CN112525204B - Spacecraft inertia and solar Doppler speed combined navigation method - Google Patents

Spacecraft inertia and solar Doppler speed combined navigation method Download PDF

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CN112525204B
CN112525204B CN202011467901.3A CN202011467901A CN112525204B CN 112525204 B CN112525204 B CN 112525204B CN 202011467901 A CN202011467901 A CN 202011467901A CN 112525204 B CN112525204 B CN 112525204B
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宁晓琳
黄玉琳
杨雨青
房建成
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Beihang University
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Abstract

The invention relates to a combined navigation method of spacecraft inertia and solar Doppler speed, which combines the inertial navigation and Doppler speed measurement methods, firstly establishes a system state model according to an error equation of an inertial navigation system, then utilizes solar Doppler speed obtained by a spectrometer as measurement, establishes a solar Doppler speed measurement model, and finally uses UKF filtering to estimate the position, speed and attitude of a spacecraft. The invention belongs to the field of autonomous navigation of a spacecraft, can provide high-precision position, speed and gesture information for the spacecraft, and has important practical significance for navigation of the spacecraft.

Description

Spacecraft inertia and solar Doppler speed combined navigation method
Technical Field
The invention belongs to the field of autonomous navigation of spacecrafts, and relates to a combined navigation method of spacecraft inertia and solar Doppler speed.
Background
The development of the spacecraft plays an important role in national defense, information communication and technological innovation, and the navigation system is used as important equipment on the spacecraft to provide relevant motion parameters for the operation or control system of the spacecraft, so that the spacecraft is guided to move from a starting point to a destination according to the required speed and track, and the navigation system has a non-negligible effect on the flight task of the spacecraft.
Inertial navigation utilizes an integral method to determine the position, speed and posture of a spacecraft according to the output of a gyroscope and an accelerometer in an inertial measurement unit (Inertial Measurement Unit, IMU), and has the characteristics of strong independence, high output frequency, good concealment, maturity and the like. The inertial measurement unit has excellent performance, is widely applied to various spacecrafts, but is often combined with other navigation systems to improve navigation performance because of unavoidable errors of gyroscopes and accelerometers in the inertial measurement unit, accumulation of errors with time and serious influence on navigation accuracy. Astronomical navigation errors do not accumulate with time and have complementarity with inertial navigation, so that the astronomical navigation is often selected for assistance, and inertial/astronomical combined navigation becomes an effective means in autonomous navigation. The traditional inertial/astronomical integrated navigation uses the attitude information provided by the star sensor in astronomical navigation to correct the attitude error and gyro drift of inertial navigation, thereby obtaining high-precision attitude and being incapable of intuitively correcting the inertial navigation speed and position error. Regardless of the field, the speed information is critical, which has a great influence on the navigation accuracy, so that it is highly desirable to find a suitable astronomical navigation method to correct the inertial navigation speed information. Research shows that in an autonomous underwater vehicle navigation system in the field of navigation, a Doppler log is often used for correcting the speed of inertial navigation, so that the speed precision of a vehicle can be remarkably improved, and the use of solar Doppler speed information for assisting inertial navigation in the navigation of the vehicle is proposed to correct the speed, and the speed and position precision of the vehicle are improved.
In the deep space exploration task, the research of a fully autonomous and high-precision navigation method has very important significance. According to the combined navigation method for the spacecraft inertia and the solar Doppler speed, disclosed by the invention, on the basis of traditional inertial navigation, solar Doppler speed navigation is assisted, the complementary advantages of the two navigation methods can be realized, the characteristics of strong autonomy and comprehensive output information of the inertial navigation are reserved, the speed precision can be directly improved, the position can be indirectly corrected, and the accuracy and the reliability of a navigation system are greatly improved. Considering the complementary characteristics of the solar Doppler speed information on the working principle and the information source, the solar Doppler speed information assisted inertial navigation is a feasible and deeply-researched method for the autonomous navigation task of the spacecraft for a long time and a long distance.
Disclosure of Invention
The invention aims to solve the technical problems that: in the traditional inertial/astronomical combined navigation method, the attitude information output by a star sensor is mostly utilized to correct the attitude of inertial navigation, the speed and position error of the inertial navigation cannot be intuitively corrected, the speed information is critical, and the navigation precision is greatly influenced. In order to solve the problem that the conventional inertial/astronomical combined navigation method in spacecraft navigation cannot intuitively correct the inertial navigation speed, an autonomous navigation method combining inertial navigation and solar Doppler speed navigation is provided for a spacecraft, and the solar Doppler speed navigation is utilized to assist in inertial navigation to obtain high-precision speed information.
