阅读说明：本技术 一种空间完全非合作目标相对位姿和惯量估计方法 (Method for estimating relative pose and inertia of space complete non-cooperative target ) 是由 冯乾 侯晓磊 杨家男 潘泉 刘勇 于 2019-10-18 设计创作，主要内容包括：本发明公开了一种空间完全非合作目标相对位姿和惯量估计方法,步骤一、由两个左右间隔设置在追踪航天器上、且参数相同的工业相机实时获取非合作目标的图像信息,计算各特征点在相机坐标系下的3D位置和速度；步骤二、根据刚体运动模型,由至少三个特征点的3D位置和速度计算非合作目标的相对角速度；估计非合作目标在任意时刻的相对姿态；步骤三、将3D位置和速度以及刚体的相对姿态和相对角速度,估计非合作目标的质心位置、质心速度及特征点的相对位置；步骤四、估计非合作目标的转动惯量参数。在无需先验已知完全非合作目标的几何形状及特征点位置的前提下,可解算出完全非合作目标的质心位置、质心速度、相对姿态、相对角速度及惯量参数。(The invention discloses a method for estimating relative pose and inertia of a space complete non-cooperative target, which comprises the steps of firstly, acquiring image information of the non-cooperative target in real time by two industrial cameras which are arranged on a tracked spacecraft at intervals and have the same parameters, and calculating the 3D position and speed of each feature point under a camera coordinate system; step two, calculating the relative angular velocity of the non-cooperative target according to the rigid motion model and the 3D positions and the velocities of at least three characteristic points; estimating the relative attitude of the non-cooperative target at any moment; estimating the centroid position, the centroid speed and the relative position of the characteristic point of the non-cooperative target by using the 3D position, the 3D speed and the relative posture and the relative angular speed of the rigid body; and step four, estimating the rotational inertia parameters of the non-cooperative target. Under the premise of not knowing the geometric shape and the position of the characteristic point of the completely non-cooperative target a priori, the centroid position, the centroid speed, the relative attitude, the relative angular speed and the inertia parameter of the completely non-cooperative target can be calculated.)

1. A method for estimating relative pose and inertia of a space complete non-cooperative target is characterized by comprising the following steps:

step one, two industrial cameras which are arranged on a tracking spacecraft at intervals at left and right and have the same parameters are used for acquiring image information of a non-cooperative target in real time, image positions and image speeds of a plurality of feature points on the non-cooperative target on the left camera and the right camera are obtained through calculation, and then the 3D positions and speeds of the feature points under a camera coordinate system are calculated;

estimating the relative angular velocity of the non-cooperative target according to the rigid motion model and the 3D positions and the velocities of the at least three characteristic points in the step one; estimating the relative posture of the non-cooperative target at any time by combining the 3D positions of the characteristic points at the front and rear times;

thirdly, estimating the centroid position, the centroid speed and the relative position of the characteristic point of the non-cooperative target by using the 3D position and the speed in the first step and the relative posture and the relative angular speed of the rigid body in the second step and combining a centroid relative motion constraint equation of the non-cooperative target;

and step four, estimating the rotational inertia parameters of the non-cooperative target.

2. The method for estimating the relative pose and inertia of the completely non-cooperative target in the space according to claim 1 is characterized in that the method is applicable to the following conditions: the distance between the non-cooperative target and the tracking spacecraft is less than 100 meters, and the motion trail of the tracking spacecraft is a circular or near-circular orbit.

