CN116734864B - Autonomous relative navigation method for spacecraft under constant observed deviation condition - Google Patents

Autonomous relative navigation method for spacecraft under constant observed deviation condition Download PDF

Info

Publication number
CN116734864B
CN116734864B CN202311017608.0A CN202311017608A CN116734864B CN 116734864 B CN116734864 B CN 116734864B CN 202311017608 A CN202311017608 A CN 202311017608A CN 116734864 B CN116734864 B CN 116734864B
Authority
CN
China
Prior art keywords
relative
time
constant
deviation
measurement
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202311017608.0A
Other languages
Chinese (zh)
Other versions
CN116734864A (en
Inventor
杨杰
贺波勇
陈刚
刘斌
汪彬
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
China Xian Satellite Control Center
Original Assignee
China Xian Satellite Control Center
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by China Xian Satellite Control Center filed Critical China Xian Satellite Control Center
Priority to CN202311017608.0A priority Critical patent/CN116734864B/en
Publication of CN116734864A publication Critical patent/CN116734864A/en
Application granted granted Critical
Publication of CN116734864B publication Critical patent/CN116734864B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/20—Instruments for performing navigational calculations
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64G—COSMONAUTICS; VEHICLES OR EQUIPMENT THEREFOR
    • B64G1/00—Cosmonautic vehicles
    • B64G1/22—Parts of, or equipment specially adapted for fitting in or to, cosmonautic vehicles
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/24—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 specially adapted for cosmonautical navigation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Remote Sensing (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Mathematical Physics (AREA)
  • Mathematical Optimization (AREA)
  • Pure & Applied Mathematics (AREA)
  • Computational Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Theoretical Computer Science (AREA)
  • Data Mining & Analysis (AREA)
  • Databases & Information Systems (AREA)
  • Algebra (AREA)
  • Automation & Control Theory (AREA)
  • Software Systems (AREA)
  • General Engineering & Computer Science (AREA)
  • Operations Research (AREA)
  • Aviation & Aerospace Engineering (AREA)
  • Astronomy & Astrophysics (AREA)
  • Computing Systems (AREA)
  • Navigation (AREA)

Abstract

The disclosure relates to an autonomous relative navigation method of a spacecraft under a constant observed deviation condition. The method comprises the following steps: acquiring an initial relative motion state of a slave spacecraft; calculating a numerical integral of the relative motion state of the slave spacecraft according to the nonlinear orbit dynamics model; based on a Kalman filtering calculation model, taking a relative measured constant observation deviation as an estimation object, and taking a relative measured random error as a correction condition; obtaining a corrected relative motion state through a nonlinear orbit dynamics model and a Kalman filtering calculation model; and performing iterative computation to obtain a final relative motion state. The present disclosure obtains a high-precision numerical solution by employing a nonlinear orbit dynamics model. And the relative navigation method has the effects of quickly detecting and inhibiting the relative measured constant observed deviation by means of closed loop calibration and relative measurement extended Kalman filtering calculation strategy for compensating the relative measured constant observed deviation in real time.

