CN114577208A - Navigation system error unified modeling method based on rotating reference coordinate system - Google Patents

Navigation system error unified modeling method based on rotating reference coordinate system Download PDF

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CN114577208A
CN114577208A CN202210107583.2A CN202210107583A CN114577208A CN 114577208 A CN114577208 A CN 114577208A CN 202210107583 A CN202210107583 A CN 202210107583A CN 114577208 A CN114577208 A CN 114577208A
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CN114577208B (en
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王大轶
孙博文
李茂登
邓润然
朱卫红
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Beijing Institute of Spacecraft System Engineering
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    • G01CMEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
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Abstract

The invention discloses a navigation system error unified modeling method based on a rotating reference coordinate system, which comprises the following steps: (1) representing the installation error of the camera by using the equivalent rotation vector; (2) obtaining a camera image plane translation error according to a camera measurement principle; (3) converting the camera image plane translation error into a camera image plane translation error in an equivalent rotation vector form by using a rotation reference coordinate system; (4) and obtaining a system error after unified modeling according to the camera image plane translation error in the equivalent rotation vector form and the installation error of the camera. The method overcomes the defect that the existing method can not simultaneously meet the requirements of estimating the installation error and the image plane translation of the satellite-borne optical camera, reduces the system error dimension, utilizes the rotary reference coordinate system to carry out unified dimension reduction representation on the system error of the satellite-borne optical camera, and realizes unified modeling of the autonomous navigation system error of the spacecraft.

Description

一种基于旋转参考坐标系的导航系统误差统一建模方法A Unified Modeling Method for Navigation System Error Based on Rotating Reference Coordinate System

技术领域technical field

本发明属于空间导航技术领域,尤其涉及一种基于旋转参考坐标系的导航系统误差统一建模方法。The invention belongs to the technical field of space navigation, and in particular relates to a unified modeling method for navigation system errors based on a rotating reference coordinate system.

背景技术Background technique

小天体探测中,航天器在轨长期运行,容易导致测量敏感器参数变化,产生系统误差,如星载光学相机可能存在诸如安装误差、镜头零偏等系统误差,这是制约航天器自主相对导航精度的主要原因。又由于航天器载荷限制,无法携带冗余的测量敏感器,同时不易在轨更换元件,所以必须要对星载光学相机系统误差进行在轨估计。目前星载光学相机系统误差在轨估计成为了研究的热点问题。In the detection of small celestial bodies, the long-term operation of the spacecraft in orbit will easily lead to changes in the parameters of the measurement sensor, resulting in systematic errors. For example, there may be systematic errors such as installation errors and lens biases in the spaceborne optical camera, which restricts the autonomous relative navigation of the spacecraft. The main reason for accuracy. In addition, due to the limitation of spacecraft load, it is impossible to carry redundant measurement sensors, and it is not easy to replace components on-orbit, so it is necessary to perform on-orbit estimation of the system error of the spaceborne optical camera. At present, on-orbit estimation of spaceborne optical camera system errors has become a hot research topic.

目前大多采用增广卡尔曼滤波方法对系统误差进行估计,即将待估计的系统误差变量扩维至状态变量中进行估计,由于系统误差个数较多,使得算法计算复杂度大大增加,同时星上计算资源严重受限,无法承担大数据量运算,所以传统的基于增广卡尔曼滤波方法无法在轨估计系统误差。At present, the augmented Kalman filtering method is mostly used to estimate the systematic error, that is, the systematic error variable to be estimated is expanded into the state variable for estimation. Due to the large number of systematic errors, the computational complexity of the algorithm is greatly increased. Computational resources are severely limited and cannot undertake large-scale operations, so the traditional augmented Kalman filter-based method cannot estimate the system error on-orbit.

发明内容SUMMARY OF THE INVENTION

本发明解决的技术问题是:克服现有技术的不足,提供了一种基于旋转参考坐标系的导航系统误差统一建模方法,克服现有方法无法同时满足估计星载光学相机安装误差与像面平移的要求,降低系统误差维数,利用旋转参考坐标系对星载光学相机系统误差进行统一降维表征,实现航天器自主导航系统误差的统一建模。The technical problem solved by the invention is: overcoming the deficiencies of the prior art, providing a unified modeling method for the errors of the navigation system based on the rotating reference coordinate system, overcoming the inability of the prior methods to simultaneously estimate the installation error and the image plane of the spaceborne optical camera To meet the requirements of translation, reduce the dimension of the system error, and use the rotating reference coordinate system to uniformly reduce the dimensionality of the system error of the spaceborne optical camera, so as to realize the unified modeling of the error of the spacecraft's autonomous navigation system.

本发明目的通过以下技术方案予以实现:一种基于旋转参考坐标系的导航系统误差统一建模方法,所述方法包括如下步骤:(1)利用等效旋转矢量表示相机的安装误差;(2)根据相机测量原理得到相机像面平移误差;(3)利用旋转参考坐标系将相机像面平移误差转化为等效旋转矢量形式的相机像面平移误差;(4)根据等效旋转矢量形式的相机像面平移误差和相机的安装误差得到统一建模后的系统误差。The object of the present invention is achieved through the following technical solutions: a unified modeling method for navigation system errors based on a rotating reference coordinate system, the method includes the following steps: (1) using an equivalent rotation vector to represent the installation error of the camera; (2) The camera image plane translation error is obtained according to the camera measurement principle; (3) the camera image plane translation error is converted into the camera image plane translation error in the form of an equivalent rotation vector by using the rotating reference coordinate system; (4) the camera image plane translation error in the form of an equivalent rotation vector The image plane translation error and the installation error of the camera are the systematic errors after unified modeling.

上述基于旋转参考坐标系的导航系统误差统一建模方法中,在步骤(1)中,相机的安装误差矩阵Cins为:In the above unified modeling method of navigation system errors based on the rotating reference coordinate system, in step (1), the installation error matrix C ins of the camera is:

Cins=I3+[θ×];C ins =I 3 +[θ×];

其中,I3为3维单位矩阵,θ为相机的安装误差。Among them, I 3 is a 3-dimensional unit matrix, and θ is the installation error of the camera.