The technical scheme adopted for solving the technical problems is as follows: a spacecraft inertia and solar Doppler speed combined navigation method is realized by the following steps:
firstly, establishing a system state model according to an error equation of an inertial navigation system;
secondly, obtaining the solar Doppler speed by utilizing a spectrometer, and establishing a solar Doppler speed measurement model;
and thirdly, estimating the position, the speed and the attitude of the spacecraft by adopting UKF filtering based on the state model in the first step and the measurement model in the second step.
The method specifically comprises the following steps:
1. establishing a system state model based on an inertial navigation error equation
The inertial navigation measures angular velocity and acceleration information of the spacecraft relative to an inertial space through an Inertial Measurement Unit (IMU), and instantaneous speed and position information of the spacecraft are automatically calculated by utilizing Newton's law of motion. Under a strapdown inertial navigation system, an IMU is typically composed of three orthogonal accelerometers and three orthogonal gyroscopes, with the entire assembly mounted directly on the spacecraft body. According to the principle of inertial navigation, the state model of the system is as follows:
Figure BDA0002835110520000023
wherein phi = [ phi ] E φ N φ U ] T Is the attitude error angle phi E 、φ N 、φ U Respectively representing the attitude errors of the east, north and sky directions in the n series;
Figure BDA0002835110520000021
is the speed of the spacecraft, v E 、v N 、v U Respectively represent the speeds of the east, north and sky in the n series,/>
Figure BDA0002835110520000022
Is the spacecraft speed error, δv E 、δv N 、δv U Respectively representing the speed errors of the east, north and the sky in the n series; r is (r) n ＝[L λ h] T Is the position of the spacecraft, L, lambda and h respectively represent the latitude, longitude and altitude under n series, and δr n ＝[δL δλ δh] T Is a spacecraft position error, δl, δλ, δh respectively representing a latitude error, a longitude error, and an altitude error under an n-system; f (f) n Is the projection of the accelerometer output in the n-series; />
Figure BDA0002835110520000031
Indicating the earth rotation angular rate of spacecraft in the n-series,/->
Figure BDA0002835110520000032
Is w of spacecraft under n series ie Error of (2);
Figure BDA0002835110520000033
is the representation of the rotation angular rate of the n-series relative to the e-series in the n-series, wherein R x and Ry The main curvature radius of the mortise and tenon circle and the meridian circle respectively,
Figure BDA0002835110520000034
is w under n en Error of (2); />
Figure BDA0002835110520000035
Represents the rotation angular velocity of n series relative to i series in n series, ++>
Figure BDA0002835110520000036
Is ω under n series in Error of (2); epsilon= (epsilon) x ε y ε z ) T The constant value drift of gyroscopes in the x, y and z directions of the inertial navigation system; />
Figure BDA0002835110520000037
Is the constant bias of the accelerometer in the x, y and z directions of the inertial navigation system; />
Figure BDA0002835110520000038
Figure BDA0002835110520000039
The n system is a geographic coordinate system, the e system is an earth coordinate system, the i system is a geocentric inertial coordinate system, and the b system is a spacecraft body coordinate system;
the above state model is written as:
X k ＝F(X k-1 ,k-1)+W k-1 (2)
wherein the state quantity is
Figure BDA00028351105200000311
The attitude error angle, the speed and the position error of the spacecraft are respectively, the constant drift of the gyroscope and the constant bias of the accelerometer are respectively X k ，X k-1 The state quantity at k time and k-1, F (X) k-1 K-1) is a nonlinear transfer function of a spacecraft inertia/solar Doppler speed combined navigation system, W k-1 Is process noise.
2. Establishing a solar Doppler speed measurement model
Obtaining spectral frequency shift by using a spectrometer, and obtaining radial velocity v of the spacecraft relative to the sun according to the frequency shift r Expressed as:
v r ＝c((f rs -f es )/f es ) (3)
wherein c is the speed of light, f rs Spectral frequency f emitted by the sun received by the spacecraft es Spectral frequencies emitted for the sun.