Description

Autonomous relative navigation method for spacecraft under constant observed deviation condition
Technical Field
The embodiment of the disclosure relates to the technical field of autonomous navigation of a spacecraft, in particular to an autonomous relative navigation method of the spacecraft under a constant observed deviation condition.
Background
The current autonomous relative navigation technology of the spacecraft is mainly based on the observation of the relative distance and the relative angle of the slave spacecraft by the master spacecraft, a Hill-ClohessyWiltshire, HCW orbit dynamics model of relative motion is often adopted, and the inhibition effect on the random error of relative measurement is difficult to generate. This is mainly limited by two drawbacks: firstly, the HCW orbit dynamics model is basically a first approximation of the gravity of the spacecraft, and has the problems of poor observability and low calculation precision in high-precision navigation filtering calculation; secondly, the constant observed deviations typically contained in the relative measurements fail to estimate the compensation in the relative navigation equations, thereby causing a large relative navigation state error.
Regarding the above technical solution, the applicant found that the following problems exist, and the relative measurement constant observation deviation in the relative navigation method cannot be detected quickly, so that the suppression effect cannot be achieved.
Accordingly, there is a need to improve one or more problems in the related art as described above.
It should be noted that the information disclosed in the above background section is only for enhancing understanding of the background of the present disclosure and thus may include information that does not constitute prior art known to those of ordinary skill in the art.
Disclosure of Invention
An objective of the embodiments of the present disclosure is to provide an autonomous relative navigation method for a spacecraft under a constant observed deviation condition, so as to at least solve one or more problems in the related technical solutions.
The application adopts the following technical scheme:
the application provides an autonomous relative navigation method of a spacecraft under a constant observed deviation condition, which comprises the following steps:
taking the center of the main spacecraft as a reference coordinate system, and acquiring an initial relative motion state of the auxiliary spacecraft; wherein the relative motion state includes a relative position vector and a relative velocity vector;
calculating a numerical integral of the relative motion state of the slave spacecraft according to a nonlinear orbit dynamics model;
based on a Kalman filtering calculation model, taking a relative measured constant observation deviation as an estimation object, and taking a relative measured random error as a correction condition;
obtaining a corrected relative motion state through the nonlinear orbit dynamics model and a Kalman filtering calculation model;
and carrying out iterative computation on the nonlinear orbit dynamics model and the Kalman filtering computation model to obtain a final relative motion state.
Optionally, the step of using the kalman filter based calculation model to observe the deviation from the measured constant value as the estimation object and using the random error from the measurement as the correction condition includes:
the constant observed deviations of the relative measurements include: relative position error, relative velocity error, constant observed deviation of relative distance, constant observed deviation of relative pitch angle, and constant observed deviation of relative azimuth angle.
Optionally, the step of using the kalman filter based calculation model to observe the deviation from the measured constant value as the estimation object and using the random error from the measurement as the correction condition includes:
the random error of the relative measurement includes: random errors in relative distance, random errors in relative azimuth, and random errors in relative pitch.
Optionally, the step of calculating a numerical integral of the relative motion state of the slave spacecraft according to a nonlinear orbit dynamics model comprises:
the equation for the nonlinear orbit dynamics model is expressed as:
wherein k+1 represents the current time, and k represents the time before the current time;is in a relative motion state, and->Is a relative position vector>Is a relative velocity vector; />Is the main spacecraft position vector, and +.>Is the orbit radius of the main spacecraft; />Is a slave spacecraft position vector; />Is the gravitational constant; 0 *×* A matrix with elements of 0; i represents a matrix with all elements being 0 except the main diagonal elements being 1;
by the formula->Obtaining, wherein->Is the orbit motion angular rate of the main spacecraft.
Optionally, the step of using the kalman filter based calculation model to observe the deviation from the measured constant value as the estimation object and using the random error from the measurement as the correction condition includes:
calculating a state transition matrix from the previous moment to the current moment of the constant observation deviation according to the Jacobian matrix of the relative motion state;
determining a state time prediction of the constant observed deviation from a previous time to a current time based on the state transition matrix;
calculating a state covariance time prediction of the state transition matrix from a previous time to a current time, and generating a corresponding gain matrix based on the state covariance time prediction and the relatively measured random error;
calculating an estimated value of a random error of the relative measurement at the current moment;
updating a constant observed deviation of the relative measurement at the current time based on the estimated value of the random error of the relative measurement at the current time, the gain matrix and the state time prediction;
updating the state covariance of the current moment, and accumulating the constant observed deviation of the relative measurement of the current moment to be used for calculating the estimated value of the random error of the relative measurement of the next moment;
and resetting the constant observed deviation of the relative measurement at the current moment and recalculating the constant observed deviation of the relative measurement at the next moment.
Optionally, the step of calculating a state transition matrix from a previous time to a current time of the constant observed deviation according to the jacobian matrix of the relative motion state includes:
jacobian matrix of the relative motion statesThe method comprises the following steps:
wherein,is a relative motion state deflection;
by the formula->Solving, wherein T is represented by formula->Obtaining;
from the slaveTime to->State transition matrix->The method comprises the following steps:
wherein,a period representing a time update;
from the slaveTime to->State time prediction of said constant observed deviation of time instant +.>The method comprises the following steps:
wherein,is->Constant observed deviations of the relative measurements of time of day.
Optionally, the step of calculating a state covariance time prediction of the state transition matrix from a previous time to a current time, and generating a corresponding gain matrix based on the state covariance time prediction, includes:
from the slaveTime to->State covariance time prediction of time of day +.>The method comprises the following steps:
wherein,is->State covariance of time; />Is->A process noise matrix of time;