上述基于旋转参考坐标系的导航系统误差统一建模方法中,在步骤(3)中,利用旋转参考坐标系将相机像面平移误差转化为等效旋转矢量形式的相机像面平移误差包括如下步骤:(31)得到统一的等效旋转轴;(32)根据相机像面平移误差和相机焦距得到统一的等效旋转轴下的旋转角度;(33)根据统一的等效旋转轴和统一的等效旋转轴下的旋转角度得到等效旋转矢量形式的相机像面平移误差。In the above-mentioned unified modeling method for navigation system errors based on a rotating reference coordinate system, in step (3), using the rotating reference coordinate system to convert the translation error of the camera image plane into the translation error of the camera image plane in the form of an equivalent rotation vector includes the following steps : (31) Obtain the unified equivalent rotation axis; (32) Obtain the rotation angle under the unified equivalent rotation axis according to the camera image plane translation error and the camera focal length; (33) According to the unified equivalent rotation axis and the unified etc. The rotation angle under the effective rotation axis can obtain the translation error of the camera image plane in the form of an equivalent rotation vector.

上述基于旋转参考坐标系的导航系统误差统一建模方法中,在步骤(31)中,统一的等效旋转轴为l=[δvu 0]T;其中,l为统一的等效旋转轴,δv为相机光轴在像面纵向方向的平移量,δu为相机光轴在像面横向方向的平移量。In the above-mentioned unified modeling method for navigation system errors based on the rotating reference coordinate system, in step (31), the unified equivalent rotation axis is l=[δ vu 0] T ; wherein, l is the unified equivalent Rotation axis, δ v is the translation amount of the camera optical axis in the longitudinal direction of the image plane, and δ u is the translation amount of the camera optical axis in the lateral direction of the image plane.

上述基于旋转参考坐标系的导航系统误差统一建模方法中,在步骤(32)中,统一的等效旋转轴下的旋转角度为:In the above-mentioned unified modeling method for navigation system errors based on the rotating reference coordinate system, in step (32), the rotation angle under the unified equivalent rotation axis is:

Figure BDA0003494433780000021
Figure BDA0003494433780000021

其中,φ为统一的等效旋转轴下的旋转角度,f为相机焦距长度,δv为相机光轴在像面纵向方向的平移量,δu为相机光轴在像面横向方向的平移量。Among them, φ is the rotation angle under the unified equivalent rotation axis, f is the focal length of the camera, δ v is the translation amount of the camera optical axis in the longitudinal direction of the image plane, and δ u is the translation amount of the camera optical axis in the lateral direction of the image plane .

上述基于旋转参考坐标系的导航系统误差统一建模方法中,在步骤(33)中,等效旋转矢量形式的相机像面平移误差为:In the above-mentioned unified modeling method for navigation system errors based on the rotating reference coordinate system, in step (33), the translation error of the camera image plane in the form of an equivalent rotation vector is:

Figure BDA0003494433780000022
Figure BDA0003494433780000022

其中,β为等效旋转矢量形式的相机像面平移误差,l为统一的等效旋转轴,φ为统一的等效旋转轴下的旋转角度。Among them, β is the translation error of the camera image plane in the form of an equivalent rotation vector, l is the unified equivalent rotation axis, and φ is the rotation angle under the unified equivalent rotation axis.

上述基于旋转参考坐标系的导航系统误差统一建模方法中,在步骤(4)中,统一建模后的系统误差为:In the above unified modeling method of navigation system error based on the rotating reference coordinate system, in step (4), the system error after unified modeling is:

α=θ+β;α=θ+β;

其中,α为统一建模后的系统误差,θ为相机的安装误差,β为等效旋转矢量形式的相机像面平移误差。Among them, α is the systematic error after unified modeling, θ is the installation error of the camera, and β is the translation error of the camera image plane in the form of an equivalent rotation vector.

一种基于旋转参考坐标系的导航系统误差统一建模系统,包括:第一模块,用于利用等效旋转矢量表示相机的安装误差;第二模块,用于根据相机测量原理得到相机像面平移误差;第三模块,用于利用旋转参考坐标系将相机像面平移误差转化为等效旋转矢量形式的相机像面平移误差;第四模块,用于根据等效旋转矢量形式的相机像面平移误差和相机的安装误差得到统一建模后的系统误差。A unified modeling system for navigation system errors based on a rotating reference coordinate system, comprising: a first module for using an equivalent rotation vector to represent the installation error of a camera; a second module for obtaining the camera image plane translation according to the camera measurement principle error; the third module is used to convert the translation error of the camera image plane into the camera image plane translation error in the form of an equivalent rotation vector by using the rotation reference coordinate system; the fourth module is used for the camera image plane translation in the form of an equivalent rotation vector The error and the installation error of the camera get the systematic error after unified modeling.

上述基于旋转参考坐标系的导航系统误差统一建模系统中,相机的安装误差矩阵Cins为:In the above unified modeling system of navigation system errors based on the rotating reference coordinate system, the installation error matrix C ins of the camera is:

Cins=I3+[θ×];C ins =I 3 +[θ×];

其中,I3为3维单位矩阵,θ为相机的安装误差。Among them, I 3 is a 3-dimensional unit matrix, and θ is the installation error of the camera.

上述基于旋转参考坐标系的导航系统误差统一建模系统中,利用旋转参考坐标系将相机像面平移误差转化为等效旋转矢量形式的相机像面平移误差包括如下步骤:(31)得到统一的等效旋转轴;(32)根据相机像面平移误差和相机焦距得到统一的等效旋转轴下的旋转角度;(33)根据统一的等效旋转轴和统一的等效旋转轴下的旋转角度得到等效旋转矢量形式的相机像面平移误差。In the above-mentioned unified modeling system for navigation system errors based on the rotating reference coordinate system, using the rotating reference coordinate system to convert the translation error of the camera image plane into the translation error of the camera image plane in the form of an equivalent rotation vector includes the following steps: (31) Obtaining a unified Equivalent rotation axis; (32) Obtain the rotation angle under the unified equivalent rotation axis according to the translation error of the camera image plane and the camera focal length; (33) According to the unified equivalent rotation axis and the rotation angle under the unified equivalent rotation axis The translation error of the camera image plane in the form of an equivalent rotation vector is obtained.