Taking the Doppler radial velocity of the spacecraft relative to the sun as a measurement quantity, and establishing a solar Doppler velocity measurement model by utilizing mathematical relation between the Doppler radial velocity and the position of the spacecraft:
Figure BDA00028351105200000310
wherein ,vr Radial velocity measurement representing spacecraft relative to sun, r ps ,v ps Respectively representing the position and the speed vector of the spacecraft relative to the sun, r ps ＝||r ps The i indicates the magnitude of the position vector, v m Representing the measured noise.
And (3) establishing a relation between a position vector of the spacecraft relative to the sun and a state quantity in the INS by utilizing coordinate transformation.
As shown in FIG. 3, in the geocentric inertial coordinate system O-xyz, r ps 、v ps The position and the speed vector of the spacecraft relative to the sun under the geocentric inertial system are respectively r pe 、v pe The position and velocity vectors of the spacecraft relative to the earth are:
Figure BDA0002835110520000041
wherein ,
Figure BDA0002835110520000042
r n 、v n is the position and speed vector of the spacecraft in the n series relative to the earth, delta r n 、δv n Is a position and velocity error obtained by the INS; r is (r) se And v se The position and velocity vectors of the sun relative to earth, respectively, may be obtained by the STK tool; />
Figure BDA0002835110520000049
Is a conversion matrix from n-series to i-series. Thereby, the state quantity in the metrology model is linked to the state model. The solar doppler velocity measurement model is expressed as:
Figure BDA0002835110520000043
the discretized solar Doppler speed measurement model is expressed as follows:
Z k ＝H(X k ,k)+V k (7)
wherein H (·) represents a nonlinear continuous measurement function of the solar Doppler velocity, V k And (5) representing the measurement error of the solar Doppler speed at the moment k.
3. UKF filtering is carried out to obtain position, speed and attitude estimation of spacecraft
The state model and the measurement model of the integrated navigation system of the inertia and the solar Doppler speed of the discrete rear spacecraft are as follows:
Figure BDA0002835110520000044
wherein ,F(Xk-1 K-1) is a nonlinear transfer function of the integrated navigation system, H (X) k K) is a nonlinear measurement function, W k-1 V (V) k Respectively representing process and measurement noise. Filtering the system model type (8) through UKF to obtain posterior state estimation of the spacecraft
Figure BDA0002835110520000045
The attitude error angle, the speed and the position error of the spacecraft, the constant drift of the gyroscope and the constant bias of the accelerometer and the posterior error covariance are respectively->
Figure BDA0002835110520000046
Will->
Figure BDA0002835110520000047
Is->
Figure BDA0002835110520000048
And outputting, and simultaneously returning the estimated value of the k moment state quantity and the error covariance to the UKF filter for obtaining the k+1 moment output.
The principle of the invention is as follows: on the basis of inertial navigation, doppler velocity information in astronomical navigation is used for assistance. According to an error equation of an inertial navigation system, a state model of the spacecraft is established, doppler velocity frequency shift quantity of solar spectrum is observed in real time by utilizing a spectrometer, the velocity of the spacecraft relative to the sun is directly obtained, position information is indirectly obtained through velocity integration, the solar Doppler velocity is used as quantity to measure, a measurement model is established according to the relation between Doppler radial velocity and the position of the spacecraft, doppler velocity navigation and inertial navigation are combined to directly correct the velocity of the spacecraft, the position is indirectly corrected, and finally navigation parameters such as the position, the velocity and the like of the spacecraft are estimated through UKF.
Compared with the prior art, the invention has the advantages that:
(1) In the existing spacecraft autonomous navigation technology, in order to meet high-precision requirements and complex tasks, a combined navigation system which adopts two or more navigation means is often applied to modern military navigation. The inertial navigation is a main mode in combined navigation due to the characteristics of strong autonomy, high accuracy in short time, comprehensive and continuous output information and the like, and is often combined with other navigation to improve navigation accuracy. The common navigation modes include astronomical navigation, visual navigation, satellite navigation and the like, but the visual navigation is not suitable for long-distance navigation in consideration of the application of the spacecraft in military national defense, the GPS navigation is limited by the United states, the availability of the GPS navigation is not high in war time, the astronomical navigation precision is high, and errors are not accumulated with time, so that the astronomical navigation is often used for assisting inertial navigation to complete the navigation task of the spacecraft.