3. The method for estimating the relative pose and inertia of the completely non-cooperative target in space according to claim 2, wherein in the first step, the characteristic point P can be obtained by a pinhole model_iThe image positions on the left and right cameras are:

wherein:

η_i＝[u_iRv_iRu_iLv_iL]^Tis the image coordinates of the ith feature point on the left and right cameras,

ρ_i＝[ρ_ixρ_iyρ_iz]^Tthe coordinates of the ith feature point in the camera coordinate system are 1,2, …, N;

f is the focal length of the camera;

b is the baseline width between the two cameras;

when considering the image noise in the actual measurement, the image position measurement model is:

wherein:

measuring image coordinates of an ith characteristic point containing noise on left and right cameras;

ε_iis modeled as a zero mean with a covariance of

and (3) obtaining the 3D position estimation of the feature point in the camera coordinate system according to the formula (1) and the noise model (A):

wherein:

the image velocity is derived from equation (1):

and (3) according to the formula (4), and considering the image noise, obtaining a speed estimation value of the ith characteristic point in the camera coordinate system as follows:

wherein:

4. The method for estimating the relative pose and inertia of the space complete non-cooperative target according to the claim 2 or 3, wherein the specific process of the second step is as follows:

at any time t, any characteristic point P on the non-cooperative target_iSatisfies the following geometrical positional relationship:

the speed satisfies the following relationship:

wherein:

ρ₀(t) is the position of the non-cooperative target centroid relative to the camera coordinate system at time t;

the angular velocity of the non-cooperative target relative to the tracked spacecraft at the time t is coordinated under a camera coordinate system;

r_icoordinates of the feature points on the non-cooperative target relative to the position of the center of mass under the non-cooperative target body;

taking any characteristic point on the non-cooperative target as a reference point, wherein the characteristic point is P_NDefine δ ρ_i(t)＝ρ_i(t)-ρ_N(t)，δr_i＝r_i-r_NCombining formula (6) and formula (7) gives:

by elimination of formulae (8) and (9)

wherein: [ δ ρ [ ]_i(t)×]Representing the vector δ ρ_i(t) the corresponding cross-multiplication matrix;

in combination of formulas (2) and (5), the following can be obtained:

the relative angular velocity estimate for the non-cooperative target is given by the following equation (12):

wherein:

the minimum value of N is 3;

setting an initial time t₀And an arbitrary time t_kWherein, t_k＝t₀+ k Δ t, k being a positive integer, Δ t being the time interval between two shots of the non-cooperative target image, according to equation (8):

defining pose variance

calculating the relative attitude estimation value of the non-cooperative target at any moment by the formula (15)

5. The method for estimating the relative pose and inertia of the space complete non-cooperative target according to the claim 2 or 3, wherein the specific process of the third step is as follows: the relative position of the non-cooperative target is described by a centroid relative motion constraint equation, which is a CW equation, then:

wherein the content of the first and second substances,

performing a second order taylor discretization on equation (19) and ignoring the higher order terms and the noise terms, we can obtain:

x_p(t_k)＝F₁x_p(t_k-Δt) (20)；

wherein:

Δ t is the time interval between two times of shooting of non-cooperative target images;

x_pa vector containing the position and the speed of the mass center of the non-cooperative target is obtained;

F₁＝I₆+Δt·F+1/2Δt²·F²；

is provided withA vector containing the relative position of the feature point with respect to the centroid of the non-cooperative target, and the position and velocity of the centroid with respect to the camera coordinate system; from equation (20) we can derive:

X₁(t_k)＝G·X₁(t_k-Δt) (21)；

wherein:

according to the formula (21), j is a positive integer for the interval j.DELTA.t, and satisfies the condition that j.DELTA.t is a positive integer for the specified time interval c.DELTA.t

X₁(t_k-j·Δt)＝G^-jX₁(t_k),k-c≤j＜k (22)；

Wherein: c is a positive integer less than k;

from equations (6) and (7), it can be found that:

C(t_k)X₁(t_k)＝Y(t_k) (23)；

wherein:

estimated values calculated according to equations (2), (5), (12) and (15)

wherein:

6. the method for estimating the relative pose and inertia of the space complete non-cooperative target according to the claim 2 or 3, wherein the process of the fourth step is as follows: angular momentum h of the non-cooperative target in an inertial coordinate system^IComprises the following steps:

wherein:

definition of

Ax_I＝0 (26)；

wherein:

|| ||₂A modulus representing a vector;

definition B ═ A^TA; the condition for minimizing the convex quadratic function f (x) according to equation (27) is:

Bx_I＝0 (28)；

for homogeneous equation (28), given x_IIs 1, i.e. the first component of

wherein: b₁₁Is a positive real number; then homogeneous equation (28) is written as:

B_rx_r＝-b₁(30)；

the inertia tensor of the non-cooperative target satisfies its own physical constraints, namely:

substitution into

then equation (30) is a quadratic equation that satisfies constraint (32) by optimizing a convex quadratic function

[ technical field ] A method for producing a semiconductor device

The invention belongs to the technical field of navigation, and particularly relates to a method for estimating relative pose and inertia of a space complete non-cooperative target.

