite, laser warning device observation model and initial relative state estimation value and its error estimation value, again the relative state information between our satellite and enemy satellite is filtered and estimated, finally the estimation value of target satellite motion information is obtained, the position and velocity information of enemy satellite can be high-precision estimation.

Description

TECHNICAL FIELD

[0001] The application relates to the field of aerospace, and particularly relates to a laser warning device passive sensing space non-cooperative target state calculation method. BACKGROUND

[0002] In recent years, along with the development of space technology, human activities in space are more and more. In the geosynchronous orbit, an enemy satellite often carries out close-range laser observation on a satellite of our side, and then obtains various parameters and load information of the satellite of our side, which will bring great threat to us. When the enemy satellite carries out laser observation on the satellite of our side, a plurality of groups of azimuth and elevation angles of incident laser can be obtained through a detector installed on the satellite of our side. How to solve the position and velocity information of the enemy satellite by using the orbit information of the satellite of our side and the obtained laser observation angle information has very important research significance. SUMMARY

[0003] The application aims to provide a laser warning device passive sensing space non-cooperative target state calculation method, so as to solve the problem that the position and velocity information of the enemy satellite cannot be solved by using the orbit information of the satellite of our side and the obtained laser observation angle information in the prior art, and realize that the satellite of our side can obtain the line-of-sight angle information of the enemy satellite through the carried laser warning device, and the position and velocity information of the enemy satellite can be estimated with high precision through the Kalman filtering method according to the initial relative state estimation value and the observation information of the two.

[0004] To achieve the above-mentioned purpose, the application provides the following technical scheme.

[0005] The laser warning device passive sensing space non-cooperative target state calculation method comprises the following steps.

[0006] S1: a relative motion state model of the satellite of our side and the enemy satellite is established;

[0007] S2: a laser warning device observation model is established;

[0008] S3: observation angle information is obtained, and initial relative state quantities and initial relative state quantity error estimation values of the satellite of our side and the enemy satellite are obtained according to the observation angle information.

[0009] S4: relative state information between the satellite of our side and the enemy satellite is obtained according to the relative motion state model of the satellite of our side and the enemy satellite obtained in S1, the laser warning device observation model obtained in S2 and the initial relative state estimation value and the error estimation value thereof obtained in S3, and the relative state information between the satellite of our side and the enemy satellite is estimated through filtering, so that an estimation value of the target satellite motion information is obtained.

[0010] Preferably, the model of relative motion state of the satellite of our side and the satellite of the enemy in S1 is specifically as follows: first, a satellite orbit coordinate system is established, a linear relative motion equation of the satellite of our side and the satellite of the enemy is obtained, and then a model of relative motion state of the satellite of our side and the satellite of the enemy is established according to the linear relative motion equation.

[0011] Preferably, the linear relative motion equation of the satellite of our side and the satellite of the enemy is as follows:

[0012]

[0013] wherein ω represents an average orbit angular velocity of the satellite of our side, x is a relative position of the satellite of our side and the satellite of the enemy in a direction of an X coordinate axis of a satellite orbit coordinate system, z is a relative position of the satellite of our side and the satellite of the enemy in a direction of a Z coordinate axis of the satellite orbit coordinate system, is a relative velocity of the satellite of our side and the satellite of the enemy in the direction of the X coordinate axis of the satellite orbit coordinate system, is a relative velocity of the satellite of our side and the satellite of the enemy in a direction of a Y coordinate axis of the satellite orbit coordinate system, is a relative acceleration of the satellite of our side and the satellite of the enemy in the direction of the X coordinate axis of the satellite orbit coordinate system, is a relative acceleration of the satellite of our side and the satellite of the enemy in the direction of the X coordinate axis of the satellite orbit coordinate system, is a relative acceleration of the satellite of our side and the satellite of the enemy in the direction of the X coordinate axis of the satellite orbit coordinate system, f x ,f y ,f z respectively represent external forces in each axial direction.