(2) The traditional inertial/astronomical integrated navigation, no matter the deep combination and the shallow combination, uses the high-precision gesture information provided by the astronomical navigation system to correct the inertial navigation system and compensates the error of an inertial device, is mainly used for correcting the gesture, and cannot directly and well correct the speed and the position information. The invention provides an inertial navigation based on the solar Doppler speed information, and the combined navigation method can realize the complementary advantages of the two navigation methods, not only maintains the characteristics of strong inertial navigation autonomy and comprehensive output information, but also can directly improve the speed precision by using the solar Doppler speed navigation, indirectly correct the position and greatly improve the accuracy and the reliability of the navigation system.
Drawings
FIG. 1 is a flow chart of a combined navigation method of spacecraft inertia and solar Doppler speed;
FIG. 2 is a schematic diagram of a combined navigation method of spacecraft inertia and solar Doppler velocity in the invention;
FIG. 3 is a schematic diagram of the positional relationship between a spacecraft and the sun in the geocentric inertial coordinate system according to the present invention;
FIG. 4 is a diagram of a combined navigation coordinate system according to the present invention.
Detailed Description
The invention will now be described in detail with reference to the accompanying drawings and examples.
As shown in fig. 1, the implementation process of the spacecraft inertia and solar doppler velocity combined navigation method provided by the invention is as follows:
1. establishing a system state model based on an inertial navigation error equation
The inertial navigation measures angular velocity and acceleration information of the spacecraft relative to an inertial space through an Inertial Measurement Unit (IMU), and instantaneous speed and position information of the spacecraft are automatically calculated by utilizing Newton's law of motion. Under a strapdown inertial navigation system, an IMU is typically composed of three orthogonal accelerometers and three orthogonal gyroscopes, with the entire assembly mounted directly on the spacecraft body. According to the principle of inertial navigation, the system state model is:
Figure BDA0002835110520000061
wherein phi = [ phi ] E φ N φ U ] T Is the attitude error angle phi E 、φ N 、φ U Respectively representing the attitude errors of the east, north and sky directions in the n series;
Figure BDA0002835110520000062
is the speed of the spacecraft, v E 、v N 、v U Respectively represent the eastern, north and heaven directions of the n seriesThe speed of the product is determined by the speed,
Figure BDA0002835110520000063
is the spacecraft speed error, δv E 、δv N 、δv U Respectively representing the speed errors of the east, north and the sky in the n series; r is (r) n ＝[L λ h] T Is the position of the spacecraft, L, lambda and h respectively represent the latitude, longitude and altitude under n series, and δr n ＝[δL δλ δh] T Is a spacecraft position error, δl, δλ, δh respectively representing a latitude error, a longitude error, and an altitude error under an n-system; f (f) n Is the projection of the accelerometer output in the n-series; />
Figure BDA0002835110520000064
Indicating the earth rotation angular rate of spacecraft in the n-series,/->
Figure BDA0002835110520000065
Is w of spacecraft under n series ie Error of (2);
Figure BDA0002835110520000066
is the representation of the rotation angular rate of the n-series relative to the e-series in the n-series, wherein R x and Ry The main curvature radius of the mortise and tenon circle and the meridian circle respectively,
Figure BDA0002835110520000067
is w under n en Error of (2); />
Figure BDA0002835110520000068
Represents the rotation angular velocity of n series relative to i series in n series, ++>
Figure BDA0002835110520000069
Is ω under n series in Error of (2); epsilon= (epsilon) x ε y ε z ) T The constant value drift of gyroscopes in the x, y and z directions of the inertial navigation system; />
Figure BDA00028351105200000610
Is the constant bias of the accelerometer in the x, y and z directions of the inertial navigation system; />
Figure BDA00028351105200000611
Figure BDA00028351105200000612
The n system is a geographic coordinate system, the e system is an earth coordinate system, the i system is a geocentric inertial coordinate system, and the b system is a spacecraft body coordinate system;
the above system state model is written as:
X k ＝F(X k-1 ,k-1)+W k-1 (2)
wherein the state quantity is
Figure BDA0002835110520000076
The attitude error angle, the speed and the position error of the spacecraft are respectively, the constant drift of the gyroscope and the constant bias of the accelerometer are respectively X k ，X k-1 The state quantity at k time and k-1, F (X) k-1 K-1) is a nonlinear transfer function of a spacecraft inertia/solar Doppler speed combined navigation system, W k-1 Is process noise.
2. Establishing a solar Doppler speed measurement model
Obtaining spectral frequency shift by using a spectrometer, and obtaining radial velocity v of the spacecraft relative to the sun according to the frequency shift r Expressed as
v r ＝c((f rs -f es )/f es ) (3)
Wherein c is the speed of light, f rs Spectral frequency f emitted by the sun received by the spacecraft es Spectral frequencies emitted for the sun.