[ background of the invention ]

In recent years, with the increasing frequency of human space activities, the number of space debris is increased sharply, and by 1 month in 2013, the number of large space debris (the size is not less than 10cm) cataloged by a space monitoring network (SSN) under the U.S. strategic commander is nearly 15000, and the space debris (including small space debris with the size less than 1mm and dangerous debris between the large space debris and the small space debris) which is not cataloged and has the size less than 10cm is difficult to estimate, so that the space debris seriously threatens the normal operation of the in-orbit spacecraft, and the research on clearing the space debris is urgently needed. Compared with cooperative targets in a traditional rendezvous and docking task, non-cooperative targets such as a fault satellite, a failed spacecraft, space debris and the like have obvious 'three-free' characteristics, namely, no cooperative measurement beacon, no interactive communication and no model parameters, and the characteristics bring great challenges to relative navigation and near-field operation of the non-cooperative targets.

Regarding the estimation of the relative pose and the state of the non-cooperative target, the following methods are adopted at present, firstly, the relative pose parameters of the non-cooperative target are solved by an iterative algorithm based on monocular vision, the method assumes that the shape and the geometric dimension of the target are known, actually, the coordinates of a plurality of reference points on the target spacecraft are under a body coordinate system of the target spacecraft, and the relative position and the attitude of the current moment are solved by the iterative method. And the other method is to provide a non-cooperative target relative pose estimation method based on gyroscope, stereo vision and accelerometer measurement under the condition that the positions and inertia tensors of a plurality of characteristic points on the non-cooperative target are known in advance, so that accurate autonomous relative navigation is realized under the condition that the non-cooperative target spacecraft dynamic data is lacked. And the other method is to use a model matching (such as ICP) based method to solve the relative pose parameters of the non-cooperative target on the premise of a CAD structure of the known non-cooperative target in advance. And on the basis of binocular stereo vision, a SLAM (simultaneous Localization and mapping) method is adopted to solve the mass center position, the linear speed, the relative attitude, the relative angular speed and the inertia parameters of the space rotation non-cooperative target.

Compared with a cooperative target in a traditional rendezvous and docking task, a complete non-cooperative target such as a fault satellite, a failed spacecraft, a space debris and the like lacks cooperative information which is convenient for navigation, such as a measurement beacon, interactive communication, model parameters and the like, so that the traditional navigation algorithm suitable for the cooperative target fails. The existing navigation algorithm applied to the non-cooperative target depends on a model of the target, or the calculation amount is too large to realize online calculation. The above method relies either on a priori known shapes and geometries, or on a priori knowledge of the locations of feature points on the object and the moment of inertia of the object, or on a priori known CAD models of the object, which are not strictly speaking completely uncooperative objects. The SLAM method is used for calculating the centroid position, the linear speed, the relative attitude, the relative angular speed and the inertia parameters of the space rotation non-cooperative target, the calculation amount is large, the time consumption is long, and only offline calculation can be performed.

[ summary of the invention ]

The invention aims to provide a method for estimating the relative pose and inertia of a space complete non-cooperative target, which can solve the centroid position, the centroid speed, the relative attitude, the relative angular speed and the inertia parameter of the complete non-cooperative target on the premise of not knowing the geometric shape and the characteristic point position of the complete non-cooperative target a priori, and provide effective navigation information for the near-field operation of the non-cooperative target in the next stage.