本发明与现有技术相比具有如下有益效果:Compared with the prior art, the present invention has the following beneficial effects:

(1)本发明通过系统误差统一建模特征,实现了系统误差统一降维表征,降低了计算复杂度,可满足航天器上受限的计算能力;(1) The present invention realizes the unified dimensionality reduction representation of the system error through the unified modeling feature of the system error, reduces the computational complexity, and can meet the limited computational capability on the spacecraft;

(2)本发明通过统一建模后系统误差的可观测性分析,给出了系统满足可观测性的情况,在满足系统可观测性的前提下进行估计,保证了滤波的收敛性;(2) The present invention provides the situation that the system satisfies the observability by analyzing the observability of the system error after the unified modeling, and performs estimation under the premise of satisfying the observability of the system, so as to ensure the convergence of the filtering;

(3)本发明通过在系统误差统一建模以及可观测性分析后,给出了对应的滤波步骤,可实现航天器导航系统误差的自校正。(3) The present invention provides the corresponding filtering steps after the unified modeling of the system error and the analysis of the observability, so that the self-correction of the error of the spacecraft navigation system can be realized.

附图说明Description of drawings

通过阅读下文优选实施方式的详细描述,各种其他的优点和益处对于本领域普通技术人员将变得清楚明了。附图仅用于示出优选实施方式的目的,而并不认为是对本发明的限制。而且在整个附图中,用相同的参考符号表示相同的部件。在附图中:Various other advantages and benefits will become apparent to those of ordinary skill in the art upon reading the following detailed description of the preferred embodiments. The drawings are for the purpose of illustrating preferred embodiments only and are not to be considered limiting of the invention. Also, the same components are denoted by the same reference numerals throughout the drawings. In the attached image:

图1是本发明实施例提供的基于旋转参考坐标系的导航系统误差统一建模方法的流程图;FIG. 1 is a flowchart of a unified modeling method for navigation system errors based on a rotating reference coordinate system provided by an embodiment of the present invention;

图2是本发明实施例提供的系统误差统一建模后的滤波估计误差的曲线示意图;2 is a schematic diagram of a filter estimation error after the unified modeling of the systematic error provided by an embodiment of the present invention;

图3是本发明实施例提供的相对导航状态变量r/|r|的滤波估计误差的曲线示意图;3 is a schematic diagram of a curve of a filter estimation error of a relative navigation state variable r/|r| provided by an embodiment of the present invention;

图4是本发明实施例提供的相对导航状态变量

Figure BDA0003494433780000041
的滤波估计误差的曲线示意图。FIG. 4 is a relative navigation state variable provided by an embodiment of the present invention
Figure BDA0003494433780000041
Schematic diagram of the curve of the filtered estimation error.

具体实施方式Detailed ways

下面将参照附图更详细地描述本公开的示例性实施例。虽然附图中显示了本公开的示例性实施例,然而应当理解,可以以各种形式实现本公开而不应被这里阐述的实施例所限制。相反,提供这些实施例是为了能够更透彻地理解本公开,并且能够将本公开的范围完整的传达给本领域的技术人员。需要说明的是,在不冲突的情况下,本发明中的实施例及实施例中的特征可以相互组合。下面将参考附图并结合实施例来详细说明本发明。Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be embodied in various forms and should not be limited by the embodiments set forth herein. Rather, these embodiments are provided so that the present disclosure will be more thoroughly understood, and will fully convey the scope of the present disclosure to those skilled in the art. It should be noted that the embodiments of the present invention and the features of the embodiments may be combined with each other under the condition of no conflict. The present invention will be described in detail below with reference to the accompanying drawings and in conjunction with the embodiments.

图1是本发明实施例提供的基于旋转参考坐标系的导航系统误差统一建模方法的流程图。如图1所示,该方法包括如下步骤:FIG. 1 is a flowchart of a unified modeling method for navigation system errors based on a rotating reference coordinate system provided by an embodiment of the present invention. As shown in Figure 1, the method includes the following steps:

(1)利用等效旋转矢量近似表示了相机的安装误差,即将相机的安装误差线性化表示;(1) The installation error of the camera is approximately represented by the equivalent rotation vector, that is, the installation error of the camera is linearized;

(2)在步骤(1)的基础上,从相机测量原理的角度给出了相机像面平移的参数化表示方法;(2) On the basis of step (1), the parametric representation method of camera image plane translation is given from the perspective of camera measurement principle;

(3)在步骤(2)的基础上,利用旋转参考坐标系将像面平移近似转化成等效旋转矢量形式,所述的旋转参考坐标系是指将加性的像面平移误差通过统一的旋转模式转化成等效旋转矢量;(3) On the basis of step (2), the image plane translation is approximately converted into an equivalent rotation vector form by using a rotating reference coordinate system, and the rotating reference coordinate system refers to converting the additive image plane translation error through a unified The rotation mode is converted into an equivalent rotation vector;

(4)根据步骤(3)给出的像面平移误差的变换方法,结合步骤(1)给出的安装误差的等效旋转矢量表示方法,将两系统误差进行统一降维表征,即统一建模,降低了待估参数个数,降低了计算复杂度。(4) According to the transformation method of image plane translation error given in step (3), combined with the equivalent rotation vector representation method of installation error given in step (1), the two system errors are characterized by unified dimension reduction, that is, unified construction It reduces the number of parameters to be estimated and reduces the computational complexity.

步骤(1)安装误差表示方法中,由于安装误差为小量,则忽略其二阶项可以将其利用等效旋转矢量进行线性化表示,并用等效旋转矢量θ的外积加单位矩阵的形式I3+[θ×]表示安装误差的旋转矩阵。Step (1) In the installation error representation method, since the installation error is small, its second-order term can be ignored and it can be linearized by the equivalent rotation vector, and the outer product of the equivalent rotation vector θ can be used to add the form of the unit matrix. I 3 +[θ×] represents the rotation matrix of the mounting error.