Taking the Doppler radial velocity of the spacecraft relative to the sun as a measurement quantity, and establishing a solar Doppler velocity measurement model by utilizing mathematical relation between the Doppler radial velocity and the position of the spacecraft:
Figure BDA0002835110520000071
wherein ,vr Radial velocity measurement representing spacecraft relative to sun, r ps ,v ps Respectively representing the position and the speed vector of the spacecraft relative to the sun, r ps ＝||r ps The i indicates the magnitude of the position vector, v m Representing the measured noise.
And (3) establishing a relation between a position vector of the spacecraft relative to the sun and a state quantity in the INS by utilizing coordinate transformation.
As shown in FIG. 3, in the geocentric inertial coordinate system O-xyz, r ps 、v ps The position and the speed vector of the spacecraft relative to the sun under the geocentric inertial system are respectively r pe 、v pe The position and velocity vectors of the spacecraft relative to the earth are:
Figure BDA0002835110520000072
wherein ,
Figure BDA0002835110520000073
r n 、v n is the position and speed vector of the spacecraft in the n series relative to the earth, delta r n 、δv n Is a position and velocity error obtained by the INS; r is (r) se And v se The position and velocity vectors of the sun relative to earth, respectively, may be obtained by the STK tool; />
Figure BDA0002835110520000074
Is a conversion matrix from n-series to i-series. Thereby, the state quantity in the metrology model is linked to the state model. The solar doppler velocity measurement model is expressed as:
Figure BDA0002835110520000075
the discretized solar Doppler speed measurement model is expressed as follows:
Z k ＝H(X k ,k)+V k (7)
wherein H (·) represents a nonlinear continuous measurement function of the solar Doppler velocity, V k And (5) representing the measurement error of the solar Doppler speed at the moment k.
3. UKF filtering is carried out to obtain position, speed and attitude estimation of spacecraft
The state model and the measurement model of the discrete rear spacecraft inertia/solar Doppler speed integrated navigation system are as follows:
Figure BDA0002835110520000081
wherein ,F(Xk-1 K-1) is a nonlinear transfer function of the integrated navigation system, H (X) k K) is a nonlinear measurement function, W k-1 V (V) k Respectively representing process and measurement noise. Filtering the system model by UKF to obtain the posterior state estimation of the spacecraft
Figure BDA0002835110520000082
The attitude error angle, the speed and the position error of the spacecraft, the constant drift of the gyroscope and the constant bias of the accelerometer and the posterior error covariance are respectively->
Figure BDA0002835110520000083
Will->
Figure BDA0002835110520000084
Is->
Figure BDA0002835110520000085
And outputting.
The method comprises the following specific steps:
A. initializing state quantity
Figure BDA0002835110520000086
And state error variance matrix P 0
Figure BDA0002835110520000087
in the formula ,
Figure BDA0002835110520000088
is the estimated value of state quantity of spacecraft at the 0 th moment (initial moment), X 0 Is the true value of the state quantity of the spacecraft at the 0 th moment.
B. Selecting sigma sampling points
At the position of
Figure BDA0002835110520000089
Selecting a series of sampling points nearby, wherein the mean value and covariance of the sampling points are respectively +.>
Figure BDA00028351105200000810
and />
Figure BDA00028351105200000811
If the state variable is 15×1, then 31 sample points are selected +.>
Figure BDA00028351105200000812
And weight w thereof 0 ,w 1 …,w 30 The method comprises the following steps:
Figure BDA00028351105200000813
where tau represents the scaling parameter,
Figure BDA00028351105200000814
representing taking the ith row or column of the square root matrix.
C. Transferring sigma sampling points and obtaining a priori estimates and a priori error covariances
One-step prediction for each sample point
Figure BDA00028351105200000815
The method comprises the following steps:
Figure BDA00028351105200000816
merging all
Figure BDA00028351105200000817
Obtaining a priori state estimate +.>
Figure BDA00028351105200000818
The method comprises the following steps:
Figure BDA00028351105200000819
prior error covariance
Figure BDA00028351105200000820
The method comprises the following steps:
Figure BDA0002835110520000091
in the formula ,Qk And the model noise covariance matrix is k moment state model noise covariance matrix.