The invention adopts the following technical scheme: a method for estimating relative pose and inertia of a space complete non-cooperative target comprises the following steps:

step one, two industrial cameras which are arranged on a tracking spacecraft at intervals at left and right and have the same parameters are used for acquiring image information of a non-cooperative target in real time, image positions and image speeds of a plurality of feature points on the non-cooperative target on the left camera and the right camera are obtained through calculation, and then the 3D positions and speeds of the feature points under a camera coordinate system are calculated;

estimating the relative angular velocity of the non-cooperative target according to the rigid motion model and the 3D positions and the velocities of the at least three characteristic points in the step one; estimating the relative posture of the non-cooperative target at any time by combining the 3D positions of the characteristic points at the front and rear times;

thirdly, estimating the centroid position, the centroid speed and the relative position of the characteristic point of the non-cooperative target by using the 3D position and the speed in the first step and the relative posture and the relative angular speed of the rigid body in the second step and combining a centroid relative motion constraint equation of the non-cooperative target;

and step four, estimating the rotational inertia parameters of the non-cooperative target.

Further, the method is applicable to the following conditions: the distance between the non-cooperative target and the tracking spacecraft is less than 100 meters, and the motion track of the tracking spacecraft is a circular or near-circular orbit.

Further, in step one, the characteristic point P can be obtained from the pinhole model_iThe image positions on the left and right cameras are:

wherein:

η_i＝[u_iRv_iRu_iLv_iL]^Tis the image coordinates of the ith feature point on the left and right cameras,

ρ_i＝[ρ_ixρ_iyρ_iz]^Tthe coordinates of the ith feature point in the camera coordinate system are 1,2, …, N;

f is the focal length of the camera;

b is the baseline width between the two cameras;

when considering the image noise in the actual measurement, the image position measurement model is:

wherein:

measuring image coordinates of an ith characteristic point containing noise on left and right cameras;

ε_iis modeled as a zero mean with a covariance of

White Gaussian noise of (1)₄Representing a 4 x 4 identity matrix.

And (3) obtaining the 3D position estimation of the feature point in the camera coordinate system according to the formula (1) and the noise model (A):

wherein:

the image velocity is derived from equation (1):

and (3) according to the formula (4), and considering the image noise, obtaining a speed estimation value of the ith characteristic point in the camera coordinate system as follows:

wherein:

representing an estimate of the corresponding quantity.

Further, the specific process of the second step is as follows:

at any time t, any characteristic point P on the non-cooperative target_iSatisfies the following geometrical position relationship：

The speed satisfies the following relationship:

wherein:

ρ₀(t) is the position of the non-cooperative target centroid relative to the camera coordinate system at time t;

is the speed of the non-cooperative target centroid relative to the camera coordinate system at time t;

is a posture rotation matrix from a non-cooperative target system to a camera coordinate system at the time t;

the angular velocity of the non-cooperative target relative to the tracked spacecraft at the time t is coordinated under a camera coordinate system;

r_icoordinates of the feature points on the non-cooperative target relative to the position of the center of mass under the non-cooperative target body;

taking any characteristic point on the non-cooperative target as a reference point, wherein the characteristic point is P_NDefinition of

δρ_i(t)＝ρ_i(t)-ρ_N(t)，δr_i＝r_i-r_NCombining formula (6) and formula (7) gives:

by elimination of formulae (8) and (9)

The following can be obtained:

wherein: [ δ ρ [ ]_i(t)×]Representing the vector δ ρ_i(t) the corresponding cross-multiplication matrix;

in combination of formulas (2) and (5), the following can be obtained:

the estimate of the relative angular velocity of the non-cooperative target is given by equation (12) as follows:

wherein:

the minimum value of N is 3;

setting an initial time t₀And an arbitrary time t_kWherein, t_k＝t₀+ k Δ t, k being a positive integer, Δ t being the time interval between two shots of the non-cooperative target image, according to equation (8):

defining pose variance

And eliminate r in formula (13)_iObtaining:

calculating the relative attitude estimation value of the non-cooperative target at any moment by the formula (15)