步骤(2)像面平移表示方法中,从相机成像原理的角度出发,结合像面平移的物理背景,给出了其参数化表示方法。Step (2) In the image plane translation representation method, from the perspective of the camera imaging principle, combined with the physical background of the image plane translation, a parameterized representation method is given.

步骤(3)基于旋转参考坐标系的近似转换方法为:Step (3) The approximate conversion method based on the rotating reference coordinate system is:

(4.1)根据相机像面平移误差特点,寻找统一的等效旋转轴l=[δvu 0]T(4.1) According to the characteristics of camera image plane translation error, find a unified equivalent rotation axis l=[δ vu 0] T ;

(4.2)根据像面平移误差的大小以及相机焦距大小,计算在步骤(4.1)所述旋转轴下的旋转角度

Figure BDA0003494433780000051
(4.2) Calculate the rotation angle under the rotation axis described in step (4.1) according to the size of the image plane translation error and the focal length of the camera
Figure BDA0003494433780000051

(4.3)结合(4.1)中的旋转轴与(4.2)中的旋转角度,得到像面平移的等效旋转矢量

Figure BDA0003494433780000052
(4.3) Combine the rotation axis in (4.1) and the rotation angle in (4.2) to obtain the equivalent rotation vector of the image plane translation
Figure BDA0003494433780000052

步骤(4)系统误差统一建模方法中,在步骤(1)与步骤(3)的基础上将安装误差与像面平移误差的等效旋转矢量相加,得到统一建模后的系统误差α=θ+β。Step (4) In the unified modeling method of systematic error, on the basis of step (1) and step (3), the equivalent rotation vector of the installation error and the image plane translation error is added to obtain the systematic error α after unified modeling =θ+β.

具体步骤如下:Specific steps are as follows:

给出测量方程,假设相机焦距为f,目标在相机系下的方向矢量为p=[px,py,pz]T,在不考虑测量噪声的情况下,相机的测量值[u,v]T满足:The measurement equation is given, assuming that the focal length of the camera is f, the direction vector of the target under the camera system is p=[p x , p y , p z ] T , without considering the measurement noise, the measurement value of the camera [u, v] T satisfies:

Figure BDA0003494433780000061
Figure BDA0003494433780000061

式中,p=rM/|rM|,r为相机系下非合作目标的相对位置矢量。In the formula, p=r M /|r M |, r is the relative position vector of the non-cooperative target under the camera system.

若光学相机存在安装误差,则有:If the optical camera has installation errors, there are:

Figure BDA0003494433780000062
Figure BDA0003494433780000062

式中,

Figure BDA0003494433780000063
为理想下轨道系到相机系的旋转矩阵,Cins为安装误差矩阵。In the formula,
Figure BDA0003494433780000063
is the rotation matrix from the orbit system to the camera system under ideal conditions, and C ins is the installation error matrix.

由于安装误差为小量,则可令等效旋转矢量θ=[θxyz]T表示安装误差,则安装误差矩阵可以表示为:Since the installation error is small, the equivalent rotation vector θ = [θ x , θ y , θ z ] T represents the installation error, and the installation error matrix can be expressed as:

Figure BDA0003494433780000064
Figure BDA0003494433780000064

若光学相机存在像面平移δ=[δuv]T,则If the optical camera has image plane translation δ=[δ uv ] T , then

Figure BDA0003494433780000065
Figure BDA0003494433780000065

给出统一建模方法:The unified modeling method is given:

将像面平移转化为旋转矩阵形式,易知满足由向量l1旋转到向量l2的旋转轴l一定有:Converting the image plane translation into the form of a rotation matrix, it is easy to know that the rotation axis l that satisfies the rotation from the vector l 1 to the vector l 2 must have:

<l,l1>=<l,l2><l,l 1 >=<l,l 2 >

由几何关系可知,存在共同旋转轴为:It can be known from the geometric relationship that there is a common axis of rotation as:

l=[δvu 0]T l=[δ vu 0] T

假设通过姿态控制使得成像点在光轴附近,则旋转角度近似为:Assuming that the imaging point is near the optical axis through attitude control, the rotation angle is approximated as:

Figure BDA0003494433780000066
Figure BDA0003494433780000066

等效旋转矢量近似为:The equivalent rotation vector is approximately:

Figure BDA0003494433780000071
Figure BDA0003494433780000071

得到光学相机系统误差的统一建模结果:The unified modeling result of the optical camera system error is obtained:

α=θ+βα=θ+β

若目标在相机系下的方向矢量为p,则观测方程为:If the direction vector of the target under the camera system is p, the observation equation is:

Figure BDA0003494433780000072
Figure BDA0003494433780000072

其中,u为目标在像面横轴上的坐标值,v为目标在像面纵轴上的坐标值,f为相机焦距长度,p为目标在相机系下的方向矢量。Among them, u is the coordinate value of the target on the horizontal axis of the image plane, v is the coordinate value of the target on the vertical axis of the image plane, f is the focal length of the camera, and p is the direction vector of the target under the camera system.

该方法还包括如下步骤:构建无距离信息的相对运动模型,并在此基础上针对统一建模后的导航系统误差进行可观测性分析,具体步骤如下:The method also includes the following steps: constructing a relative motion model without distance information, and on this basis, performing an observability analysis on the errors of the navigation system after unified modeling. The specific steps are as follows:

(2.1)给出线性化相对轨道动力学方程,不考虑噪声情况下,位置矢量r与速度矢量

Figure BDA0003494433780000073
以及系统误差α可表示为:(2.1) The linearized relative orbital dynamics equation is given. Without considering the noise, the position vector r and the velocity vector
Figure BDA0003494433780000073
And the systematic error α can be expressed as:

Figure BDA0003494433780000074
Figure BDA0003494433780000074

式中,

Figure BDA0003494433780000075
ω为航天器轨道角速度,F1
Figure BDA0003494433780000076
关于r的一阶Jacobi矩阵,F2
Figure BDA0003494433780000077
关于
Figure BDA0003494433780000078
的一阶Jacobi矩阵。In the formula,
Figure BDA0003494433780000075
ω is the orbital angular velocity of the spacecraft, and F 1 is
Figure BDA0003494433780000076
Regarding the first - order Jacobi matrix of r, F2 is
Figure BDA0003494433780000077
about
Figure BDA0003494433780000078
The first-order Jacobi matrix of .

为简便可观测性分析,不妨令归一化后的[-u,-v,f]T为测量值,则不考虑测量噪声的情况下时刻的测量方程为:In order to simplify the observability analysis, let the normalized [-u,-v,f] T be the measured value, then the measurement equation at the moment without considering the measurement noise is:

Figure BDA0003494433780000079
Figure BDA0003494433780000079

式中,Cα=I3+[α×],ζ为目标相对方向矢量的测量值,Cα为统一建模后系统误差的等效旋转矩阵,

Figure BDA0003494433780000081
为理想条件下轨道系到相机系的旋转矩阵,
Figure BDA0003494433780000082
为目标在相机系下的单位方向矢量。In the formula, C α =I 3 +[α×], ζ is the measured value of the relative direction vector of the target, C α is the equivalent rotation matrix of the system error after unified modeling,
Figure BDA0003494433780000081
is the rotation matrix from the orbital system to the camera system under ideal conditions,
Figure BDA0003494433780000082
is the unit direction vector of the target in the camera system.

(2.2)由于相机仅测得目标的方向矢量,为了直观地对系统误差进行可观测性分析,我们去除相对运动中的距离信息,给出无距离信息的相对运动方程:(2.2) Since the camera only measures the direction vector of the target, in order to intuitively analyze the observability of the system error, we remove the distance information in the relative motion, and give the relative motion equation without distance information:

Figure BDA0003494433780000083
Figure BDA0003494433780000083

式中,

Figure BDA0003494433780000084
In the formula,
Figure BDA0003494433780000084

(2.3)将无距离尺度的状态方程与测量方程离散化(2.3) Discretize the state equation and measurement equation without distance scale

无距离尺度状态方程离散化:Discretization of the distance-free scale equation of state:

Figure BDA0003494433780000085
Figure BDA0003494433780000085

其中,

Figure BDA0003494433780000086
为k+1时刻位置矢量的微分与距离的比值,
Figure BDA0003494433780000087
为k+1时刻位置矢量的二阶微分与距离的比值,αk为统一建模后k时刻系统误差,
Figure BDA0003494433780000088
统一建模后k+1时刻系统误差的微分,
Figure BDA0003494433780000089
为k时刻位置矢量的微分与距离的比值,
Figure BDA00034944337800000810
为k时刻位置矢量与距离的比值,Φk+1,k为k时刻到k+1时刻的状态转移矩阵。in,
Figure BDA0003494433780000086
is the ratio of the differential of the position vector at time k+1 to the distance,
Figure BDA0003494433780000087
is the ratio of the second derivative of the position vector at time k+1 to the distance, α k is the systematic error at time k after unified modeling,
Figure BDA0003494433780000088
The differential of the systematic error at time k+1 after unified modeling,
Figure BDA0003494433780000089
is the ratio of the differential of the position vector at time k to the distance,
Figure BDA00034944337800000810
is the ratio of the position vector at time k to the distance, Φ k+1, k is the state transition matrix from time k to time k+1.

测量方程离散化:Discretize the measurement equation:

Figure BDA00034944337800000811
Figure BDA00034944337800000811

其中,ζk为k时刻目标相对方向矢量的测量值,

Figure BDA00034944337800000812
为k时刻理想条件下轨道系到相机系的旋转矩阵。Among them, ζ k is the measured value of the relative direction vector of the target at time k,
Figure BDA00034944337800000812
is the rotation matrix from the orbital system to the camera system under ideal conditions at time k.

测量矩阵为:The measurement matrix is:

Figure BDA00034944337800000813
Figure BDA00034944337800000813

(2.4)构建可观测性矩阵O,并分析系统可观测性:(2.4) Construct the observability matrix O and analyze the system observability:

Figure BDA0003494433780000091
Figure BDA0003494433780000091

式中,In the formula,

Figure BDA0003494433780000092
Figure BDA0003494433780000092

Figure BDA0003494433780000093
Figure BDA0003494433780000093

Figure BDA0003494433780000094
Figure BDA0003494433780000094

其中,Hk为k时刻的测量矩阵,Hk+1为k+1时刻的测量矩阵,Hk+2为k+2时刻的测量矩阵,Φk+1,k为k时刻到k+1时刻的状态转移矩阵,Φk+2,k+1为k+1时刻到k+2时刻的状态转移矩阵,O11为可观测性矩阵O中3×3维的分块矩阵,O12为为可观测性矩阵O中3×3维的分块矩阵,O13为为可观测性矩阵O中3×3维的分块矩阵,O21为为可观测性矩阵O中3×3维的分块矩阵,O22为为可观测性矩阵O中3×3维的分块矩阵,O23为为可观测性矩阵O中3×3维的分块矩阵,O31为为可观测性矩阵O中3×3维的分块矩阵,O32为为可观测性矩阵O中3×3维的分块矩阵,O33为为可观测性矩阵O中3×3维的分块矩阵,