D. Measurement update
According to the measurement equation, calculate each sampling point
Figure BDA0002835110520000092
Is measured in predictive quantity->
Figure BDA0002835110520000093
Figure BDA0002835110520000094
Merging all
Figure BDA0002835110520000095
Obtaining predictive measurements Y k The method comprises the following steps:
Figure BDA0002835110520000096
calculating predicted metrology covariance P yy,k Cross covariance P xy,k ：
Figure BDA0002835110520000097
wherein Rk The measured noise covariance matrix of the k-time system is obtained. Calculating a filter gain K k The method comprises the following steps:
Figure BDA0002835110520000098
computing posterior state estimates
Figure BDA0002835110520000099
Figure BDA00028351105200000910
Calculating posterior error covariance
Figure BDA00028351105200000911
Figure BDA00028351105200000912
Will be
Figure BDA00028351105200000913
Is->
Figure BDA00028351105200000914
And outputting, and simultaneously returning the estimated values to the filter for obtaining the output at the time k+1.
Fig. 2 shows a schematic diagram of a combined navigation method of spacecraft inertia and solar doppler velocity, and introduces the basic principle of each navigation system.
(1) Inertial navigation system
The inertial navigation system mainly comprises an Inertial Measurement Unit (IMU) and corresponding inertial navigation mechanization, and is based on Newton's law of mechanics. In strapdown inertial navigation, the IMU is typically composed of three orthogonal accelerometers and three orthogonal gyroscopes, with the entire assembly mounted directly on the spacecraft body. The gyroscope and the accelerometer respectively obtain the angular velocity and the added non-gravitation acceleration of the spacecraft relative to the inertial coordinate system, and the position, the velocity and the gesture information of the spacecraft in the navigation coordinate system can be determined by converting the measurement data into an n-system.
(2) Doppler velocity navigation system
Doppler shift refers to the change in phase and frequency of a spectral line due to relative motion between a light source and a moving object based on its wavelength. When the navigation celestial body is the sun, the radial speed of the spacecraft relative to the sun can be obtained by observing Doppler frequency shift measurement caused by relative movement of the spacecraft and the sun, the radial speed is taken as Doppler speed measurement, and the position of the spacecraft can be obtained by integration.
An error equation based on an inertial navigation system is used for establishing a state model of the integrated navigation system, a spectrometer is used for observing Doppler velocity frequency shift quantity of solar spectrum in real time, the velocity of a spacecraft relative to the sun is directly obtained, position information is indirectly obtained through velocity integration, the solar Doppler velocity is used as quantity to measure, a measurement model is established according to the relation between Doppler radial velocity and the position of the spacecraft, doppler velocity navigation and inertial navigation are combined to directly correct the velocity of the spacecraft, the position is indirectly corrected, and finally the estimation of navigation parameters such as the position, the velocity and the like of the spacecraft is realized through UKF.
Fig. 3 shows a schematic diagram of the positional relationship between a spacecraft and the sun in a geocentric inertial coordinate system. In the geocentric inertial coordinate system, r ps 、v ps The position and the speed vector of the spacecraft relative to the sun, r pe 、v pe The position and the velocity vector of the spacecraft relative to the earth, r se And v se The position and velocity vectors of the sun relative to the earth. From the vector geometry, r can be determined ps Denoted as r pe 、r se The difference, v ps Denoted as v pe 、v se The difference between the Doppler radial velocity and the position of the spacecraft in the earth-centered system is established.
Fig. 4 shows a schematic diagram of a combined navigation coordinate system, and since some measured values are represented by different coordinate systems, some calculation and transformation are needed, and a common coordinate system involved in combined navigation for spacecraft inertia and solar doppler speed is described herein, including a geocentric inertial coordinate system (i-system), an earth coordinate system (e-system), a geographic coordinate system (n-system), and a spacecraft body coordinate system (b-system).
(1) Inertial coordinate system (i system, O i x i y i z i )
The origin of the inertial coordinate system is located at the earth centroid O i ，x i The axis being in the equatorial plane and pointing in the direction of the spring point, z i The axis being perpendicular to the equatorial plane and coincident with the direction of the earth's axis of rotation, y i Axis and x i Axis and z i The axes are all vertical and form a right-hand rectangular coordinate system.
(2) Earth coordinate system (e system, O i x e y e z e )
The origin of the earth coordinate system is located at the earth centroid O i ，z e The axis is perpendicular to the equatorial plane and is consistent with the direction of rotation of the earth, x e The axis being in the equatorial plane and pointing towards the principal meridian, y e The axis being perpendicular to x e Axis and z e And the shaft and forms a right-hand rectangular coordinate system. The coordinate system is fixedly connected with the earth and rotates together with the earth.