Further, the specific process of the third step is as follows: the relative position of the non-cooperative target is described by a centroid relative motion constraint equation, wherein the centroid relative motion constraint equation is a CW equation, and then:

wherein the content of the first and second substances,

acceleration noise generated for including spatial disturbance forces; n is the average orbital angular velocity of the tracked spacecraft;

performing a second order taylor discretization on equation (19) and ignoring the higher order terms and the noise terms, we can obtain:

x_p(t_k)＝F₁x_p(t_k-Δt) (20)；

wherein:

Δ t is the time interval between two times of shooting of non-cooperative target images;

x_pa vector containing the position and the speed of the mass center of the non-cooperative target is obtained;

F₁＝I₆+Δt·F+¹/₂Δt²·F²；

is provided with

Including the relative position, and mass, of the feature point with respect to the centroid of the non-cooperative objectA vector including the position and velocity of the heart relative to the camera coordinate system; from equation (20) we can derive:

X₁(t_k)＝G·X₁(t_k-Δt) (21)；

wherein:

I₃is a 3 × 3 identity matrix;

according to the formula (21), j is a positive integer for the interval j.DELTA.t, and satisfies the condition that j.DELTA.t is a positive integer for the specified time interval c.DELTA.t

X₁(t_k-j·Δt)＝G^-jX₁(t_k),k-c≤j＜k (22)；

Wherein: c is a positive integer less than k;

from equations (6) and (7), it can be found that:

C(t_k)X₁(t_k)＝Y(t_k) (23)；

wherein:

estimated values calculated according to equations (2), (5), (12) and (15)

And

x can be obtained by combining the formulas (22) and (23)₁(t_k) The least squares estimation of (d) is:

wherein:

further, the process of the fourth step is as follows: angular momentum h of non-cooperative target under inertial coordinate system^IComprises the following steps:

wherein:

then:

to track the angular velocity of the spacecraft;

an angular velocity of a non-cooperative target;

is an attitude rotation matrix from a non-cooperative target system to an inertial system;

is a pose rotation matrix from a tracking spacecraft camera coordinate system to an inertial system;

definition of

Wherein I^*＝[I_txxI_txyI_txzI_tyyI_tyzI_tzz]^TAre components of the moment of inertia of non-cooperative targets,

each component of the non-cooperative target angular momentum under an inertial system; from equation (25) we can obtain:

Ax_I＝0 (26)；

wherein:

wherein the content of the first and second substances,

is an estimate of the angular velocity of a non-cooperative target

Each component of (a);

solving equation (26) is equivalent to minimizing equation (27):

|| ||₂a modulus representing a vector;

definition B ═ A^TA; the condition for minimizing the convex quadratic function f (x) according to equation (27) is:

Bx_I＝0 (28)；

for homogeneous equation (28), given x_IIs 1, i.e. the first component of

The block matrix of matrix B is then represented as follows:

wherein: b₁₁Is a positive real number; then homogeneous equation (28) is written as:

B_rx_r＝-b₁(30)；

the inertia tensor of the non-cooperative target satisfies its own physical constraints, namely:

substitution intoThen:

then equation (30) is a quadratic equation that satisfies constraint (32) by optimizing a convex quadratic function

Solving for x_r。

The invention has the beneficial effects that: 1. for a completely non-cooperative target, the 3D position and speed of the feature points in the camera coordinate system are calculated according to the image positions and image speeds of a plurality of feature points on the target acquired by the industrial camera.

2. Solving and converting the inertia parameters of the completely non-cooperative target into a quadratic optimization problem with constraint.

3. Least square, q-method and quadratic optimization are mainly adopted, the calculated amount is small, and online estimation can be realized.

4. When the inertia parameters are estimated, the constraint among components of the inertia tensor is considered, and the estimation result is more reliable.

[ description of the drawings ]

FIG. 1 is a geometric relationship diagram of feature points;

FIG. 2 is a diagram of the relative error of the centroid positions of non-cooperative targets;

FIG. 3 is a graph of the non-cooperative target centroid velocity relative error;

FIG. 4 is a graph of non-cooperative target relative attitude error;

FIG. 5 is a graph of the relative angular velocity error of the non-cooperative target;

FIG. 6 is a graph of non-cooperative target x-axis rotational inertia relative error;

FIG. 7 is a graph of non-cooperative target y-axis rotational inertia relative error;

FIG. 8 is a graph of non-cooperative target z-axis rotational inertia relative error;

fig. 9 shows the relative error of a feature point on a non-cooperative target with respect to the centroid position of the non-cooperative target.

[ detailed description ] embodiments

The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

The invention discloses a method for estimating relative pose and inertia of a space complete non-cooperative target, which comprises the following steps:

step one, two industrial cameras which are arranged on a tracking spacecraft at intervals at left and right and have the same parameters are used for acquiring image information of a non-cooperative target in real time, image positions and image speeds of a plurality of feature points on the non-cooperative target on the left camera and the right camera are obtained through calculation, and then the 3D positions and speeds of the feature points under a camera coordinate system are calculated;

estimating the relative angular velocity of the non-cooperative target according to the rigid motion model and the 3D positions and the velocities of the at least three characteristic points in the step one; estimating the relative posture of the non-cooperative target at any time by combining the 3D positions of the characteristic points at the front and rear times; as shown in fig. 1.

Thirdly, estimating the centroid position, the centroid speed and the relative position of the characteristic point of the non-cooperative target by using the 3D position and the speed in the first step and the relative posture and the relative angular speed of the rigid body in the second step and combining a centroid relative motion constraint equation of the non-cooperative target;

and step four, estimating the rotational inertia parameters of the non-cooperative target.

The method is applicable to the following conditions: the distance between the non-cooperative target and the tracking spacecraft is less than 100 meters, and the motion track of the tracking spacecraft is a circular or near-circular orbit.

In the first step, the characteristic point P can be obtained from the pinhole model_iThe image positions on the left and right cameras are:

wherein:

η_i＝[u_iRv_iRu_iLv_iL]^Tis the image coordinates of the ith feature point on the left and right cameras,

ρ_i＝[ρ_ixρ_iyρ_iz]^Tthe coordinates of the ith feature point in the camera coordinate system are 1,2, …, N; n is the number of the characteristic points;

f is the focal length of the camera;

b is the baseline width between the two cameras;

when considering the image noise in the actual measurement, the image position measurement model is:

wherein:

measuring image coordinates of an ith characteristic point containing noise on left and right cameras;

ε_iis modeled as a zero mean with a covariance ofWhite Gaussian noise of (1)₄Representing a 4 x 4 identity matrix.

And (3) obtaining the 3D position estimation of the feature point in the camera coordinate system according to the formula (1) and the noise model (A):

wherein:

the image velocity is derived from equation (1):

and (3) according to the formula (4), and considering the image noise, obtaining a speed estimation value of the ith characteristic point in the camera coordinate system as follows:

wherein:

representing an estimate of the corresponding quantity.

The specific process of the second step is as follows:

as shown in FIG. 1, at any time t, any feature point P on the non-cooperative target_iSatisfies the following geometrical positional relationship:

the speed satisfies the following relationship:

wherein:

ρ₀(t) is the position of the non-cooperative target centroid relative to the camera coordinate system at time t;

is the speed of the non-cooperative target centroid relative to the camera coordinate system at time t;

is a posture rotation matrix from a non-cooperative target system to a camera coordinate system at the time t;

the angular velocity of the non-cooperative target relative to the tracked spacecraft at the time t is coordinated under a camera coordinate system;

r_icoordinates of the feature points on the non-cooperative target relative to the position of the center of mass under the non-cooperative target body;

taking any characteristic point on the non-cooperative target as a reference point, wherein the characteristic point is P_NDefinition of

δρ_i(t)＝ρ_i(t)-ρ_N(t)，δr_i＝r_i-r_NCombining formula (6) and formula (7) gives:

by elimination of formulae (8) and (9)

The following can be obtained:

wherein: [ δ ρ [ ]_i(t)×]Representing the vector δ ρ_i(t) the corresponding cross-multiplication matrix;

combining equations (2) and (5), only the estimated values of the feature point position and velocity can be obtained, and then the following equation (10) can be obtained:

the estimate of the relative angular velocity of the non-cooperative target is given by the following equation (12):

wherein:

due to the fact thatThe determinant is 0, namely the rank of the matrix is 2, and the minimum value of the number N of the characteristic points is required to be 3 in order to solve the three-dimensional relative angular velocity of the non-cooperative target.