Figure BDA0003494433780000095
为k时刻轨道系到相机系的旋转矩阵,
Figure BDA0003494433780000096
为k时刻目标在相机系下的单位方向矢量,
Figure BDA0003494433780000097
为k+1时刻轨道系到相机系的旋转矩阵,
Figure BDA0003494433780000098
为k+2时刻轨道系到相机系的旋转矩阵,
Figure BDA0003494433780000099
为k+1时刻目标位置矢量与距离的比值,
Figure BDA00034944337800000910
为k+2时刻目标位置矢量与距离的比值,
Figure BDA00034944337800000911
为k+1时刻目标在相机系下的单位方向矢量,
Figure BDA00034944337800000912
为k+2时刻目标在相机系下的单位方向矢量。Among them, H k is the measurement matrix at time k, H k+1 is the measurement matrix at time k+1, H k+2 is the measurement matrix at time k+2, Φ k+1, k is the time k to k+1 The state transition matrix at time, Φ k+2, k+1 is the state transition matrix from time k+1 to time k+2, O 11 is the 3×3-dimensional block matrix in the observability matrix O, O 12 is is the 3×3-dimensional block matrix in the observability matrix O, O 13 is the 3×3-dimensional block matrix in the observability matrix O, and O 21 is the 3×3-dimensional block matrix in the observability matrix O Block matrix, O 22 is the block matrix of 3×3 dimensions in the observability matrix O, O 23 is the block matrix of 3×3 dimensions in the observability matrix O, O 31 is the observability matrix The block matrix of 3×3 dimensions in O, O 32 is the block matrix of 3×3 dimensions in the observability matrix O, O 33 is the block matrix of 3×3 dimensions in the observability matrix O,
Figure BDA0003494433780000095
is the rotation matrix from the orbit system to the camera system at time k,
Figure BDA0003494433780000096
is the unit direction vector of the target in the camera system at time k,
Figure BDA0003494433780000097
is the rotation matrix from the orbit system to the camera system at time k+1,
Figure BDA0003494433780000098
is the rotation matrix from the orbit system to the camera system at time k+2,
Figure BDA0003494433780000099
is the ratio of the target position vector to the distance at time k+1,
Figure BDA00034944337800000910
is the ratio of the target position vector to the distance at time k+2,
Figure BDA00034944337800000911
is the unit direction vector of the target under the camera system at time k+1,
Figure BDA00034944337800000912
is the unit direction vector of the target in the camera system at time k+2.

可以看出,若目标在相机系下的方向矢量不变时,系统不满足可观测性。此时需要通过姿态机动使得目标在相机系下方向矢量变化,以满足系统可观测性。It can be seen that if the direction vector of the target under the camera system is unchanged, the system does not satisfy the observability. At this time, it is necessary to change the direction vector of the target under the camera system through attitude maneuvering to meet the observability of the system.

该方法还包括步骤:根据无距离信息的相对运动学方程、统一建模后的观测方程以及可观测性分析结果给出滤波步骤。The method also includes the step of: providing a filtering step according to the relative kinematic equation without distance information, the observation equation after unified modeling and the observability analysis result.

①状态变量一步预测Xk+1,k,其中

Figure BDA0003494433780000101
其中,Xk+1,k为k时刻对下一时刻状态变量的预测值,Xk为k时刻状态变量的估计值,αk为k时刻系统误差。①The state variable predicts X k+1,k in one step, where
Figure BDA0003494433780000101
Among them, X k+1,k is the predicted value of the state variable at time k at the next time, X k is the estimated value of the state variable at time k, and α k is the system error at time k.

②状态协方差一步预测值Pk+1,k②State covariance one-step predicted value P k+1,k :

Figure BDA0003494433780000102
Figure BDA0003494433780000102

式中,Φk+1,k为k到k+1時刻的状态转移矩阵,Qk为k时刻的状态噪声协方差,Pk+1,k为k时刻对下一时刻状态协方差矩阵的预测值,Pk为k时刻的状态协方差矩阵。In the formula, Φ k+1,k is the state transition matrix from time k to k+1, Q k is the state noise covariance at time k, P k+1,k is the state covariance matrix at time k to the next time. Predicted value, P k is the state covariance matrix at time k.

③计算增益矩阵Kk③Calculate the gain matrix K k :

Figure BDA0003494433780000103
Figure BDA0003494433780000103

式中,Hk为k时刻的测量矩阵,Rk为k时刻的测量噪声协方差;where H k is the measurement matrix at time k, and R k is the measurement noise covariance at time k;

④实际测量值归一化后得ζk+1④The actual measured value is normalized to get ζ k+1 :

Figure BDA0003494433780000104
Figure BDA0003494433780000104

其中,ζk+1为k+1时刻目标相对方向矢量的测量值,uk+1为k+1时刻目标在像面横轴上的坐标值,vk+1为k+1时刻目标在像面纵轴上的坐标值。Among them, ζ k+1 is the measured value of the relative direction vector of the target at time k+1, u k+1 is the coordinate value of the target on the horizontal axis of the image plane at time k+1, and v k+1 is the target at time k+1. The coordinate value on the vertical axis of the image plane.

⑤状态变量更新:⑤ State variable update:

Figure BDA0003494433780000105
Figure BDA0003494433780000105

⑥状态协方差更新⑥ State covariance update

Pk+1=(I9-KkHk)Pk+1,kP k+1 =(I 9 -K k H k )P k+1,k ;

其中,Pk+1为k+1时刻的状态协方差矩阵,I9为9维单位矩阵。Among them, P k+1 is the state covariance matrix at time k+1, and I 9 is a 9-dimensional identity matrix.

试验结果test results

图2是本发明实施例提供的系统误差统一建模后的滤波估计误差的曲线示意图;图3是本发明实施例提供的相对导航状态变量r/|r|的滤波估计误差的曲线示意图;图4是本发明实施例提供的相对导航状态变量

Figure BDA0003494433780000111
的滤波估计误差的曲线示意图。如图2至图4所示:FIG. 2 is a schematic diagram of a curve of the filtering estimation error after the unified modeling of the system error provided by an embodiment of the present invention; FIG. 3 is a schematic diagram of a curve of the filtering estimation error of the relative navigation state variable r/|r| provided by an embodiment of the present invention; FIG. 4 is the relative navigation state variable provided by the embodiment of the present invention
Figure BDA0003494433780000111
Schematic diagram of the curve of the filtered estimation error. As shown in Figure 2 to Figure 4:

航天器与非合作目标的轨道六根数如表1所示,实验所需参数如表2所示。The number of orbits of the spacecraft and the non-cooperative target is shown in Table 1, and the parameters required for the experiment are shown in Table 2.