[0014] Preferably, the model of relative motion state of the satellite of our side and the satellite of the enemy is as follows:

[0015]

[0016] wherein X0 is a relative motion state of the satellite of our side and the satellite of the enemy at t0, U is a thrust acceleration, Φ(t, t0) is a state transition matrix from t0 to t, u is an integral step, Φ v (t, u) is a solution matrix of the thrust acceleration U to the velocity v.

[0017] Preferably, the laser warning device observation model in S2 is specifically as follows: first, a conversion relationship between a spacecraft orbit coordinate system and a laser warning device observation coordinate system is obtained, a relative position of the satellite of our side and the satellite of the enemy in the laser warning device observation coordinate system is obtained according to the conversion relationship between the spacecraft orbit coordinate system and the laser warning device observation coordinate system, and then the laser warning device observation model is obtained.

[0018] Preferably, the laser warning device observation model is as follows:

[0019]

[0020] ε is the pitch angle of the incident laser, θ is the azimuth angle of the incident laser, x m is the relative position of the satellite of the enemy in the X-axis of the laser warning device observation coordinate system, y m is the relative position of the satellite of the enemy in the Y-axis of the laser warning device observation coordinate system, z m is the relative position of the satellite of the enemy in the Z-axis of the laser warning device observation coordinate system.

[0021] Preferably, the S3 observation angle information is obtained by the laser warning device, and the number of groups of the obtained information is greater than or equal to 3 groups.

[0022] Preferably, the S4 estimated value of the target satellite motion information is obtained by the following steps: first, a discrete system is established by the relative motion state model of the satellite of the enemy and the laser warning device observation model; second, an initial error covariance matrix is obtained according to the initial relative state quantity error estimation value obtained by S3; third, a sampling point is generated according to the initial relative state quantity error estimation value and the initial error covariance matrix; fourth, the current state quantity and the error covariance matrix of the current state quantity are updated according to the discrete system to obtain an uncorrected state quantity and an error covariance matrix; fifth, the sampling point is predicted according to the updated state quantity and the error covariance matrix of the state quantity; sixth, the updated observation quantity mean and the error covariance matrix of the observation quantity and the error covariance matrix of the state quantity and the observation quantity are obtained by solving the observation model of the discrete system; seventh, the Kalman gain is obtained by solving the two covariance matrices; and finally, the state quantity and the error covariance matrix of the next moment are solved to obtain the estimated value of the target satellite motion information.

[0023] Preferably, the discrete system is as follows:

[0024]

[0025] wherein X k+1 is the relative motion state value, Z k+1 is the laser warning device observation quantity, f(X k ) is the relative motion state model, h(X k+1 ) is the observation model, W k is the process noise, and V k+1 is the observation noise.

[0026] Preferably, the state quantity and the error covariance matrix of the next moment are as follows:

[0027]

[0028]

[0029] wherein, is a next time state quantity, is a current time state quantity, Z k+1 is a next time observation quantity, is a current time observation quantity, K k+1 is a Kalman gain, is an error covariance matrix of the next time state quantity, is an error covariance matrix of the current time state quantity, is an error covariance matrix of the current time observation quantity.

[0030] Compared with the prior art, the present application has the following beneficial effects: the present application provides a laser warning device passive sensing space non-cooperative target state calculation method, first, a relative motion state model of our satellite and enemy satellite and a laser warning device observation model are established, then observation angle information is obtained, according to the observation angle information, initial relative state quantity and initial relative state quantity error estimation value of our spacecraft and enemy satellite are obtained, according to the relative motion state model of our satellite and enemy satellite, the laser warning device observation model and the initial relative state estimation value and its error estimation value, relative state information between our satellite and enemy satellite is obtained, then the relative state information between our satellite and enemy satellite is filtered and estimated, finally, the estimation value of target satellite motion information is obtained, which can high-precision estimate the position and velocity information of enemy satellite. BRIEF DESCRIPTION OF DRAWINGS

[0031] Figure 1 is a flowchart of the present application

[0032] Figure 2 is an observation vector diagram of the present application;