process noise matrix->The method comprises the following steps:
wherein,by the formula->Obtaining, wherein->Representing the original process noise matrix,/>Representing a process noise distribution matrix->；
Gain matrix +.>The method comprises the following steps:
wherein,by the formula->Obtaining, wherein E [. Times.]A mathematical expectation calculation formula is obtained;representation->Random error of relative measurement of time of day;
wherein,by the formula->The method can be used for obtaining the product,
wherein,；is a relative position vector +.>In the x component; />Is a relative position vector +.>At the y component; />Is a relative position vector +.>In the z component;a measurement representing the relative distance; a represents a measurement of relative azimuth; e represents a measurement of the relative pitch angle.
Optionally, the step of calculating an estimated value of the random error of the relative measurement at the current time comprises:
estimate of random error of relative measurement of time of day +.>The method comprises the following steps:
wherein,an estimate of the random error of the relative distance; />An estimate of random error of relative azimuth; />An estimate of random error of relative pitch angle; />Is->Relative position vector of time,/>Is thatElement 1 of->Is->Element 2 of->Is->Is the 3 rd element of (2);
wherein,is->An estimate of the relative distance of the moments in time and by the formula +.>Obtaining, wherein->Is->A measure of relative distance from time of day; />Is->Observing deviation of constant values of relative distances at moment;
wherein,is->An estimate of the relative azimuth of the moment and by the formula +.>Obtaining, wherein->Is->A measurement of relative azimuth of time; />Is->Observing deviation of constant values of relative azimuth angles at moment;
wherein,is->Estimated value of relative pitch angle at time and by the formula +.>Obtaining, wherein->Is->A measurement of relative pitch angle at time; />Is->Observing deviation of constant values of relative pitch angles at moment;
constant observed deviation of relative measurement of time of day +.>The updated equation of (2) is:
。
optionally, the step of updating the state covariance at the current moment includes:
state covariance of time of day->The updated equation of (2) is:
。
optionally, the step of accumulating constant observed deviations of the relative measurements at the current time for calculating an estimated value of random error of the relative measurements at the next time comprises:
the cumulative equation for the constant observed bias for the relative measurement of time of day is:
wherein,is->Observing deviation of constant values of relative distances at moment; />For update +.>Constant observed deviation of relative measurement of time of day +.>Is the 7 th element of (2); />Is->Observing deviation of constant values of relative azimuth angles at moment; />For update +.>Constant observed deviation of relative measurement of time of day +.>Is the 8 th element of (2);is->Observing deviation of constant values of relative pitch angles at moment; />For update +.>Constant observed deviation of relative measurement of time of day +.>Is the 9 th element of (c).
In the embodiment of the disclosure, a nonlinear orbit dynamics model is adopted to obtain a high-precision numerical solution, and an extended Kalman filtering calculation strategy for relatively measuring constant observed deviation and compensating the relatively measured constant observed deviation in real time is adopted to realize rapid and accurate estimation of the relative motion state, so that the relative navigation method has rapid detection and inhibition effects on the relatively measured constant observed deviation.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the disclosure.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the disclosure and together with the description, serve to explain the principles of the disclosure. It will be apparent to those of ordinary skill in the art that the drawings in the following description are merely examples of the disclosure and that other drawings may be derived from them without undue effort.
FIG. 1 illustrates a flow diagram of a method for autonomous relative navigation of a spacecraft under constant observed bias conditions in an exemplary embodiment of the disclosure;
FIG. 2 shows a schematic flow diagram based on a Kalman filter calculation model in an exemplary embodiment of the present disclosure;
FIG. 3 illustrates a logic diagram of a spacecraft autonomous relative navigation method under constant observed bias conditions in an exemplary embodiment of the disclosure;
FIG. 4 illustrates a schematic diagram of a relative motion trajectory of a slave spacecraft with respect to a master spacecraft in an exemplary embodiment of the disclosure;
FIG. 5 is a schematic diagram showing simulated calculation results of relative distances in a relative navigation of group 1 in an exemplary embodiment of the present disclosure;
FIG. 6 is a schematic diagram showing simulated calculation results of relative velocity in a relative navigation of group 1 in an exemplary embodiment of the present disclosure;
FIG. 7 is a schematic diagram showing simulated calculation results of constant observed deviations in 1 set of relative navigation in an exemplary embodiment of the present disclosure;
FIG. 8 is a schematic diagram showing simulated calculation results of relative distances in 100 sets of relative navigation in an exemplary embodiment of the present disclosure;
FIG. 9 is a schematic diagram showing simulated calculation results of relative velocity in 100 sets of relative navigation in an exemplary embodiment of the present disclosure;
FIG. 10 is a schematic diagram showing simulated calculation results of 100 sets of constant observed deviations in relative navigation in an exemplary embodiment of the present disclosure;
fig. 11 illustrates a schematic diagram of a storage medium in an exemplary embodiment of the present disclosure.
Detailed Description
Example embodiments will now be described more fully with reference to the accompanying drawings. However, the exemplary embodiments may be embodied in many forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the concept of the example embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.
Furthermore, the drawings are merely schematic illustrations of the present disclosure and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and thus a repetitive description thereof will be omitted. Some of the block diagrams shown in the figures are functional entities and do not necessarily correspond to physically or logically separate entities. These functional entities may be implemented in software or in one or more hardware modules or integrated circuits or in different networks and/or processor devices and/or microcontroller devices.
In this exemplary embodiment, first, a method for autonomous relative navigation of a spacecraft under a constant observed deviation condition is provided, and referring to fig. 1, the method may include the following steps:
step S101: and taking the center of the master spacecraft as a reference coordinate system to acquire the initial relative motion state of the slave spacecraft.
Step S102: numerical integration of the relative motion states from the spacecraft is calculated from the nonlinear orbit dynamics model.
Step S103: the Kalman filtering based calculation model takes the relative measured constant observed deviation as an estimation object and takes the relative measured random error as a correction condition.
Step S104: and obtaining a corrected relative motion state through a nonlinear orbit dynamics model and a Kalman filtering calculation model.