表1轨道六根数Table 1 Number of six rails

Figure BDA0003494433780000112
Figure BDA0003494433780000112

表2实验参数Table 2 Experimental parameters

Figure BDA0003494433780000113
Figure BDA0003494433780000113

根据统一建模方法,可知统一建模后的等效旋转矢量为α=[5.20,8.69,3.49]T(单位:rad),按照滤波方法可得基于统一建模的自主相对导航估计误差统计结果,如表3所示。According to the unified modeling method, it can be seen that the equivalent rotation vector after unified modeling is α=[5.20, 8.69, 3.49] T (unit: rad). According to the filtering method, the statistical results of the autonomous relative navigation estimation error based on unified modeling can be obtained. ,as shown in Table 3.

表3估计误差统计结果Table 3 Estimation error statistics

Figure BDA0003494433780000114
Figure BDA0003494433780000114

本实施例还提供了一种种基于旋转参考坐标系的导航系统误差统一建模系统,该系统包括:第一模块,用于利用等效旋转矢量表示相机的安装误差;第二模块,用于根据相机测量原理得到相机像面平移误差;第三模块,用于利用旋转参考坐标系将相机像面平移误差转化为等效旋转矢量形式的相机像面平移误差;第四模块,用于根据等效旋转矢量形式的相机像面平移误差和相机的安装误差得到统一建模后的系统误差。This embodiment also provides a variety of unified modeling systems for navigation system errors based on a rotating reference coordinate system. The system includes: a first module, used to represent the installation error of the camera by using an equivalent rotation vector; a second module, used according to The camera measurement principle is used to obtain the translation error of the camera image plane; the third module is used to convert the translation error of the camera image plane into the camera image plane translation error in the form of an equivalent rotation vector by using the rotating reference coordinate system; the fourth module is used according to the equivalent The translation error of the camera image plane and the installation error of the camera in the form of the rotation vector are the systematic errors after unified modeling.

本发明通过系统误差统一建模特征,实现了系统误差统一降维表征,降低了计算复杂度,可满足航天器上受限的计算能力;本发明通过统一建模后系统误差的可观测性分析,给出了系统满足可观测性的情况,在满足系统可观测性的前提下进行估计,保证了滤波的收敛性;本发明通过在系统误差统一建模以及可观测性分析后,给出了对应的滤波步骤,可实现航天器导航系统误差的自校正。Through the unified modeling feature of the system error, the invention realizes the unified dimensionality reduction representation of the system error, reduces the computational complexity, and can meet the limited computing capability on the spacecraft; the invention analyzes the observability of the system error after the unified modeling , the situation that the system satisfies the observability is given, and the estimation is carried out on the premise of satisfying the observability of the system, which ensures the convergence of the filtering; the present invention provides a unified modeling and observability analysis of the system error after the The corresponding filtering step can realize the self-correction of the spacecraft navigation system error.

本发明虽然已以较佳实施例公开如上,但其并不是用来限定本发明,任何本领域技术人员在不脱离本发明的精神和范围内,都可以利用上述揭示的方法和技术内容对本发明技术方案做出可能的变动和修改,因此,凡是未脱离本发明技术方案的内容,依据本发明的技术实质对以上实施例所作的任何简单修改、等同变化及修饰,均属于本发明技术方案的保护范围。Although the present invention has been disclosed above with preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can use the methods and technical contents disclosed above to improve the present invention without departing from the spirit and scope of the present invention. The technical solutions are subject to possible changes and modifications. Therefore, any simple modifications, equivalent changes and modifications made to the above embodiments according to the technical essence of the present invention without departing from the content of the technical solutions of the present invention belong to the technical solutions of the present invention. protected range.

Claims (10)