[0033] Figure 3 is a tracking trajectory diagram of the present application;

[0034] Figure 4 is a pitch angle tracking effect diagram of the present application;

[0035] Figure 5 is an azimuth angle tracking effect diagram of the present application;

[0036] Figure 6 is a relative error change condition of the real position and estimated position in the x-axis direction of the satellite orbit coordinate system of the present application;

[0037] Figure 7 is a relative error change condition of the real position and estimated position in the y-axis direction of the satellite orbit coordinate system of the present application;

[0038] Figure 8 is a relative error change condition of the real position and estimated position in the z-axis direction of the satellite orbit coordinate system of the present application. DETAILED DESCRIPTION

[0039] The application will be described in further detail below with specific embodiments, which are explanatory rather than limiting of the application.

[0040] The working condition targeted by the present scheme is described as follows: an enemy reconnaissance satellite approaches our satellite and performs a companion flight, and through the carried laser radar, the enemy satellite performs multiple irradiations on our satellite within a short time. Due to the working characteristics of the laser radar, the enemy satellite needs to keep the attitude stable and not perform an orbit maneuver during the irradiation period. During this period, our satellite can obtain the line-of-sight angle information of the enemy satellite through the carried laser warning device. According to the initial relative state estimation value and the observation information, the position and velocity information of the enemy satellite can be estimated with high precision through the Kalman filtering method. The specific implementation steps are as follows:

[0041] Step 1: Establish a spacecraft relative motion state model. For the spacecraft orbit warning task, the enemy satellite is generally a reconnaissance satellite, and the effective working load is a laser radar. It can be considered that the relative distance between our spacecraft and the enemy satellite is relatively close, especially the orbit altitude difference is not large.

[0042] The orbit of our satellite is set as a circular orbit or a near-circular orbit. Our satellite is taken as the main spacecraft, and the LVLH of our satellite is established. The coordinate system origin is the mass center O of the satellite, the Ox axis is along the radial direction of the spacecraft orbit, the Oy axis is in the orbit plane and along the velocity direction of the spacecraft, and the Oz axis is parallel to the normal of the orbit plane and forms a right-handed orthogonal coordinate system with the Ox and Oy axes.

[0043] The enemy satellite observes our spacecraft in the form of companion flight. The influence of external perturbation is ignored, and the linear relative motion equation of our satellite and the enemy satellite is established as follows:

[0044]

[0045] wherein ω represents the average orbit angular velocity of our satellite, and [x, y, z] represents the relative position, relative velocity and relative acceleration of our satellite and the enemy satellite along the coordinate axes of the spacecraft orbit coordinate system, respectively. f T 、 f x ,f y ,f z represent the external forces in each axis direction, respectively. The relative state quantity If the relative state X0 at t0 is known and the thrust acceleration U at any time is known, the relative state X tThe relative motion state model between our satellite and the enemy satellite is established as follows by calculation:

[0046]

[0047] wherein Φ(t, t0) is a state transition matrix from t0 to t, and is specifically expressed as follows:

[0048]

[0049] wherein n is the average orbit angular velocity of our spacecraft, and τ = ω(t-t0).

[0050] When the target orbit is a general elliptical orbit, the relative orbit motion between the two spacecrafts is described by the TH equation, and its homogeneous solution is a state transition matrix:

[0051] Φ(t, t0) = Φ θ (f)Φ θ -1 (f) (4)

[0052] wherein:

[0053]

[0054]

[0055] wherein f and f0 are the true anomaly angles at t and t0, k = 1+e cosf, c k = k cosf, s k = k sinf, h is the modulus of the orbit angular momentum, c k ' and s k ' are the first-order derivatives with respect to f.

[0056] Step 2: Establish the observation model of the laser warning device. According to the geometric relationship between the relative position between the enemy satellite and our satellite and the laser incidence angle, the observation model of the laser warning device is established.