Transformation matrix for converting earth system into geocentric inertial system
Figure BDA0002835110520000101
Represented as
Figure BDA0002835110520000102
wherein ,ωie For the earth to rotate aroundThe rotation angular rate of the shaft, t, is a time parameter.
(3) Geographic coordinate system (n system O x) n y n z n )
The geographic coordinate system is a local northeast coordinate system, also referred to herein as a navigation coordinate system, with its origin at the spacecraft centroid O, O x n The axis pointing in the local horizontal east direction O y n The axis pointing to the local horizontal north direction O z n The shaft is directed toward the zenith in the direction of the vertical line.
Transformation matrix for transforming from geographic system to earth coordinate system
Figure BDA0002835110520000111
Expressed as:
Figure BDA0002835110520000112
wherein L and lambda are the latitude and longitude of the spacecraft on the earth. A transformation matrix for transforming from geographic to geocentric inertial system can be obtained
Figure BDA0002835110520000113
Figure BDA0002835110520000114
(4) Spacecraft body coordinate system (b system, O x b y b z b )
The spacecraft body coordinate system is a coordinate system fixed on the spacecraft, and the origin of the spacecraft body coordinate system is positioned at the centroid O of the spacecraft and the longitudinal axis O y of the spacecraft body coordinate system b The transverse axis O x is directed longitudinally forward of the body b Point to its right, oz b Perpendicular to O x b y b A right hand coordinate system is constructed.
(5) IMU coordinate system
The IMU coordinate system is a coordinate system fixed on the IMU, is a coordinate system specially set for an inertial navigation system, and has three axes pointing in the direction of the sensitive axis of the IMU and consistent with the body coordinate system.
What is not described in detail in the present specification belongs to the prior art known to those skilled in the art.

Claims (2)

1. The spacecraft inertia and solar Doppler speed combined navigation method is characterized by comprising the following steps of:
firstly, establishing a system state model according to an error equation of an inertial navigation system;
secondly, obtaining the solar Doppler speed by utilizing a spectrometer, and establishing a solar Doppler speed measurement model;
thirdly, estimating the position, the speed and the gesture of the spacecraft by adopting UKF filtering based on the system state model in the first step and the measurement model in the second step, thereby completing the combined navigation of the inertia and the solar Doppler speed of the spacecraft;
the first step, a system state model is established according to an error equation of an inertial navigation system, and the method comprises the following steps: inertial navigation measures angular velocity and acceleration information of a spacecraft relative to an inertial space through an Inertial Measurement Unit (IMU), instantaneous speed and position information of the spacecraft are automatically calculated by utilizing Newton's law of motion, the IMU consists of three orthogonal accelerometers and three orthogonal gyroscopes under a strapdown inertial navigation system, the IMU is directly installed on a spacecraft body, and a system state model is as follows according to an inertial navigation principle:
Figure FDA0004214852660000011
wherein phi = [ phi ] E φ N φ U ] T Is the attitude error angle phi E 、φ N 、φ U Respectively representing the attitude errors of the east, north and sky directions in the n series;
Figure FDA0004214852660000012
is the speed of the spacecraft, v E 、v N 、v U Respectively represent the speeds of the inner east, the north and the sky directions of the n series,
Figure FDA0004214852660000013
is the spacecraft speed error, δv E 、δv N 、δv U Respectively representing the speed errors of the east, north and the sky in the n series; r is (r) n ＝[L λ h] T Is the position of the spacecraft, L, lambda and h respectively represent the latitude, longitude and altitude under n series, and δr n ＝[δL δλ δh] T Is a spacecraft position error, δl, δλ, δh respectively representing a latitude error, a longitude error, and an altitude error under an n-system; f (f) n Is the projection of the accelerometer output in the n-series; />
Figure FDA0004214852660000014
Indicating the earth rotation angular rate of spacecraft in the n-series,/->
Figure FDA0004214852660000015
Is w of spacecraft under n series ie Error of (2);
Figure FDA0004214852660000016
is the representation of the rotation angular rate of the n-series relative to the e-series in the n-series, wherein R x and Ry The main curvature radius of the mortise and tenon circle and the meridian circle respectively,
Figure FDA0004214852660000021
is w under n en Error of (2); />
Figure FDA0004214852660000022