Step S105: and carrying out iterative computation on the nonlinear orbit dynamics model and the Kalman filtering computation model to obtain a final relative motion state.
Wherein the relative motion state includes a relative position vector and a relative velocity vector.
It is to be understood that the constant observed deviations from the measurements include: relative position error, relative velocity error, constant observed deviation of relative distance, constant observed deviation of relative pitch angle, and constant observed deviation of relative azimuth angle.
It is also understood that the random error of the relative measurement includes: random errors in relative distance, random errors in relative azimuth, and random errors in relative pitch.
It should be further understood that, considering the influence of the relative measurement constant observation deviation on the relative motion state, 9 state relative navigation equations are established, unlike the traditional relative navigation equations which generally select the relative position and the relative speed as state variables, the present application selects the relative position error, the relative speed error and the relative measurement constant observation deviation as the system state, and considers the influence of the constant observation deviation on the relative motion state; meanwhile, unlike the traditional relative navigation equation, which usually selects relative measurement as a measured value, the application selects random error of relative measurement as the measured value, so that the state equation and the measured equation of the relative navigation filtering system are both in a linear form, and the application has the characteristic of simple calculation.
It should be further understood that in the framework of the extended kalman filter computing system state transition matrix and the measurement matrix, a relative navigation computing strategy is designed for updating the relative motion state, estimating the relative measurement constant observation deviation and synchronously carrying out the relative measurement random error compensation. Under the high-precision numerical integration constraint condition of the complete nonlinear orbit dynamics model of the relative motion of the master spacecraft and the slave spacecraft, the relative navigation calculation strategy meets the observability constraint of unbiased estimation of the system state, and ensures that the relative navigation state and covariance can be converged to theoretical values.
It is further understood that the autonomous relative navigation method of the spacecraft under the condition of the relative measurement constant observation deviation is suitable for autonomous relative navigation of the near-earth spacecraft in the short-range space, is independent of ground orbit calculation support, has high convergence accuracy of relative navigation states and high calculation speed, and has certain rapid detection and inhibition effects on the relative measurement constant observation deviation.
It should also be understood that in step S101, assuming that the main spacecraft is a circular orbit, the orbit radius r may be obtained in advance c . The local vertical and local horizontal coordinate system, namely the LVLH (local-vertical/local-horizontal) coordinate system is established by taking the geocentric inertial coordinate system as a reference. In the LVLH coordinate system of the main spacecraft, the relative position and relative speed vector of the slave spacecraft relative to the main spacecraft in the short range are. And x, y and z represent relative position vectors, initial values are obtained by directly measuring the spacecraft, and more accurate relative position vectors are obtained by the method provided by the patent. The relative velocity vector is the same. The master spacecraft makes relative measurements to the slave spacecraft, including relative ranging, azimuth and pitch angles, typically with error characteristics of random errors and constant deviations. Therefore, a relative navigation model with 9 states is established, and calculation strategies of relative measurement constant deviation calibration compensation and relative navigation synchronization and parallelism are adopted, so that the performance of autonomous relative navigation of the main spacecraft under the condition of relative measurement constant observation deviation is improved.
It should also be understood that in step S104, the correction of the relative motion state may be expressed as:
（1）
that is to say:
（2）
the relative motion state is obtained through a nonlinear orbit dynamics model; />Obtaining a relative position error and a relative speed error which are obtained through a Kalman filtering calculation model; />The corrected relative motion state.
According to the method, a nonlinear orbit dynamics model is adopted to obtain a high-precision numerical solution, and an extended Kalman filtering calculation strategy for relatively measuring constant observed deviation is calibrated through a closed loop and compensating the relatively measured constant observed deviation in real time, so that the rapid and accurate estimation of the relative motion state is realized, and the relative navigation method has rapid detection and inhibition effects on the relatively measured constant observed deviation.
Next, each step of the above-described method in the present exemplary embodiment will be described in more detail with reference to fig. 1 to 6.
In one embodiment, referring to fig. 3, step S102 may further include:
the equation for the nonlinear orbit dynamics model is expressed as:
（3）
（4）
wherein k+1 represents the current time, and k represents the time before the current time;is in a relative motion state, and->Is a relative position vector>Is a relative velocity vector; />Is the main spacecraft position vector, and +.>Is the orbit radius of the main spacecraft; />Is a slave spacecraft position vector; />Is the gravitational constant; 0 *×* A matrix with elements of 0; i represents a matrix with all elements being 0 except the main diagonal elements being 1;
by the formula->Obtaining, wherein->Is the orbit motion angular rate of the main spacecraft.
It should be understood that in addition to、/>Other variables in the formula are constants, all being a function of time t. Each different time t corresponds to a different r. The time t hereinafter is omitted.
In the calculation of relative navigation filtering, the system state variable quantity is obtained as a constant observed deviation of relative position error, relative speed error, relative distance, relative azimuth angle and relative pitch angle, namely:
these errors can all be obtained simultaneously by simulation settings.
In one embodiment, referring to fig. 2, step S103 may further include:
step S201: and calculating a state transition matrix from the previous moment to the current moment of the constant observed deviation according to the Jacobian matrix of the relative motion state.
Step S202: a state time prediction of a constant observed deviation from a previous time to a current time is determined based on the state transition matrix.
Step S203: calculating a state covariance time prediction of a state transition matrix from a previous time to a current time, and generating a corresponding gain matrix based on the state covariance time prediction and the random error of the relative measurement.
Step S204: an estimate of the random error of the relative measurement at the current time is calculated.