[0057] First, according to the conversion relationship between the spacecraft orbit coordinate system and the laser warning device observation coordinate system, the relative position in the warning device observation coordinate system is obtained:

[0058]

[0059] wherein, is the coordinate conversion matrix from the spacecraft orbit coordinate system to the laser warning device observation coordinate system. The observation quantity of the laser warning device observation model can be obtained as follows:

[0060]

[0061] where ε and θ are the pitch angle and azimuth angle of the incident laser respectively. The angle information is shown as Figure 1 Step 3: Obtain N (N≥3) sets of observation angle information by using the laser warning device, to estimate the initial relative state quantity and the corresponding error. According to the measurement of the line-of-sight angle, the unit line-of-sight vector i los :

[0062]

[0063] where r d is the installation position of the laser warning device. When the observation times is 3, for the first three observation angle information satisfies the following equation:

[0064]

[0065]

[0066]

[0067] where k represents the scale factor of the line-of-sight vector, Φ rr is the position relative position state transition matrix, Φ rv is the velocity relative position state transition matrix, by combining the three observation equations, selecting the unknown quantity X=[k1,k2,k3,r(1),v(1)] T , the matrix form solution can be obtained:

[0068] AX=B (11)

[0069] where:

[0070]

[0071]

[0072] Simulation proves that the A matrix is generally a non-singular matrix, so it can uniquely determine the initial relative state value:

[0073]

[0074] After N times of estimation operation, the initial state estimation accuracy can be represented by the error mean and its covariance:

[0075]

[0076]

[0077] Step 4: Continue to use the observation angle information obtained by the laser warning device, the relative motion state model and the observation model obtained by step 1 and step 2 to establish a discrete system, and use the initial relative motion state estimation value and the initial state error covariance matrix obtained by step 3 to complete the estimation of the state quantity by using the UKF filtering tracking algorithm as shown below.

[0078] (1) Filter initialization

[0079] A discrete system is established by using the relative motion state model and the observation model:

[0080]

[0081] where X k+1 is the relative motion state value, Z k+1 is the laser warning device observation quantity, f(X k ) is the relative motion state model, h(X k+1 ) is the observation model, W k and V k+1 are the process noise and the observation noise respectively, and in the scheme, they are set as zero-mean Gaussian white noise. Given the initial relative motion state estimation value and the initial error covariance matrix

[0082] (2) Generate sample points

[0083] Generate Sigma sample points according to the state estimation value and the error covariance matrix estimation value at time k. For an n-dimensional state vector, the number of sample points is 2n+1. Take 6 points on both sides, a total of 13 points

[0084] χ i,k are as follows:

[0085]

[0086] Use and to represent the first-order and second-order statistical characteristic coefficients of the sample points respectively. The Sigma weight coefficient is selected as follows:

[0087]

[0088] where λ=(α 2 -1)n, α is a proportional scaling factor, and the value is 0≤α≤1, and β reflects the state history high-order characteristics, and the optimal value for Gaussian distribution is β=2.

[0089] (3) Realize the state quantity and the error covariance matrix of the state quantity​ update

[0090]

[0091]

[0092]

[0093] where Q k is the process noise covariance matrix.

[0094] (4) Sample point prediction

[0095] The obtained and are regenerated by the method in (2), denoted as χ i,k+1|k .

[0096] (5) Prediction of the observation mean the error covariance matrix of the observation and the error covariance matrix of the state and the observation

[0097] z k+1|k = h(χ k+1|k ) + V k+1|k (23)

[0098]

[0099]

[0100]

[0101] where R k is the process noise covariance matrix.

[0102] (6) Kalman gain K k+1 update

[0103]

[0104] (7) State and state error covariance matrix update

[0105]

[0106]

[0107] Embodiment:

[0108] ​The simulation case is that the local satellite reconnaissance system GSSAP approaches the satellite in GEO orbit of our side for reconnaissance, wherein the mass of each satellite of GASSP is about 650 to 700 kg, the satellite orbits in the vicinity of the geostationary orbit, the orbit height is 36780.9 km, the orbit inclination is 0.5°, and the satellite drifts above and below the geostationary belt, moves 2.36° per day, and has a drift period of about 154 days, and has the ability of continuous monitoring and approaching reconnaissance of all satellites in GEO orbit. According to the approaching reconnaissance of the practical number satellite in GEO orbit by GASSP, the relative initial state of the satellite is set, and the state estimation and precision analysis of the tracking satellite are realized through the initial state estimation and navigation filtering algorithm.

[0109] The enemy satellite and our satellite are set to be in the geostationary orbit, the enemy satellite approaches or moves away from our satellite at a constant speed by using the common ellipse approach, and the relative initial state satisfies: X = [x0, 0, z0, -1.5nz0, 0, 0] T The noise is set to be Gaussian zero-mean white noise, and the simulation conditions are set as follows:

[0110] Table 1 Simulation parameter setting

[0111]

[0112] The simulation result is analyzed as follows:

[0113] The trajectory tracking effect diagram is shown in Figure 2 .

[0114] Figure 2 The initial position is the initial relative position of the satellite of our side and the satellite of the enemy side, the true trajectory is the motion trajectory calculated by the linear relative motion equation, and the filtering trajectory is the motion trajectory calculated by the algorithm of the scheme.

[0115] The pitch angle and azimuth angle tracking effect diagram is shown in Figure 4 and Figure 5 . The true value of the observation angle is calculated by substituting the true motion state quantity into the observation model equation, and the estimated value is obtained by substituting the estimated relative state quantity into the observation model equation. The error mean change diagram is shown in Figure 6 , Figure 7 and Figure 8 . The relative error change of the true position and the estimated position along the spacecraft orbit coordinate system x-axis, y-axis and z-axis is shown.

[0116] The final targeting result shows that in the filtering process, the angle prediction value can track the real observation value, and the prediction value fluctuates above and below the real value due to the measurement noise. However, due to the limitation of the orbit height and the observation time, the observation angle changes little in the running time, and is greatly affected by the noise, which has a great influence on the navigation accuracy. In addition, when the process noise is too large and the filtering parameter setting is unreasonable, the final error of navigation will diverge. By reasonably setting the parameters, the final position error in the three directions can be close to zero under the condition of a certain number of observations, and a high-precision navigation algorithm of the satellite in the GEO orbit can be realized.

[0117] Although the embodiments of the present application are described above in combination with the drawings, the present application is not limited to the above-mentioned specific embodiments and application fields, and the above-mentioned specific embodiments are only illustrative and guiding, but not limiting. Those skilled in the art can make many forms under the guidance of the specification without departing from the scope protected by the claims of the present application, and these all belong to the protection of the present application.

Claims

1. A method for calculating the state of a passive spatial non-cooperative target by a laser warning device, characterized in that, The method comprises the following steps: S1: establishing a relative motion state model of the satellite of the side and the satellite of the enemy; S2: establishing an observation model of the laser warning device; S3: obtaining angle information, and obtaining initial relative state quantity and initial relative state quantity error estimation value of the spacecraft of the side and the satellite of the enemy according to the angle information; S4: obtaining relative state information between the satellite of the side and the satellite of the enemy according to the relative motion state model of the satellite of the side and the satellite of the enemy obtained in S1, the observation model of the laser warning device obtained in S2 and the initial relative state estimation value and the initial relative state quantity error estimation value obtained in S3, and performing filtering estimation on the relative state information between the satellite of the side and the satellite of the enemy to obtain an estimation value of target satellite motion information. Wherein the S3 observation angle information is acquired by a laser alarm, the number of groups acquired is greater than or equal to three groups, and the laser alarm is used to acquire N The observation angle information of the group is estimated, the initial relative state quantity and the corresponding error are estimated, and the unit line-of-sight vector is calculated according to the measurement of the line-of-sight angle : wherein, is the installation position of the laser warning device, is the coordinate transformation matrix from the spacecraft orbital coordinate system to the laser warning device observation coordinate system, when the observation times are 3, for the first three observation angle information satisfy the following equation: wherein denotes a scale factor for the line-of-sight vector, is a position relative position state transition matrix, is a velocity relative position state transition matrix.