Represents the rotation angular velocity of n series relative to i series in n series, ++>
Figure FDA0004214852660000023
Is ω under n series in Error of (2); epsilon= (epsilon) x ε y ε z ) T The constant value drift of gyroscopes in the x, y and z directions of the inertial navigation system; />
Figure FDA0004214852660000024
Is used byConstant bias of accelerometers in three directions of x, y and z of the sexual navigation system; />
Figure FDA0004214852660000025
Figure FDA0004214852660000026
The n system is a geographic coordinate system, the e system is an earth coordinate system, the i system is a geocentric inertial coordinate system, and the b system is a spacecraft body coordinate system;
the above system state model is written as:
X k ＝F(X k-1 ,k-1)+W k-1 (2)
wherein the state quantity is
Figure FDA0004214852660000027
The attitude error angle, the speed and the position error of the spacecraft are respectively, the constant drift of the gyroscope and the constant bias of the accelerometer are respectively X k ，X k-1 The state quantity at k time and k-1, F (X) k-1 K-1) is a nonlinear transfer function of a spacecraft inertia and solar Doppler speed combined navigation system, W k-1 Is process noise;
the second step, the step of establishing a solar Doppler speed measurement model is as follows:
obtaining spectral frequency shift by using a spectrometer, and obtaining radial velocity v of the spacecraft relative to the sun according to the frequency shift r Expressed as:
v r ＝c((f rs -f es )/f es ) (3)
wherein c is the speed of light, f rs Spectral frequency f emitted by the sun received by the spacecraft es Spectral frequencies emitted for the sun;
taking Doppler radial velocity of the spacecraft relative to the sun as a quantity measurement, and establishing a solar Doppler velocity measurement model by utilizing mathematical relation between the Doppler radial velocity and the position of the spacecraft:
Figure FDA0004214852660000028
wherein ,vr Radial velocity measurement representing spacecraft relative to sun, r ps ,v ps The position and the speed vector of the spacecraft relative to the sun under the geocentric inertial system are respectively r ps ＝||r ps The i indicates the magnitude of the position vector, v m Representing measurement noise;
establishing a relation between a position vector of the spacecraft relative to the sun and a state quantity in the INS by utilizing coordinate transformation;
in the geocentric inertial coordinate system O-xyz, r ps 、v ps The position and the speed vector of the spacecraft relative to the sun under the geocentric inertial system are respectively r pe 、v pe The position and velocity vectors of the spacecraft relative to the earth are respectively
Figure FDA0004214852660000031
wherein ,
Figure FDA0004214852660000032
r n 、v n is the position and speed vector of the spacecraft in the n series relative to the earth, delta r n 、δv n Is a position and velocity error obtained by the INS; r is (r) se And v se The position and the velocity vector of the sun relative to the earth are obtained by an STK tool; />
Figure FDA0004214852660000033
A transition matrix from n-line to i-line, whereby the state quantity in the measurement model is linked to the state model, the solar doppler velocity measurement model is expressed as:
Figure FDA0004214852660000034
the discretized solar Doppler speed measurement model is expressed as follows:
Z k ＝H(X k ,k)+V k (7)
wherein H (g) represents a nonlinear continuous measurement function of solar Doppler velocity, V k And (5) representing the measurement error of the solar Doppler speed at the moment k.
2. The spacecraft inertial and solar doppler velocity integrated navigation method of claim 1, wherein: in the third step, UKF filtering is performed to obtain the position, speed and attitude estimation of the spacecraft as follows:
the state model and the measurement model of the integrated navigation system of the inertia and the solar Doppler speed of the discrete rear spacecraft are as follows:
Figure FDA0004214852660000035
wherein ,F(Xk-1 K-1) is a nonlinear transfer function of the integrated navigation system, H (X) k K) is a nonlinear measurement function, W k-1 V (V) k Respectively representing the process and the measurement noise, filtering the process and the measurement noise through UKF to obtain the posterior state estimation of the spacecraft
Figure FDA0004214852660000036
The attitude error angle, the speed and the position error of the spacecraft, the constant drift of the gyroscope and the constant bias of the accelerometer and the posterior error covariance are respectively->
Figure FDA0004214852660000037
Will->
Figure FDA0004214852660000038
Is->
Figure FDA0004214852660000039
Outputting, and simultaneously returning the estimated value of the k moment state quantity and the error covariance to the UKF filter for obtaining the k+1 momentIs provided.
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