Relative navigation method and system of spacecraft

Abstract

The invention discloses a relative navigation method and system for a spacecraft, and relates to the technical field of spacecraft navigation, and the method comprises the following steps: obtaining a relative target unit measurement value of the spacecraft through a satellite-borne sensor; constructing a system unified error model; establishing a spacecraft augmented state system; establishing a forecasting module of a spacecraft augmented state system; calculating a filtering gain coefficient matrix; according to the spacecraft augmented state forecast value, the spacecraft augmented state forecast error covariance matrix and the filtering gain coefficient matrix, obtaining an updating result of the spacecraft augmented state estimated value; and the relative position of the spacecraft, the relative speed of the spacecraft, the dynamic disturbance force borne by the spacecraft and the estimated value of the error of unified modeling are obtained. The relative navigation system is used for implementing the relative navigation method. According to the method, augmented state estimation update under relative navigation is established, dynamic disturbing force is actively estimated, system errors of modeling are unified, and the estimation precision of the relative position of the spacecraft is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of spacecraft navigation, and in particular to a relative navigation method and system for spacecraft. Background Art

[0002] Currently, using relative information such as the relative distance and relative line-of-sight angle between spacecraft is a typical autonomous navigation method. Navigation using relative information involves transformation relationships in multiple coordinate systems such as the sensor coordinate system and the spacecraft body coordinate system, which need to be characterized by rotation matrices. However, there are deviations in the calculation accuracy of rotation matrices. At the same time, navigation using relative information depends on the measurement results of ranging devices. When the system operates for a long time, the ranging devices will form cumulative deviation amounts, affecting the positioning accuracy.

[0003] At the same time, in addition to various deviations in the measurement level, the measurement data often contains random noise. At the same time, the spacecraft will be affected by various disturbances in space, and the dynamic equation generates unmodeled uncertainty terms. Existing spacecraft navigation methods do not comprehensively consider the effects of measurement deviation, measurement noise, and dynamic uncertainty, and cannot overcome the above-mentioned multiple uncertainties at the same time.

[0004] Therefore, in the case of relative information navigation, it is necessary to consider the influence of rotation matrix deviation and ranging device cumulative error on the navigation result, and it is necessary to design a relative information autonomous navigation method that can correct various deviations in the measurement level, which has the ability of active estimation or adaptability. Summary of the Invention

[0005] In order to solve the existing problems such as low navigation and positioning accuracy, the present invention provides a relative navigation method and system for spacecraft; in the scenario of spacecraft relative information navigation, the influences of measurement deviation, measurement noise, and dynamic uncertainty are comprehensively considered, and through unified modeling of observation errors and augmented estimation methods, active estimation of dynamic disturbance forces and systematically modeled systematic errors is realized, and the relative navigation accuracy of the spacecraft is improved.

[0006] In order to achieve the purpose of the present invention, the following scheme is adopted in the present invention:

[0007] A relative navigation method for a spacecraft, comprising the following steps: Step S1, obtaining the relative target unit measurement value of the spacecraft through an on-board sensor; Step S2, constructing a unified error model based on the relative target unit measurement value through unified modeling; Step S3, obtaining the discrete equations of the spacecraft dynamics and measurement under dynamic interference and the discrete equation of the augmented state based on the spacecraft dynamics formula, and establishing a spacecraft augmented state system; Step S4, establishing a prediction module for the spacecraft augmented state system; Step S5, calculating a filter gain coefficient matrix according to the spacecraft augmented state prediction error covariance matrix; Step S6, obtaining an updated result of the spacecraft augmented state estimate according to the spacecraft augmented state prediction value, the spacecraft augmented state prediction error covariance matrix, and the filter gain coefficient matrix; Step S7, obtaining the estimated values of the relative position of the spacecraft, the relative velocity of the spacecraft, the dynamic interference force received by the spacecraft, and the error of the unified modeling according to the updated spacecraft augmented state estimate value.

[0008] Based on the above technical solution, further, in Step S1, the relative target unit measurement value of the spacecraft is defined as Y(t), and the acquisition process of Y(t) is as follows:

[0009]

[0010] where N(t) ∈ R 3 , representing the random noise of the relative position measurement of the spacecraft in the sensor coordinate system at time t, R 3 represents three-dimensional real space; p C represents the distance vector from the center of the sensor coordinate system to the target centroid in the sensor coordinate system; |p C | represents the Euclidean norm of the vector p C ; X B represents the distance vector from the center of the body coordinate system to the target in this system; X represents the relative position of the spacecraft in the orbital system; d B represents the distance vector between the origins of the sensor coordinate system and the body coordinate system in this system; represents the rotation matrix from Γ O to Γ B ; represents the rotation matrix from Γ B to Γ C ; where Γ O represents the orbital coordinate system, Γ B represents the body coordinate system, Γ C represents the on-board sensor coordinate system;

[0011] The finally obtained relative target unit measurement value Y(t) through comprehensive calculation is:

[0012] Wherein, T represents the transpose of a matrix or a vector; I3 represents a 3×3 identity matrix.

[0013] Based on the above technical solution, further, in step S2, the construction process of the unified error model is as follows:

[0014] Wherein, represents the nominal value of Y(t); represents the nominal value of; represents d B the nominal value of; represents p C the nominal value of; The vector α represents the error of unified modeling.

[0015] Based on the above technical solution, further, in step S3, the process of obtaining the discrete equations of spacecraft dynamics and measurement under dynamic interference is as follows:

[0016] Wherein, h represents the sampling step; X k+1 represents the relative position of the spacecraft at the (k + 1)-th sampling step; X k represents the relative position of the spacecraft at the k-th sampling step; V k+1 represents the relative velocity of the spacecraft at the (k + 1)-th sampling step; V k represents the relative velocity of the spacecraft at the k-th sampling step; F k represents the active driving force of the spacecraft at the k-th sampling step; D k represents the dynamic interference force received by the spacecraft at the k-th sampling step; Y k represents the position measurement value of the spacecraft at the k-th sampling step; N k represents the random noise of the spacecraft position measurement at the k-th sampling step.

[0017] Based on the above technical solution, further, in step S3, by introducing an augmented state including the relative position of the spacecraft, the relative velocity of the spacecraft, the dynamic interference force received by the spacecraft, the modeling error and its reciprocal, the discrete equation of the augmented state is expressed as:

[0018]

[0019] Wherein, Z k+1 represents the augmented state of the spacecraft at the (k + 1)-th sampling step; Z k represents the augmented state of the spacecraft at the k-th sampling step; A represents the augmented state system matrix of the spacecraft; B represents the external input matrix of the augmented state system of the spacecraft; C represents the measurement matrix of the augmented state system of the spacecraft.

[0020] Based on the above technical solution, further, in step S4, the prediction module includes the predicted value of the augmented state of the spacecraft and the predicted error covariance matrix of the augmented state of the spacecraft, and the establishment process is as follows:

[0021]

[0022] In the formula, represents the predicted value of the augmented state of the spacecraft at the (k + 1)-th sampling step; represents the estimated value of the augmented state of the spacecraft at the k-th sampling step; represents the predicted error covariance matrix of the augmented state of the spacecraft at the (k + 1)-th sampling step; P k represents the estimated error covariance matrix of the augmented state of the spacecraft at the k-th sampling step.

[0023] Based on the above technical solution, further, in step S5, the calculation process of the filtering gain coefficient matrix is as follows: In the formula, K k+1 represents the estimated gain coefficient matrix of the spacecraft at the (k + 1)-th sampling step; Q k+1 represents the measurement noise covariance matrix of the spacecraft at the (k + 1)-th sampling step.

[0024] Based on the above technical solution, further, in step S6, the process of obtaining the updated result of the estimated value of the augmented state of the spacecraft is as follows:

[0025] In the formula, I 15 represents a 15×15 identity matrix; represents the estimated value of the augmented state of the spacecraft at the (k + 1)-th sampling step; P k+1 represents the estimated error covariance matrix of the augmented state of the spacecraft at the (k + 1)-th sampling step.

[0026] Based on the above technical solution, further, in step S7, the process is as follows:

[0027]

[0028] Among them, represents the estimated value of the relative position of the spacecraft at the (k + 1)-th sampling step; represents the estimated value of the relative velocity of the spacecraft at the (k + 1)-th sampling step; represents the estimated value of the dynamic interference force acting on the spacecraft at the (k + 1)-th sampling step; represents the estimated value of the systematic error of the unified modeling at the (k + 1)-th sampling step.

[0029] A relative navigation system for a spacecraft, which is used to implement a relative navigation method for a spacecraft. Compared with the prior art, the beneficial effects of the present invention are specifically reflected in:

[0030] (1) First, the present invention establishes the spacecraft dynamics equation under disturbed conditions and the line-of-sight vector measurement equation of the on-board sensor. Secondly, considering the rotation matrix deviation and the cumulative error of the ranging device, the unified modeling of the observation error is carried out, and the unified error model of the system dynamics is established. Then, according to the observation unified error and the dynamic interference force, the augmented state is designed, and the discretized equation under the augmented state is established. Further, a prediction estimation module is designed to realize the prediction of the augmented state under relative navigation. At the same time, according to the predicted value of the augmented state, the estimation gain coefficient matrix is updated. Finally, the update of the augmented state estimation under relative navigation is established, and the dynamic interference force and the systematically modeled error are actively estimated to improve the estimation accuracy of the relative position of the spacecraft.

[0031] (2) The present invention considers the problems of deviation in the calculation of the rotation matrix and cumulative deviation in the measurement of the ranging device during the relative navigation process. Through the unified modeling of the observation error and the introduction of the augmented state, the active estimation of the observation unified error is realized, the influence of the measurement deviation on the relative navigation accuracy is eliminated, and the reliability of the relative navigation is improved. For the situation where the spacecraft is affected by unknown dynamic interference, the augmented state is designed to actively estimate the dynamic interference. And in the link of updating the estimation gain coefficient matrix, the prediction error covariance matrix in the dynamic interference estimation process is used to improve the estimation ability of the dynamic interference, and finally the improvement of the relative navigation accuracy is realized. Description of the Drawings

[0032] Figure 1 is the flow chart of the navigation method of the present invention;

[0033] Figure 2 is the schematic diagram of the relative navigation coordinate system of the spacecraft in the present invention. Detailed Embodiments

[0034] The present invention will be further elaborated and described below in conjunction with the drawings and specific embodiments. The technical features of each embodiment of the present invention can be combined correspondingly without conflict.

[0035] In order to make the above objects, features, and advantages of the present invention more obvious and understandable, the specific embodiments of the present invention will be described in detail below with reference to the drawings. Many specific details are set forth in the following description in order to fully understand the present invention. However, the present invention can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without departing from the connotation of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed below. The technical features of each embodiment of the present invention can be combined correspondingly without conflict.

[0036] Example 1

[0037] Combined with Figure 1 As shown, this embodiment provides a relative navigation method for a spacecraft, which specifically includes the following steps:

[0038] Step S1: Obtain the relative target unit measurement value of the spacecraft through an on-board sensor.

[0039] In this embodiment, the unit line-of-sight vector of the target in the sensor coordinate system is measured through the on-board sensor, that is, the relative target unit measurement value Y(t) of the spacecraft, where Y(t) ∈ R 3 , R 3 represents three-dimensional real space. Due to the influence of random measurement noise of the on-board sensor, the calculation process of obtaining the relative target unit measurement value of the spacecraft is as follows:

[0040]

[0041] In the formula, N(t) ∈ R 3 , which represents the random noise of the relative position measurement of the spacecraft in the sensor coordinate system at time t, where t represents the running time of the system, t ∈ [0, ∞); p C represents the distance vector from the center of the sensor coordinate system to the centroid of the target in the sensor coordinate system; |p C | represents the Euclidean norm of the vector p C ; X B represents the distance vector from the center of the body coordinate system to the target in this system; X ∈ R 3 , which represents the relative position of the spacecraft in the orbital system; d B represents the distance vector between the origins of the sensor coordinate system and the body coordinate system in this system; represents the rotation matrix from Γ O to Γ B ; represents the rotation matrix from Γ B to Γ C ; Among them, combined with Figure 2 as shown, Γ O represents the orbital coordinate system, Γ B represents the body coordinate system, Γ C represents the on-board sensor coordinate system; O O(B) represents the center coordinate of the orbital coordinate system Γ O and the body coordinate system Γ B , and the two coordinate systems have the same center coordinate; O C represents the center coordinate of the on-board sensor coordinate system Γ C .

[0042] The comprehensive calculation process finally obtains the relative target unit measurement value as:

[0043] In the formula, the superscript T represents the transpose of a matrix or vector; I3 represents a 3×3 identity matrix.

[0044] Step S2: Based on the relative target unit measurement value, a unified error model of the system is constructed through unified modeling. Among them, this unified error model is composed of the relative target unit measurement value Y(t) of the spacecraft and its nominal value It should be noted that the system mentioned here refers to the relative navigation system of the spacecraft.

[0045] In this embodiment, due to the long-term operation of the spacecraft, the rotation matrix and the distance vector d B will have the situation of error accumulation. Set the nominal values of the corresponding parameter deviations Finally, it leads to the deviation of the relative target unit measurement value Y(t) from its nominal value Specifically, the calculation process is as follows:

[0046]

[0047] In the formula, represents the nominal value; represents the nominal value of; represents the nominal value of d B ; represents the nominal value of p C ; I3 represents a 3×3 identity matrix, I3∈R 3×3 , this R 3×3 represents a 3×3 physical space matrix; among them, the vector α = [α x α y α z T ∈R 3 is the unified modeling error of the navigation system. The cross product matrix of the vector α is denoted as [α×] and is expressed as follows,

[0048]

[0049] And there is

[0050] where represents the second derivative of α.

[0051] Step S3: Based on the spacecraft dynamics formula, obtain the discrete equations of the spacecraft dynamics and measurement under dynamic interference and the discrete equation of the augmented state, and establish the spacecraft augmented state system.

[0052] In this embodiment, considering the dynamic interference, based on the spacecraft dynamics formula under the orbit system under interference:

[0053]

[0054] In the formula, X(t) ∈ R 3 , representing the relative position of the spacecraft in the orbit system at time t, where represents the derivative of X(t); V(t) ∈ R 3 , representing the relative velocity in the orbit system at time t, where represents the derivative of V(t); M ∈ R, representing the mass of the spacecraft, where R is the set composed of all real numbers; F(t) ∈ R 3 , representing the active driving force of the spacecraft at time t; D(t) ∈ R 3 , which represents the dynamic interference force received by the spacecraft at time t.

[0055] In this embodiment, considering the actual sampling process, discretization is performed to obtain the discrete equations of spacecraft dynamics and measurement under dynamic interference:

[0056]

[0057] Among them, h ∈ R, representing the sampling step; X k+1 ∈ R 3 , representing the relative position of the spacecraft at the (k + 1)-th sampling step; X k ∈ R 3 , representing the relative position of the spacecraft at the k-th sampling step; V k+1 ∈ R 3 , representing the relative velocity of the spacecraft at the (k + 1)-th sampling step; V k ∈ R 3 , representing the relative velocity of the spacecraft at the k-th sampling step; F k ∈ R 3 , representing the active driving force of the spacecraft at the k-th sampling step; D k ∈ R 3 , representing the dynamic interference force received by the spacecraft at the k-th sampling step; Y k ∈ R 3 , the measured value of the relative unit vector of the spacecraft to the target in the sensitive coordinate system at the k-th sampling step; N k ∈ R 3 , representing the random noise of the spacecraft position measurement at the k-th sampling step.

[0058] Furthermore, an augmented state including the relative position of the spacecraft, the relative velocity of the spacecraft, the dynamic interference force received by the spacecraft, the modeling error, and its reciprocal is introduced to obtain the discrete equation representation of the augmented state:

[0059]

[0060] Among them, \(Z\) k+1 \(\in\mathbb{R}\) 15 , represents the augmented state of the spacecraft at the \((k + 1)\)-th sampling step, where \(\mathbb{R}\) 15 represents a 15-dimensional real space; \(Z\) k \(\in\mathbb{R}\) 15 , represents the augmented state of the spacecraft at the \(k\)-th sampling step; \(A\in\mathbb{R}\) 15×15 , represents the augmented state system matrix of the spacecraft; \(B\in\mathbb{R}\) 15×3 , represents the external input matrix of the augmented state system of the spacecraft; \(C\in\mathbb{R}\) 3×15 , represents the measurement matrix of the augmented state system of the spacecraft. Among them, \(\mathbb{R}\) 15×15 represents a \(15\times15\) real space matrix; \(\mathbb{R}\) 3×15 represents a \(3\times15\) real space matrix; \(\mathbb{R}\) 15×3 represents a \(15\times3\) real space matrix.

[0061] Furthermore, \(Z\) k , \(A\), \(B\), and \(C\) satisfy the following expressions:

[0062]

[0063] Among them, \(I_3\in\mathbb{R}\) 3×3 , which represents a \(3\times3\) identity matrix; \(0_3\in\mathbb{R}\) 3×3 , which represents a \(3\times3\) zero matrix.

[0064] Step S4, establish a prediction module for the augmented state system of the spacecraft. Among them, this prediction module includes the predicted value of the augmented state of the spacecraft and the predicted error covariance matrix of the augmented state of the spacecraft.

[0065]

[0066] Among them, represents the predicted value of the augmented state of the spacecraft at the \((k + 1)\)-th sampling step; represents the estimated value of the augmented state of the spacecraft at the \(k\)-th sampling step; represents the predicted error covariance matrix of the augmented state of the spacecraft at the \((k + 1)\)-th sampling step; \(P\) k \(\in\mathbb{R}\) 15×15 , represents the estimated error covariance matrix of the augmented state of the spacecraft at the \(k\)-th sampling step. It should be noted that this \(\mathbb{R}\) 15 represents a 15-dimensional real space.

[0067] Step S5, calculate the filtering gain coefficient matrix according to the predicted error covariance matrix of the augmented state of the spacecraft.

[0068] In this embodiment, the specific calculation process is as follows: where K k+1 ∈R 15 ×3 represents the spacecraft estimation gain coefficient matrix at the (k + 1)-th sampling step;

[0069] Q k+1 ∈R 3×3 represents the spacecraft measurement noise covariance matrix at the (k + 1)-th sampling step.

[0070] Step S6: Obtain the updated result of the spacecraft augmented state estimate based on the spacecraft augmented state prediction value, the spacecraft augmented state prediction error covariance matrix, and the filtering gain coefficient matrix.

[0071] In this embodiment, the specific process is as follows: In the formula,

[0072] I 15 ∈R 15×15 represents a 15×15 identity matrix; represents the spacecraft augmented state estimate at the (k + 1)-th sampling step; P k+1 ∈R 15×15 represents the spacecraft augmented state estimation error covariance matrix at the (k + 1)-th sampling step.

[0073] Step S7: Obtain the estimated values of the spacecraft relative position, the spacecraft relative velocity, the dynamic interference force acting on the spacecraft, and the error of the unified modeling based on the updated spacecraft augmented state estimate:

[0074]

[0075] where represents the estimated value of the spacecraft relative position at the (k + 1)-th sampling step; represents the estimated value of the spacecraft relative velocity at the (k + 1)-th sampling step; represents the estimated value of the dynamic interference force acting on the spacecraft at the (k + 1)-th sampling step; represents the estimated value of the system error of the unified modeling at the (k + 1)-th sampling step.

[0076] In this embodiment, through the above filtering estimates obtained, a high-precision autonomous relative navigation effect can be achieved. Among them, the smaller the estimated value, the better the navigation effect.

[0077] The present invention aims at the problem of autonomous relative navigation of spacecraft under unknown dynamic interference forces, and provides an autonomous navigation method for spacecraft with active perception of interference forces, realizing the active estimation of the relative position, relative velocity, interference forces and unified modeling errors of the spacecraft. It mainly includes the design of the augmented state of the spacecraft in the sampling scenario and its discrete equation representation, the prediction module of the augmented state system of the spacecraft, the calculation process of the estimation gain coefficient matrix, the update module of the estimated value of the augmented state of the spacecraft, etc. First, the relative dynamics equation of the spacecraft under dynamic interference forces and the position measurement equation of the spacecraft under random noise are established, and a unified error model of the system is established. Secondly, the discrete equations of the relative dynamics and measurement of the spacecraft in the sampling scenario are given, and the discrete equation of the augmented state of the spacecraft is established by introducing the augmented state of the spacecraft. Then, the prediction module of the augmented state system of the spacecraft is designed, and further, according to the prediction error covariance matrix of the augmented state of the spacecraft, the estimation gain coefficient matrix is calculated. Then, according to the predicted value of the augmented state of the spacecraft, the prediction error covariance matrix of the augmented state of the spacecraft, and the filtering gain coefficient matrix, the updated result of the estimated value of the augmented state of the spacecraft is given. Finally, according to the estimated value of the augmented state of the spacecraft, the estimated values of the position of the spacecraft, the velocity of the spacecraft, and the dynamic interference forces received by the spacecraft are obtained.

[0078] In other embodiments, a relative navigation system for a spacecraft is further provided, which is used to execute the relative navigation method for the spacecraft provided above.

[0079] The above are only the embodiments of the present invention, and the description thereof is relatively specific and detailed, but it should not be construed as a limitation on the scope of the patent of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several modifications and improvements can still be made, and these all belong to the protection scope of the present invention.

Claims

1. A relative navigation method for a spacecraft, characterized in that: The following steps are involved: Step S1, obtaining a relative target unit measurement value of a spacecraft through a satellite-borne sensor; Step S2, performing unified modeling based on the relative target unit measurement value to construct a unified error model; Step S3, based on the spacecraft dynamics formula, obtaining the discrete equations of spacecraft dynamics and measurement under dynamic interference and the discrete equation of augmented state, and establishing a spacecraft augmented state system; Step S4, establishing a prediction module of a spacecraft augmented state system; Step S5, calculating the filter gain coefficient matrix according to the spacecraft augmented state prediction error covariance matrix; Step S6, obtaining an update result of the spacecraft augmented state estimation value according to the spacecraft augmented state prediction value, the spacecraft augmented state prediction error covariance matrix, and the filter gain coefficient matrix; Step S7: Obtain estimated values ​​of the spacecraft relative position, spacecraft relative velocity, dynamic disturbance force on the spacecraft, and unified modeling error based on the updated spacecraft augmented state estimate.

2. A relative navigation method for a spacecraft according to claim 1, characterized in that: In step S1, the relative target unit measurement value of the spacecraft is defined as Y(t), and the process of obtaining Y(t) is as follows: Where N(t) represents the random noise of the relative position measurement of the spacecraft in the sensor coordinate system at time t; C represents the distance vector from the center of the sensor coordinate system to the target mass center in the sensor coordinate system; |p C | represents vector p C The Euclidean norm of B represents the distance vector from the center of the body coordinate system to the target mass center in this system; X represents the relative position of the spacecraft in the orbital system; d B Represents the distance vector between the origin of the sensor coordinate system and the body coordinate system in this system; Represents Γ O to Γ B The rotation matrix of Represents Γ B to Γ C The rotation matrix of O represents the orbital coordinate system, Γ B represents the body coordinate system, Γ C represents the sensor coordinate system; the relative target unit measurement value Y(t) obtained by comprehensive calculation is: Wherein, T represents the transpose of a matrix or vector; I3 represents a 3×3 unit matrix.

3. A relative navigation method for a spacecraft according to claim 2, characterized in that: In step S2, the construction process of the unified error model is: In the formula, represents the nominal value of Y(t); express The nominal value of Indicates d B The nominal value of Indicates p C The nominal value of ; the vector α represents the error of unified modeling.

4. A relative navigation method for a spacecraft according to claim 3, characterized in that: In step S3, the process of obtaining the discrete equations of spacecraft dynamics and measurement under dynamic disturbance is: In the formula, h represents the sampling step; X k+1 represents the relative position of the spacecraft at the k+1th sampling step; X k represents the relative position of the spacecraft at the kth sampling step; V k+1 represents the relative velocity of the spacecraft at the k+1th sampling step; V k represents the relative velocity of the spacecraft at the kth sampling step; F k represents the active driving force of the spacecraft at the kth sampling step; D k represents the dynamic disturbance force on the spacecraft at the kth sampling step; Y k N represents the measured value of the spacecraft position at the kth sampling step; k represents the random noise of the spacecraft position measurement at the kth sampling step.

5. A relative navigation method for a spacecraft according to claim 4, characterized in that: In step S3, an augmented state including the relative position of the spacecraft, the relative speed of the spacecraft, the dynamic disturbance force on the spacecraft, the modeling error and its reciprocal is introduced, and the discrete equation of the augmented state is expressed as: In the formula, Z k+1 represents the spacecraft augmented state at the k+1th sampling step; Z k represents the spacecraft augmented state at the kth sampling step; A represents the spacecraft augmented state system matrix; B represents the external input matrix of the spacecraft augmented state system; C represents the measurement matrix of the spacecraft augmented state system.

6. A relative navigation method for a spacecraft according to claim 5, characterized in that: In step S4, the prediction module includes the spacecraft augmented state prediction value and the spacecraft augmented state prediction error covariance matrix, and the establishment process is: In the formula, represents the predicted value of the spacecraft augmented state at the k+1th sampling step; represents the estimated value of the spacecraft augmented state at the kth sampling step; represents the spacecraft augmented state prediction error covariance matrix at the k+1th sampling step; P k represents the spacecraft augmented state estimation error covariance matrix at the kth sampling step.

7. A relative navigation method for a spacecraft according to claim 6, characterized in that: In step S5, the calculation process of the filter gain coefficient matrix is: In the formula, K k+1 represents the spacecraft estimated gain coefficient matrix at the k+1th sampling step; Q k+1 represents the spacecraft measurement noise covariance matrix at the k+1th sampling step.

8. A relative navigation method for a spacecraft according to claim 7, characterized in that: In step S6, the process of obtaining the updated result of the spacecraft augmented state estimate is as follows: In the formula, I 15 represents the 15×15 identity matrix; represents the estimated value of the spacecraft augmented state at the k+1th sampling step; P k+1 Represents the spacecraft augmented state estimation error covariance matrix at the k+1th sampling step.

9. A relative navigation method for a spacecraft according to claim 8, characterized in that: In step S7, the process is: in, represents the estimated relative position of the spacecraft at the k+1th sampling step; represents the estimated value of the spacecraft relative velocity at the k+1th sampling step; represents the estimated value of the dynamic disturbance force on the spacecraft at the k+1th sampling step; Represents the systematic error estimate of unified modeling at the k+1th sampling step.

10. A relative navigation system for a spacecraft, characterized in that: Used to execute a relative navigation method for a spacecraft as described in any one of claims 1-9.

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