Setting an initial time t₀And an arbitrary time t_kWherein, t_k＝t₀+ k Δ t, k being a positive integer, Δ t being the time interval between two shots of the non-cooperative target image, according to equation (8):

defining pose variance

And eliminate r in formula (13)_iObtaining:

since equation (2) can only obtain an estimate of the location of the feature points, it is obtained from equation (14):

calculating the relative attitude estimation value of the non-cooperative target at any moment by the formula (15)

The above formula (15) is transformed into the classical Wahba problem and solved using q-method. Selection weight { a }_i1,2, N-1, and defines the following matrix:

wherein the content of the first and second substances,

the unit feature vector corresponding to the largest feature root of L (B) is the attitude variation

Corresponding quaternion

Here, the quaternion q ═ q₁q₂q₃q₄]^TThe corresponding attitude matrix is:

given an initial relative pose of a non-cooperative target

Can be arbitrarily given, and then combines the relative attitude variation

Calculating the relative attitude of the non-cooperative target at any time from equation (14)

The concrete process of the third step is as follows: the relative position of the non-cooperative objects is described by a centroid relative motion constraint equation, the centroid relative motion constraint equation is a CW equation, CW is a reference of Clohessy-Wiltshire, then:

wherein:

for acceleration noise including spatial disturbance force

Then formula (19) is obtained:

wherein the content of the first and second substances,

acceleration noise generated for including spatial disturbance forces; n is the average orbital angular velocity of the tracked spacecraft;

performing a second order taylor discretization on equation (19) and ignoring the higher order terms and the noise terms, we can obtain:

x_p(t_k)＝F₁x_p(t_k-Δt) (20)；

wherein:

Δ t is the time interval between two times of shooting of non-cooperative target images;

x_pa vector containing the position and the speed of the mass center of the non-cooperative target is obtained;

F₁＝I₆+Δt·F+¹/₂Δt²·F²；

is provided with

A vector containing the relative position of the feature point with respect to the centroid of the non-cooperative target, and the position and velocity of the centroid with respect to the camera coordinate system; from equation (20) we can derive:

X₁(t_k)＝G·X₁(t_k-Δt) (21)；

wherein:

I₃is a 3 × 3 identity matrix;

according to the formula (21), j is a positive integer for the interval j.DELTA.t, and satisfies the condition that j.DELTA.t is a positive integer for the specified time interval c.DELTA.t

X₁(t_k-j·Δt)＝G^-jX₁(t_k),k-c≤j＜k (22)；

Wherein: c is a positive integer less than k;

from equations (6) and (7), and taking into account the feature point positions and velocities, the relative angular velocities and attitudes of the non-cooperative targets are both estimated values, which can be derived:

C(t_k)X₁(t_k)＝Y(t_k) (23)；

wherein:

estimated values calculated according to equations (2), (5), (12) and (15)

And

x can be obtained by combining the formulas (22) and (23)₁(t_k) The least squares estimation of (d) is:

wherein:

the process of the fourth step is as follows: for totally non-cooperative targets such as fault satellites, failure spacecrafts, space debris and the like, the active moment effect is not generated in outer space, so that the angular momentum of the targets is conserved in an inertial system, and the angular momentum h of the non-cooperative targets is under the inertial coordinate system^IComprises the following steps:

wherein:

the angular velocity and attitude of the above-mentioned tracked spacecraft can be obtained by the measurement equipment of the spacecraft itself, in known quantities, i.e.

And

in the known manner, it is known that,

and

estimated from equations (12) and (15), then:

to track the angular velocity of the spacecraft;

an angular velocity of a non-cooperative target;

is an attitude rotation matrix from a non-cooperative target system to an inertial system;

is a pose rotation matrix from a tracking spacecraft camera coordinate system to an inertial system;

(12) and (15) estimating the result of the estimation,

definition of

Wherein I^*＝[I_txxI_txyI_txzI_tyyI_tyzI_tzz]^TAre components of the moment of inertia of non-cooperative targets,

each component of the non-cooperative target angular momentum under an inertial system; from equation (25) we can obtain:

Ax_I＝0 (26)；

wherein:

is an estimate of the angular velocity of a non-cooperative target

Each component of (a); solving equation (26) is equivalent to minimizing equation (27):

|| ||₂a modulus representing a vector;

definition B ═ A^TA; according to equation (27), the condition for obtaining the minimum of the quadratic function f (x) is:

Bx_I＝0 (28)；

for homogeneous equation (28), given x_IIs 1, i.e. the first component of

The block matrix of matrix B is then represented as follows:

wherein: b₁₁Is a positive real number; then homogeneous equation (28) is written as:

B_rx_r＝-b₁(30)；

according to B being a positive definite matrix, an

In the knowledge that B_rIs also positive; the inertia tensor of the non-cooperative target satisfies its own physical constraints, namely:

substitution into

Then:

then equation (30) is a quadratic equation that satisfies constraint (32) by optimizing a convex quadratic function

Solving for x_r。

And (3) experimental verification:

in order to verify the performance of the algorithm in the invention, a non-cooperative target with a certain size of 3m × 3m × 3m in space is selected as an experimental object. The simulation parameters in the experiment are designed as follows:

the number of the feature points: 4;

relative position of feature points with respect to the non-cooperative target centroid: taking a random number in the interval [ -1.51.5] m;

initial angular velocity of non-cooperative target:

initial value of non-cooperative target centroid position: ρ (t)₀)＝[10 25 30]^Tm；

Initial value of non-cooperative target centroid velocity:

initial relative attitude of non-cooperative target: q. q.s_ct(t₀)＝[0 0 0 1]^T；

Non-cooperative target acceleration noise of

Simulation duration: 2500 s;

time interval of two times of shooting non-cooperative target images: Δ t ═ 1 s;

the time interval c is 50.

In the simulation experiment, assuming that the image extraction and matching work is finished, the image position and speed with measurement noise can be directly obtained, wherein the noise modeling is that the mean value is 0, and the standard deviation amplitude is 2 multiplied by 10-⁵White gaussian noise of rad.

To measure the estimated performance of the designed method, the following relative estimation errors are now defined:

representing the corresponding quantity estimator, | | | | luminance₂Represents the norm of the vector, | | represents the absolute value, D represents the non-cooperative target size, here 3, since here the feature point is in the interval [ -1.51.5 []m is a random number, only the error of one characteristic point is taken as a representative, and the inertia parameter error is only the main moment of inertia, namely I_xx,I_yyAnd I_zzThe relative error is taken as a representative.

The non-cooperative target relative attitude error is defined as:

e_θ＝2cos^-1(q_e4)

wherein q is_e4Is a quaternion q of the attitude error_eScalar part of q_eByAnd (4) obtaining.

From the above simulation results, as shown in fig. 2, 3, 4, 5, 6, 7, 8 and 9, in the range where the distance from the non-cooperative target to the tracked spacecraft is less than 100m, the centroid position estimation error of the completely non-cooperative target is less than 0.1%, the centroid speed estimation error is less than 2%, the attitude estimation error of the non-cooperative target is less than 0.035rad, i.e. 2 °, the relative angular speed estimation relative error is less than 3%, the main moment of inertia relative error of the non-cooperative target is less than 0.15%, and the position estimation relative error of the non-cooperative target feature point relative to the centroid thereof is less than 1.5%, which are within the allowable range. By verification, the method can effectively estimate the relative state of the non-cooperative target and provide required navigation information for the space near-field operation of the next stage.