Step S205: the constant observed bias of the relative measurement at the current time is updated based on the estimate of the random error of the relative measurement at the current time, the gain matrix, and the state time prediction.
Step S206: the state covariance at the current time is updated, and the constant observed bias of the relative measurement at the current time is accumulated for calculating an estimate of the random error of the relative measurement at the next time.
Step S207: and resetting the constant observed deviation of the relative measurement at the current moment and recalculating the constant observed deviation of the relative measurement at the next moment.
It should be understood that the process of clearing the constant observed deviation of the relative measurement at the present time in step S207 may be performed by the formulaThe expression is carried out and substituted into the next time.
In one embodiment, in step S201:
jacobian matrix of relative motion statesThe method comprises the following steps:
（6）
wherein,is a relative motion state deflection;
by the formula->Solving, wherein T is represented by formula->Obtaining the product.
It should be understood that the relative measurement noise is assumed to be Gaussian white noiseEstablishing a continuous system state equation representation:
（7）
in a continuous system state matrixExpressed as:
（8）
process noise distribution matrixExpressed as:
（9）/>
process noise vectorThe mean and variance of (a) are:
（10）
the slave in step S201Time to->State transition matrix->The method comprises the following steps:
（11）
wherein,representing the period of the time update.
It is to be understood that the discretized state equation is expressed as:
（12）
from which a slave can be derivedTime to->State transition matrix->State transition matrix->To take a matrix of 6 th order truncated approximations.
In one embodiment, referring to FIG. 3, in step S202:
from the slaveTime to->State time prediction of constant observed deviation of time of day +.>The method comprises the following steps:
（13）
wherein,is->Constant observed deviations of the relative measurements of time of day.
In one embodiment, referring to fig. 3, in step S203:
from the slaveTime to->State covariance time prediction of time of day +.>The method comprises the following steps:
（14）
wherein,is->State covariance of time; />Is->A process noise matrix of time;
process noise matrix->The method comprises the following steps:
（15）
wherein,by the formula->Obtaining, wherein->Representing the original process noise matrix,/>Is expressed byCheng Zaosheng distribution matrix->。
The values are as follows:
（16）
gain matrix +.>The method comprises the following steps: />
（17）
Wherein,by the formula->Obtaining, wherein E [. Times.]A mathematical expectation calculation formula is obtained;representation->Random error of relative measurement of time of day;
wherein,by the formula->The method can be used for obtaining the product,
wherein,；is a relative position vector +.>In the x component; />Is a relative position vector +.>At the y component; />Is a relative position vector +.>In the z component;a measurement representing the relative distance; a represents a measurement of relative azimuth; e represents a measurement of the relative pitch angle.
It should be understood that the measurement model represents:
（18）
in the method, in the process of the application,，/>the random error of the relative distance, the random error of the relative azimuth angle and the random error of the relative pitch angle are respectively.
In one embodiment, referring to FIG. 3, in step S204:
estimate of random error of relative measurement of time of day +.>The method comprises the following steps:
（19）
wherein,an estimate of the random error of the relative distance; />An estimate of random error of relative azimuth; />An estimate of random error of relative pitch angle; />Is->Relative position vector of time,/>Is thatElement 1 of->Is->Element 2 of->Is->Is the 3 rd element of (2);
wherein,is->An estimate of the relative distance of the moments in time and by the formula +.>Obtaining, wherein->Is->A measure of relative distance from time of day; />Is->Observing deviation of constant values of relative distances at moment;
wherein,is->An estimate of the relative azimuth of the moment and by the formula +.>Obtaining, wherein->Is->A measurement of relative azimuth of time; />Is->Observing deviation of constant values of relative azimuth angles at moment;
wherein,is->Estimated value of relative pitch angle at time and by the formula +.>Obtaining, wherein->Is->A measurement of relative pitch angle at time; />Is->The constant value of the relative pitch angle at the moment observes the deviation.
In one embodiment, referring to fig. 3, in step S205:
constant observed deviation of relative measurement of time of day +.>The updated equation of (2) is:
（20）
in one embodiment, referring to fig. 3, in step S206:
state covariance of time of day->The updated equation of (2) is:
（21）
it should be understood that the number of steps,the initial covariance matrix is represented and used in equation (16). When k=0 time, calculate +.>I.e. +.>Use of +.>I.e. +.>. Follow-up when k>At time 0, no more +.>And sequentially iterating the calculation.
In one embodiment, referring to FIG. 3, in step S206:
the cumulative equation for the constant observed bias for the relative measurement of time of day is:
（22）
wherein,is->Observing deviation of constant values of relative distances at moment; />For update +.>Constant observed deviation of relative measurement of time of day +.>Is the 7 th element of (2); />Is->Observing deviation of constant values of relative azimuth angles at moment; />For update +.>Constant observed deviation of relative measurement of time of day +.>Is the 8 th element of (2);is->Observing deviation of constant values of relative pitch angles at moment; />For update +.>Constant observed deviation of relative measurement of time of day +.>Is the 9 th element of (c). />Residual estimate representing the observed deviation of the constant relative distance measurement,/->Residual estimate representing constant observed bias of relative azimuth measurement, +.>The remaining estimate representing the constant observed deviation from pitch angle measurement.
The above embodiments are integrated according to the present exemplary embodiment, and a more specific embodiment is disclosed, and referring to fig. 3, the specific steps are as follows:
step 1: the relative navigation filtering calculation is initialized. Determining a semi-long axis of a main spacecraft orbitAn initial relative motion state, an initial covariance matrix, a process noise matrix, and a measurement noise matrix are set.
Step 2: from the slaveMoment numerical integration of the relative motion nonlinear orbit dynamics equation to +.>The time is:
step 3: calculation ofTime jacobian matrix->：
Step 4: computing the slaveTime to->Time state transition matrix->：
Step 5: calculation ofTime course noise matrix->：/>
Step 6: state time prediction:
step 7: state covariance time prediction:
step 8: gain matrix calculation:
step 9: correction of relative measurements:
step 10: and (3) calculating measurement information:
step 11: status measurement update:
step 12: state covariance measurement update:
/>
step 13: accumulating relative measured constant observed deviations:
step 14: relative motion state correction:
step 15: zero clearing the system state:
step 16: and (5) circulating the steps 2 to 15 until the relative navigation calculation is finished, and completing the relative navigation calculation under the observation condition of the relative measurement constant value.
Through the specific implementation manner, a simulation example is also provided:
the initial orbit parameters of the master spacecraft and the slave spacecraft are respectively set as follows:
TABLE 1 Master-slave spacecraft initial orbit parameters (epoch: 2023-01-01:0:0:0.00)
According toThe initial orbit parameters in table 1 are shown,six satellite orbits are represented, and The orbit dynamics models of The space motions of The master spacecraft and The slave spacecraft adopt a High-precision orbit prediction (HPOP) model, so that The relative motion trail is shown in figure 4.
Wherein a constant observed deviation of the relative measurementsAnd random error->The settings were as follows:
in the relative navigation filtering calculation, the initial position and the velocity error are set as follows:
in the relative navigation filtering calculation, the initial state covariance matrix is set as follows:
referring to fig. 5, 6 and 7, 1 set of relative navigation simulation calculation results are formed together. Referring to fig. 8, 9 and 10, 100 sets of monte carlo relative navigation simulation calculations are collectively formed. As can be seen from fig. 5 to 10, for the master-slave spacecraft, based on the HPOP dynamics model and the 9-state navigation model, the relative navigation position error is smaller than 30m, the speed error is smaller than 0.005m/s, and the estimation accuracy of the relative ranging and relative angular constant observation errors is better than 90% after 0.5 orbit periods by taking the relative ranging 100m constant observation error and 100m random error, the relative azimuth angle 0.3 degree constant observation error and 0.3 degree random error, and the relative pitch angle 0.3 degree constant observation error and 0.3 degree random error into consideration and adopting the relative navigation calculation strategy of synchronously estimating the relative ranging constant observation error and the relative motion state.
There is also provided in this example embodiment a terminal device, including:
one or more processors;
a memory;
one or more applications, wherein the one or more applications are stored in the memory and configured to be executed by the one or more processors, the one or more applications configured to: a spacecraft autonomous relative navigation method according to any of the above embodiments is performed.
The specific manner in which the terminal device performs the operation has been described in detail in relation to the implementation of the autonomous relative navigation method of the spacecraft, which will not be described in detail here.
Further, in this example embodiment, a virtual device for implementing the above method is also provided. The virtual device may include virtual modules that implement the steps of the methods described above, respectively.
The specific manner in which the various modules perform the operations have been described in detail in connection with embodiments of the method, and will not be described in detail herein.
It should be noted that although in the above detailed description several modules or units of a device for action execution are mentioned, such a division is not mandatory. Indeed, the features and functionality of two or more modules or units described above may be embodied in one module or unit in accordance with embodiments of the present disclosure. Conversely, the features and functions of one module or unit described above may be further divided into a plurality of modules or units to be embodied. The components shown as modules or units may or may not be physical units, may be located in one place, or may be distributed across multiple network elements. Some or all of the modules may be selected according to actual needs to achieve the objectives of the disclosed solution. Those of ordinary skill in the art will understand and implement the present application without undue burden.
In an exemplary embodiment of the present disclosure, there is also provided a computer-readable storage medium having stored thereon a computer program that, when executed by a processor, can implement the steps of the autonomous relative navigation method of a spacecraft in any of the above embodiments. In some possible embodiments, the various aspects of the application may also be implemented in the form of a program product comprising program code for causing a terminal device to carry out the steps according to the various exemplary embodiments of the application as described in the control method section of this specification, when said program product is run on the terminal device.
Referring to fig. 11, a program product 110 for implementing the above-described method according to an embodiment of the present application is described, which may employ a portable compact disc read-only memory (CD-ROM) and include program code, and may be run on a terminal device, such as a personal computer. However, the program product of the present application is not limited thereto, and in this document, a readable storage medium may be any tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device.
The program product may employ any combination of one or more readable media. The readable medium may be a readable signal medium or a readable storage medium. The readable storage medium can be, for example, but is not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or a combination of any of the foregoing. More specific examples (a non-exhaustive list) of the readable storage medium would include the following: an electrical connection having one or more wires, a portable disk, a hard disk, a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.
The computer readable storage medium may include a data signal propagated in baseband or as part of a carrier wave, with readable program code embodied therein. Such a propagated data signal may take any of a variety of forms, including, but not limited to, electro-magnetic, optical, or any suitable combination of the foregoing. A readable storage medium may also be any readable medium that can communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device. Program code embodied on a readable storage medium may be transmitted using any appropriate medium, including but not limited to wireless, wireline, optical fiber cable, RF, etc., or any suitable combination of the foregoing.
Program code for carrying out operations of the present application may be written in any combination of one or more programming languages, including an object oriented programming language such as Java, C++ or the like and conventional procedural programming languages, such as the "C" programming language or similar programming languages. The program code may execute entirely on the user's computing device, partly on the user's device, as a stand-alone software package, partly on the user's computing device, partly on a remote computing device, or entirely on the remote computing device or server. In the case of remote computing devices, the remote computing device may be connected to the user computing device through any kind of network, including a Local Area Network (LAN) or a Wide Area Network (WAN), or may be connected to an external computing device (e.g., connected via the Internet using an Internet service provider).
Other embodiments of the disclosure will be apparent to those skilled in the art from consideration of the specification and practice of the disclosure disclosed herein. This application is intended to cover any adaptations, uses, or adaptations of the disclosure following, in general, the principles of the disclosure and including such departures from the present disclosure as come within known or customary practice within the art to which the disclosure pertains. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the disclosure being indicated by the following claims.