2. The method of claim 1, wherein the laser warning passive sensing space non-cooperative target state calculation method is characterized in that, The relative motion state model of the satellite of the side and the satellite of the enemy is as follows:

3. The method of claim 2, wherein the laser warning passive sensing space non-cooperative target state calculation method is characterized by, The observation model of the laser warning device is as follows: （1） wherein, represents the average orbital angular velocity of our satellite, is the relative position of our satellite and the enemy satellite along the X-axis direction of the satellite orbit coordinate system, z is the relative position of our satellite and the enemy satellite along the Z-axis direction of the satellite orbit coordinate system, is the relative velocity of our satellite and the enemy satellite along the X-axis direction of the satellite orbit coordinate system, is the relative velocity of our satellite and the enemy satellite along the Y-axis direction of the satellite orbit coordinate system, is the relative acceleration of our satellite and the enemy satellite along the X-axis direction of the satellite orbit coordinate system, is the relative acceleration of our satellite and the enemy satellite along the X-axis direction of the satellite orbit coordinate system, is the relative acceleration of our satellite and the enemy satellite along the X-axis direction of the satellite orbit coordinate system, respectively represent the external forces in each axis direction.

4. The method of claim 2, wherein, S4: obtaining an estimation value of target satellite motion information, specifically, first, a discrete system is established through the relative motion state model of the satellite of the side and the satellite of the enemy and the observation model of the laser warning device, an initial error covariance matrix is obtained according to the initial relative state quantity error estimation value obtained in S3, sampling points are generated according to the initial relative state quantity error estimation value and the initial error covariance matrix, the current state quantity and the error covariance matrix of the current state quantity are updated according to the discrete system to obtain an uncorrected state quantity and an error covariance matrix, the sampling points are predicted according to the updated state quantity and the error covariance matrix of the state quantity, the updated observation quantity mean and the error covariance matrix of the observation quantity and the error covariance matrix of the state quantity and the observation quantity are obtained by solving the observation model of the discrete system according to the updated sampling points, the Kalman gain is solved according to the two covariance matrices, and finally the state quantity and the error covariance matrix at the next moment are solved to obtain the estimation value of the target satellite motion information. （2） wherein X 0 is the state of relative motion between our satellite and the enemy satellite at time is the thrust acceleration, is t to t the state transition matrix from time 0 to time is the integration step size, is the solution matrix of the thrust acceleration U to the velocity v.

5. The method of claim 1, wherein, The discrete system is as follows:

6. The method of claim 5, wherein the laser warning passive sensing space non-cooperative target state calculation method is characterized by, The state quantity and the error covariance matrix at the next moment are as follows: （3） is the elevation angle of the incident laser, is the azimuth angle of the incident laser, is the relative position of the satellite of our side and the satellite of the enemy side in the X axis of the laser warning device observation coordinate system, is the relative position of the satellite of our side and the satellite of the enemy side in the Y axis of the laser warning device observation coordinate system, is the relative position of the satellite of our side and the satellite of the enemy side in the Z axis of the laser warning device observation coordinate system.

7. The method of claim 1, wherein the laser warning passive sensing space non-cooperative target state calculation method is characterized by, ​ 8. The method of claim 7, wherein the laser warning passive sensing space non-cooperative target state calculation method is characterized by, ​ （4） wherein is a relative motion state value, is a laser warning sensor observation, is a relative motion state model, is an observation model, is a process noise, is an observation noise.

9. The method of claim 7, wherein the laser warning passive sensing space non-cooperative target state calculation method is characterized by, ​ （5） （6） wherein is the state quantity of the next time instant, is the state quantity of the current time instant, is the observation quantity of the next time instant, is the observation quantity of the current time instant, is the Kalman gain, is the error covariance matrix of the state quantity of the next time instant, is the error covariance matrix of the state quantity of the current time instant, is the error covariance matrix of the observation quantity of the current time instant.

Images