1.一种基于旋转参考坐标系的导航系统误差统一建模方法,其特征在于,所述方法包括如下步骤:1. a unified modeling method of navigation system error based on rotating reference coordinate system, is characterized in that, described method comprises the steps: (1)利用等效旋转矢量表示相机的安装误差;(1) Use the equivalent rotation vector to represent the installation error of the camera; (2)根据相机测量原理得到相机像面平移误差;(2) According to the camera measurement principle, the translation error of the camera image plane is obtained; (3)利用旋转参考坐标系将相机像面平移误差转化为等效旋转矢量形式的相机像面平移误差;(3) Using the rotation reference coordinate system to convert the translation error of the camera image plane into the translation error of the camera image plane in the form of an equivalent rotation vector; (4)根据等效旋转矢量形式的相机像面平移误差和相机的安装误差得到统一建模后的系统误差。(4) According to the translation error of the camera image plane and the installation error of the camera in the form of the equivalent rotation vector, the system error after unified modeling is obtained. 2.根据权利要求1所述的基于旋转参考坐标系的导航系统误差统一建模方法,其特征在于:在步骤(1)中,相机的安装误差矩阵Cins为:2. the unified modeling method of navigation system error based on the rotating reference coordinate system according to claim 1, is characterized in that: in step (1), the installation error matrix C ins of camera is: Cins=I3+[θ×];C ins =I 3 +[θ×]; 其中,I3为3维单位矩阵,θ为相机的安装误差。Among them, I 3 is a 3-dimensional unit matrix, and θ is the installation error of the camera. 3.根据权利要求1所述的基于旋转参考坐标系的导航系统误差统一建模方法,其特征在于:在步骤(3)中,利用旋转参考坐标系将相机像面平移误差转化为等效旋转矢量形式的相机像面平移误差包括如下步骤:3. the unified modeling method of navigation system error based on the rotating reference coordinate system according to claim 1, is characterized in that: in step (3), utilize the rotating reference coordinate system to convert the camera image plane translation error into equivalent rotation The camera image plane translation error in vector form includes the following steps: (31)得到统一的等效旋转轴;(31) Obtain a unified equivalent rotation axis; (32)根据相机像面平移误差和相机焦距得到统一的等效旋转轴下的旋转角度;(32) According to the translation error of the camera image plane and the focal length of the camera, the rotation angle under the unified equivalent rotation axis is obtained; (33)根据统一的等效旋转轴和统一的等效旋转轴下的旋转角度得到等效旋转矢量形式的相机像面平移误差。(33) According to the unified equivalent rotation axis and the rotation angle under the unified equivalent rotation axis, the translation error of the camera image plane in the form of the equivalent rotation vector is obtained. 4.根据权利要求3所述的基于旋转参考坐标系的导航系统误差统一建模方法,其特征在于:在步骤(31)中,统一的等效旋转轴为l=[δvu 0]T;其中,l为统一的等效旋转轴,δv为相机光轴在像面纵向方向的平移量,δu为相机光轴在像面横向方向的平移量。4. The method for unified modeling of navigation system errors based on a rotating reference coordinate system according to claim 3, characterized in that: in step (31), the unified equivalent rotation axis is l=[δ v −δ u 0 ] T ; where, l is the uniform equivalent rotation axis, δ v is the translation amount of the camera optical axis in the longitudinal direction of the image plane, and δ u is the translation amount of the camera optical axis in the lateral direction of the image plane. 5.根据权利要求3所述的基于旋转参考坐标系的导航系统误差统一建模方法,其特征在于:在步骤(32)中,统一的等效旋转轴下的旋转角度为:5. the unified modeling method of the navigation system error based on the rotating reference coordinate system according to claim 3, is characterized in that: in step (32), the rotation angle under the unified equivalent rotation axis is:
Figure FDA0003494433770000021
Figure FDA0003494433770000021
其中,φ为统一的等效旋转轴下的旋转角度,f为相机焦距长度,δv为相机光轴在像面纵向方向的平移量,δu为相机光轴在像面横向方向的平移量。Among them, φ is the rotation angle under the unified equivalent rotation axis, f is the focal length of the camera, δ v is the translation amount of the camera optical axis in the longitudinal direction of the image plane, and δ u is the translation amount of the camera optical axis in the lateral direction of the image plane .
6.根据权利要求3所述的基于旋转参考坐标系的导航系统误差统一建模方法,其特征在于:在步骤(33)中,等效旋转矢量形式的相机像面平移误差为:6. the unified modeling method of navigation system error based on rotating reference coordinate system according to claim 3, is characterized in that: in step (33), the camera image plane translation error of equivalent rotation vector form is:
Figure FDA0003494433770000022
Figure FDA0003494433770000022
其中,β为等效旋转矢量形式的相机像面平移误差,l为统一的等效旋转轴,φ为统一的等效旋转轴下的旋转角度。Among them, β is the translation error of the camera image plane in the form of an equivalent rotation vector, l is the unified equivalent rotation axis, and φ is the rotation angle under the unified equivalent rotation axis.
7.根据权利要求1所述的基于旋转参考坐标系的导航系统误差统一建模方法,其特征在于:在步骤(4)中,统一建模后的系统误差为:7. the unified modeling method of navigation system error based on rotating reference coordinate system according to claim 1, is characterized in that: in step (4), the systematic error after unified modeling is: α=θ+β;α=θ+β; 其中,α为统一建模后的系统误差,θ为相机的安装误差,β为等效旋转矢量形式的相机像面平移误差。Among them, α is the systematic error after unified modeling, θ is the installation error of the camera, and β is the translation error of the camera image plane in the form of an equivalent rotation vector. 8.一种基于旋转参考坐标系的导航系统误差统一建模系统,其特征在于包括:8. A unified modeling system for navigation system errors based on a rotating reference coordinate system, characterized in that it comprises: 第一模块,用于利用等效旋转矢量表示相机的安装误差;The first module is used to represent the installation error of the camera by using the equivalent rotation vector; 第二模块,用于根据相机测量原理得到相机像面平移误差;The second module is used to obtain the translation error of the camera image plane according to the camera measurement principle; 第三模块,用于利用旋转参考坐标系将相机像面平移误差转化为等效旋转矢量形式的相机像面平移误差;The third module is used to convert the translation error of the camera image plane into the translation error of the camera image plane in the form of an equivalent rotation vector by using the rotation reference coordinate system; 第四模块,用于根据等效旋转矢量形式的相机像面平移误差和相机的安装误差得到统一建模后的系统误差。The fourth module is used to obtain the system error after unified modeling according to the translation error of the camera image plane and the installation error of the camera in the form of an equivalent rotation vector. 9.根据权利要求8所述的基于旋转参考坐标系的导航系统误差统一建模系统,其特征在于:相机的安装误差矩阵Cins为:9. The navigation system error unified modeling system based on the rotating reference coordinate system according to claim 8, is characterized in that: the installation error matrix C ins of the camera is: Cins=I3+[θ×];C ins =I 3 +[θ×]; 其中,I3为3维单位矩阵,θ为相机的安装误差。Among them, I 3 is a 3-dimensional unit matrix, and θ is the installation error of the camera. 10.根据权利要求8所述的基于旋转参考坐标系的导航系统误差统一建模系统,其特征在于:利用旋转参考坐标系将相机像面平移误差转化为等效旋转矢量形式的相机像面平移误差包括如下步骤:10. The unified navigation system error modeling system based on a rotating reference coordinate system according to claim 8, characterized in that: using the rotating reference coordinate system to convert the camera image plane translation error into the camera image plane translation in the form of an equivalent rotation vector Errors include the following steps: (31)得到统一的等效旋转轴;(31) Obtain a unified equivalent rotation axis; (32)根据相机像面平移误差和相机焦距得到统一的等效旋转轴下的旋转角度;(32) According to the translation error of the camera image plane and the focal length of the camera, the rotation angle under the unified equivalent rotation axis is obtained; (33)根据统一的等效旋转轴和统一的等效旋转轴下的旋转角度得到等效旋转矢量形式的相机像面平移误差。(33) According to the unified equivalent rotation axis and the rotation angle under the unified equivalent rotation axis, the translation error of the camera image plane in the form of the equivalent rotation vector is obtained.
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