Claims (6)

1. The autonomous relative navigation method for the spacecraft under the condition of constant observed deviation is characterized by comprising the following steps:
taking the center of the main spacecraft as a reference coordinate system, and acquiring an initial relative motion state of the auxiliary spacecraft; wherein the relative motion state includes a relative position vector and a relative velocity vector;
calculating a numerical integral of the relative motion state of the slave spacecraft according to a nonlinear orbit dynamics model;
based on a Kalman filtering calculation model, taking a relative measured constant observation deviation as an estimation object, and taking a relative measured random error as a correction condition;
obtaining a corrected relative motion state through the nonlinear orbit dynamics model and a Kalman filtering calculation model;
performing iterative computation on the nonlinear orbit dynamics model and the Kalman filtering computation model to obtain a final relative motion state;
wherein the constant observed deviations of the relative measurements include: relative position error, relative speed error, constant observed deviation of relative distance, constant observed deviation of relative pitch angle and constant observed deviation of relative azimuth angle; the random error of the relative measurement includes: random error of relative distance, random error of relative azimuth angle and random error of relative pitch angle;
the equation for the nonlinear orbit dynamics model is expressed as:
；
；
wherein k+1 represents the current time, and k represents the time before the current time;is of the phaseFor the movement state, and->Is a relative position vector>Is a relative velocity vector; />Is the main spacecraft position vector, and +.>Is the orbit radius of the main spacecraft; />Is a slave spacecraft position vector; />Is the gravitational constant;0 *×* a matrix with elements of 0;Ia matrix representing all elements 0 except the main diagonal elements are 1; t represents time, < >>Representation->A function that varies with time t;
by the formula->Obtaining, wherein n is the orbital motion angular rate of the main spacecraft;
the step of using the Kalman filtering calculation model to take the relative measured constant observed deviation as an estimation object and the relative measured random error as a correction condition comprises the following steps:
calculating a state transition matrix from the previous moment to the current moment of the constant observation deviation according to the Jacobian matrix of the relative motion state;
determining a state time prediction of the constant observed deviation from a previous time to a current time based on the state transition matrix;
calculating a state covariance time prediction of the state transition matrix from a previous time to a current time, and generating a corresponding gain matrix based on the state covariance time prediction and the relatively measured random error;
calculating an estimated value of a random error of the relative measurement at the current moment;
updating a constant observed deviation of the relative measurement at the current time based on the estimated value of the random error of the relative measurement at the current time, the gain matrix and the state time prediction;
updating the state covariance of the current moment, and accumulating the constant observed deviation of the relative measurement of the current moment to be used for calculating the estimated value of the random error of the relative measurement of the next moment;
and resetting the constant observed deviation of the relative measurement at the current moment and recalculating the constant observed deviation of the relative measurement at the next moment.
2. The autonomous relative navigation method of a spacecraft of claim 1, wherein the step of calculating a state transition matrix of the constant observed deviation from a previous time to a current time from a jacobian matrix of the relative motion state comprises:
jacobian matrix of the relative motion statesThe method comprises the following steps:
；
wherein,is a relative motion state deflection;
by the formula->The method comprises the steps of carrying out a first treatment on the surface of the Solving, wherein T is represented by formula->Obtaining;
from the slaveTime to->State transition matrix->The method comprises the following steps:
；
wherein,a period representing a time update;
from the slaveTime to->State time prediction of said constant observed deviation of time instant +.>The method comprises the following steps:
；
wherein,is->Constant observed deviations of the relative measurements of time of day.
3. The method of autonomous relative navigation of a spacecraft of claim 2, wherein said step of calculating a state covariance time prediction of said state transition matrix from a previous time instant to a current time instant and generating a corresponding gain matrix based on said state covariance time prediction comprises:
from the slaveTime to->State covariance time prediction of time of day +.>The method comprises the following steps:
；
wherein,is->State covariance of time; />Is->A process noise matrix of time;
process noise matrix->The method comprises the following steps:
；
wherein,by the formula->Obtaining, wherein->Representing the original process noise matrix,/>Representing a process noise distribution matrix->，/>For->Transposing; />By the formulaObtaining; />By the formula->Obtaining; />By the formula->Obtaining;
gain matrix +.>The method comprises the following steps:
；
wherein,by the formula->The method comprises the steps of obtaining, wherein,E[*]a mathematical expectation calculation formula is obtained; />Representation->Random error of relative measurement of time of day;
wherein,by the formula->Obtaining，
Wherein,；/>is a relative position vector +.>In the x component; />Is a relative position vector +.>At the y component; />Is a relative position vector +.>In the z component; />A measurement representing the relative distance;Aa measurement representing the relative azimuth angle;Erepresenting a measurement of the relative pitch angle.
4. A method of autonomous relative navigation of a spacecraft as claimed in claim 3, wherein the step of calculating an estimate of the random error of the relative measurement at the current time comprises:
estimate of random error of relative measurement of time of day +.>The method comprises the following steps:
；
wherein,an estimate of the random error of the relative distance; />An estimate of random error of relative azimuth;an estimate of random error of relative pitch angle; />Is->Relative position vector of time,/>Is->Element 1 of->Is->Element 2 of->Is->Is the 3 rd element of (2);
wherein,is->An estimate of the relative distance of the moments in time and by the formula +.>Obtaining, wherein->Is->A measure of relative distance from time of day; />Is->Observing deviation of constant values of relative distances at moment;
wherein,is->An estimate of the relative azimuth of the moment and by the formula +.>Obtaining, wherein->Is->A measurement of relative azimuth of time; />Is->Observing deviation of constant values of relative azimuth angles at moment;
wherein,is->Estimated value of relative pitch angle at time and by the formula +.>Obtaining, wherein->Is->A measurement of relative pitch angle at time; />Is->Observing deviation of constant values of relative pitch angles at moment;
constant observed deviation of relative measurement of time of day +.>The updated equation of (2) is:
。
5. the method of autonomous relative navigation of a spacecraft of claim 4, wherein the step of updating the state covariance at the current time comprises:
state covariance of time of day->The updated equation of (2) is:
。
6. the autonomous relative navigation method of a spacecraft of claim 4, wherein the step of accumulating constant observed deviations of the relative measurements at the current time for calculating an estimate of random error of the relative measurements at the next time comprises:
the cumulative equation for the constant observed bias for the relative measurement of time of day is:
；
wherein,is->Observing deviation of constant values of relative distances at moment; />For update +.>Constant observed deviation of relative measurement of time of day +.>Is the 7 th element of (2)A hormone; />Is->Observing deviation of constant values of relative azimuth angles at moment; />For update +.>Constant observed deviation of relative measurement of time of day +.>Is the 8 th element of (2); />Is->Observing deviation of constant values of relative pitch angles at moment; />For update +.>Constant observed deviation of relative measurement of time of day +.>Is the 9 th element of (c).
CN202311017608.0A 2023-08-14 2023-08-14 Autonomous relative navigation method for spacecraft under constant observed deviation condition Active CN116734864B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202311017608.0A CN116734864B (en) 2023-08-14 2023-08-14 Autonomous relative navigation method for spacecraft under constant observed deviation condition

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202311017608.0A CN116734864B (en) 2023-08-14 2023-08-14 Autonomous relative navigation method for spacecraft under constant observed deviation condition

Publications (2)

Publication Number Publication Date
CN116734864A CN116734864A (en) 2023-09-12
CN116734864B true CN116734864B (en) 2023-11-28

Family

ID=87904758

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202311017608.0A Active CN116734864B (en) 2023-08-14 2023-08-14 Autonomous relative navigation method for spacecraft under constant observed deviation condition

Country Status (1)

Country Link
CN (1) CN116734864B (en)

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117367436B (en) * 2023-12-08 2024-02-23 中国西安卫星测控中心 Real-time estimation method for inter-satellite relative measurement linear time-varying error

Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108692729A (en) * 2018-05-04 2018-10-23 北京空间飞行器总体设计部 A kind of space non-cooperative target Relative Navigation covariance adaptive correction filtering method
CN108717198A (en) * 2018-05-04 2018-10-30 北京空间飞行器总体设计部 A kind of space non-cooperative target relative navigation system error compensation amendment filtering method
CN109631913A (en) * 2019-01-30 2019-04-16 西安电子科技大学 X-ray pulsar navigation localization method and system based on nonlinear prediction strong tracking Unscented kalman filtering
WO2020087846A1 (en) * 2018-10-31 2020-05-07 东南大学 Navigation method based on iteratively extended kalman filter fusion inertia and monocular vision
CN112325886A (en) * 2020-11-02 2021-02-05 北京航空航天大学 Spacecraft autonomous attitude determination system based on combination of gravity gradiometer and gyroscope
CN115856977A (en) * 2022-12-26 2023-03-28 上海航天控制技术研究所 Relative navigation method based on differential GNSS

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US11733399B2 (en) * 2019-08-16 2023-08-22 California Institute Of Technology Systems and methods for robust and accurate relative navigation

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108692729A (en) * 2018-05-04 2018-10-23 北京空间飞行器总体设计部 A kind of space non-cooperative target Relative Navigation covariance adaptive correction filtering method
CN108717198A (en) * 2018-05-04 2018-10-30 北京空间飞行器总体设计部 A kind of space non-cooperative target relative navigation system error compensation amendment filtering method
WO2020087846A1 (en) * 2018-10-31 2020-05-07 东南大学 Navigation method based on iteratively extended kalman filter fusion inertia and monocular vision
CN109631913A (en) * 2019-01-30 2019-04-16 西安电子科技大学 X-ray pulsar navigation localization method and system based on nonlinear prediction strong tracking Unscented kalman filtering
CN112325886A (en) * 2020-11-02 2021-02-05 北京航空航天大学 Spacecraft autonomous attitude determination system based on combination of gravity gradiometer and gyroscope
CN115856977A (en) * 2022-12-26 2023-03-28 上海航天控制技术研究所 Relative navigation method based on differential GNSS

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
基于改进型两步卡尔曼滤波的相对导航方法;刘勇;徐世杰;徐鹏;马骏;;中国空间科学技术(第03期);全文 *
基于视线测量的航天器相对导航滤波方法研究;李轶;张善从;;仪器仪表学报(第06期);全文 *

Also Published As

Publication number Publication date
CN116734864A (en) 2023-09-12

Similar Documents

Publication Publication Date Title
Kulikov et al. Accurate continuous–discrete unscented Kalman filtering for estimation of nonlinear continuous-time stochastic models in radar tracking
CN108225337B (en) Star sensor and gyroscope combined attitude determination method based on SR-UKF filtering
RU2701194C2 (en) Method of estimating navigation state in conditions of limited possibility of observation
CN106767837B (en) Spacecraft attitude estimation method based on the estimation of volume quaternary number
Gross et al. A comparison of extended Kalman filter, sigma-point Kalman filter, and particle filter in GPS/INS sensor fusion
CN116734864B (en) Autonomous relative navigation method for spacecraft under constant observed deviation condition
CN114018274B (en) Vehicle positioning method and device and electronic equipment
WO2008120145A1 (en) Method and system for orientation sensing
Zhang et al. Robust H‐infinity CKF/KF hybrid filtering method for SINS alignment
CN112146655A (en) Elastic model design method for BeiDou/SINS tight integrated navigation system
Xiong et al. Adaptive iterated extended Kalman filter for relative spacecraft attitude and position estimation
CN108508463B (en) Fourier-Hermite orthogonal polynomial based extended ellipsoid collective filtering method
Zhang et al. Attitude determination using gyros and vector measurements aided with adaptive kinematics modeling
CN114139109A (en) Target tracking method, system, equipment, medium and data processing terminal
Wang et al. A robust backtracking CKF based on Krein space theory for in-motion alignment process
CN112782732A (en) Navigation signal analysis method based on particle swarm algorithm and computer storage readable medium
Avzayesh et al. Improved-Performance Vehicle’s State Estimator Under Uncertain Model Dynam
Fiedler et al. A probabilistic moving horizon estimation framework applied to the visual-inertial sensor fusion problem
CN114705223A (en) Inertial navigation error compensation method and system for multiple mobile intelligent bodies in target tracking
KR101860810B1 (en) System and method for navigation with nonlinear measurement model
CN109059915B (en) Gravity compensation method, system and device
Woodburn et al. Effect of coordinate selection on orbit determination
Peng et al. Online Self-calibration of Camera-IMU External Parameters and IMU Initialization for Stereo VI-SLAM
Girrbach et al. Adaptive compensation of measurement delays in multi-sensor fusion for inertial motion tracking using moving horizon estimation
CN116817928B (en) Method for multi-source fusion positioning of guard/inertial navigation train based on factor graph optimization

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant