CN103954279B - Doppler's differential speed measuring model and the method with X-ray pulsar integrated navigation - Google Patents
Doppler's differential speed measuring model and the method with X-ray pulsar integrated navigation Download PDFInfo
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Abstract
The invention discloses a kind of Doppler's differential speed measuring model and the method with X-ray pulsar integrated navigation, its Doppler's differential speed measuring model is Ys(t)=hs(X,t)+ωv, wherein, ωvFor Doppler measurement noise, YsAnd hsRepresent measured value respectively and measure equation, Ys=vD2-vD1,The method of integrated navigation comprises the following steps: step 1: set up the dynamics of orbits model of deep space probe；Step 2: set up X-ray pulsar navigational range model；Step 3: set up Doppler's differential speed measuring model；Step 4: utilize extended Kalman filter to filter.Present invention advantage compared with prior art is: (1), compared with existing pulsar/doppler combined navigation method, the present invention remains to normal table work under unstable solar spectrum；(2) compared with pulsar navigation method and Doppler navigation method, the present invention takes full advantage of multiple navigation information, has complete observability, is provided that the location information of higher precision.
Description
Technical Field
The invention belongs to the technical field of autonomous navigation of deep space probes, and particularly relates to a Doppler differential velocity measurement model and an X-ray pulsar combined navigation method.
Background
Astronomical autonomous navigation techniques are crucial for deep space probes. The astronomical autonomous navigation system obtains navigation information by measuring astronomical data. The astronomical navigation measurement method comprises three methods of angle measurement, distance measurement and speed measurement. In the deep space detection transfer orbit, the distance between the deep space detector and the near celestial body is very far, which causes the positioning precision of the angle measurement navigation method to be very low and can not meet the requirement of the deep space detection task on the positioning precision. The performance of the distance measurement navigation method (namely the X-ray pulsar navigation method) is limited by the area of the X-ray sensor, and the precision is limited. The speed measurement navigation method utilizes the solar spectrum frequency shift to invert the speed of the deep space detector, and the speed measurement precision is very high and can reach 1cm/s magnitude. However, the system is not completely observable, cannot work alone for a long time, and can only be used as an auxiliary means.
In an academic paper Doppler/XNAV-integrated Navigation system using small-area X-ray sensor (Doppler/pulsar integrated Navigation system using small-area X-ray sensors), published in IET Radar, Sonar & Navigation in 2011, a pulsar and Doppler integrated Navigation method is proposed. The method can provide high-precision positioning and constant-speed information under a stable solar light source. However, in practice, the solar spectrum is not stable due to the influence of interference factors such as solar flare, solar lugs, and blackens. This will cause a large deviation of the navigation speed measurement information in some time periods, which will affect the performance of the whole integrated navigation system.
Disclosure of Invention
In order to solve the technical problems, the invention provides a Doppler differential velocity measurement model and a navigation method combining the Doppler differential velocity measurement model and X-ray pulsar navigation, and aims to provide high-precision position and speed information for a deep space detector.
The technical scheme adopted by the Doppler differential velocity measurement model is as follows: a Doppler differential velocity measurement model is characterized in that:
first assume that the deep space probe is at t1The positions of time and t are r1And r, Mars at t1Position of time andvelocity is respectively rMAnd vMTwo spectrometers are carried on the deep space probe, the first spectrometer is at t1The spectral frequency shift of the direct solar light is measured at the moment, the spectral frequency shift of the solar light reflected by the mars is measured by the second spectrometer at the moment t, and t1The relationship of t to t is as follows:
wherein c is the speed of light;
based on the above assumptions, the establishment of the doppler difference velocity model comprises the following steps:
step A1: at t1Before the moment, t is determined according to t and formula one1A value of (d);
step A2: at t1At the moment, the Doppler velocity v in the solar radial direction is acquired by using a first spectrometerD1(ii) a At the time t, a second spectrometer is used for acquiring the Doppler velocity v in the radial direction of the MarsD2；
Step A3: establishing a Doppler difference velocity measurement model:
Ys(t)＝hs(X,t)+ωv(two)
Wherein, ω isvFor Doppler measurement of noise, YsAnd hsRespectively representing the measured values and the measurement equation, Ys＝vD2－vD1，
The technical scheme adopted by the combined navigation method of the Doppler differential velocity measurement model and the X-ray pulsar is as follows: a Doppler difference velocity measurement model and pulsar combined navigation method is characterized by comprising the following steps:
step B1: establishing a track dynamics model of the deep space probe;
step B2: establishing an X-ray pulsar navigation ranging model;
step B3: establishing a Doppler differential velocity measurement model;
step B4: and filtering by using an extended Kalman filter.
Preferably, the establishing of the orbit dynamics model of the deep space probe in the step B1 includes the following sub-steps:
step 1.1: determining the state vector X of the deep space probe as follows:
wherein r ═ x, y, z]TAnd v ═ vx,vy,vz]TRespectively the position and velocity vector of the deep space probe, x, y, z are the components of the position of the deep space probe in three axes, respectively, vx,vy,vzThe components of the speed of the deep space probe on three axes are respectively;
step 1.2: determining the orbit dynamics model of the deep space probe as follows:
wherein,are respectively x, y, z, vx,vy,vzThe derivative of (a) of (b),
formula four can be expressed as:
wherein,is the derivative of X and is the sum of,at a time tf (X, t) is the state transition model of the deep space probe, [ X ]1,y1,z1]And [ x ]2,y2,z2]The relative position vectors, μ, of Mars and Earth, respectively, with respect to the center of mass of the solar systems,μm,μeThe gravitational constants, r, of the sun, Mars and Earth, respectivelyps,rpm,rpeThe distances from the deep space probe to the sun centroid, the mars centroid and the earth centroid respectively have the calculation formula: respectively the distances from the Mars centroid and the earth centroid to the sun centroid; navigation system noise omega of deep space probe is [0,0, 0, delta F ═x,ΔFy,ΔFz]TWherein, Δ Fx，ΔFyAnd Δ FzIs the pickup force, and omega (t) is the system noise of the deep space probe at the moment t.
Preferably, the establishing of the X-ray pulsar navigation ranging model in the step B2 includes the following sub-steps:
step 2.1: determining the number of X-ray pulsar used for navigation and orientation parameters thereof;
step 2.2: establishing an X-ray pulse arrival time conversion model as follows:
wherein,the projection of the distance between the deep space detector and the solar system centroid in the direction of the jth pulsar; n isjIs the direction vector of the jth pulsar, j is 1,2, … I, I is the number of X-ray pulsar employed, αjAndjthe right ascension and the declination of the jth pulsar respectively,andthe time of the pulse reaching the deep space detector and the time of the pulse reaching the center of mass of the solar system are respectively, c is the speed of light,the distance from the jth pulsar to the solar system centroid is shown, b is the position vector of the solar system centroid relative to the sun, and | b | is the length of the position vector b; mu.sSunThe constant is a solar attraction constant, r is a position vector of the deep space detector relative to the center of mass of the solar system, and | r | is the length of the position vector r;
step 2.3: determining X-ray pulsar navigation observation model hX(X(t),t)；
First, suppose X-ray pulsar navigation observed quantity YXComprises the following steps:
and the corresponding measurement noise is V, the X-ray pulsar navigation observation model can be expressed as follows:
YX＝hX(X (t), t) + V (t) (formula Jiu)
Wherein V (t) is the measurement noise at time t, and observation model hX(X (t), t) is as follows:
wherein, the corresponding term h of the jth pulsarj(X (t), t) is as follows:
preferably, the filtering in step B4 by using an extended kalman filter is implemented by: firstly, establishing a measurement model of a pulsar middle filter, wherein during pulsar observation, the measurement model h (X, t) and a measurement value Y are as follows:
h(X,t)＝hs(X, t) (formula twelve)
Y＝Ys(thirteen formula)
Once the pulse arrival time is obtained, the measurement h (X, t) and measurement model Y are then expressed as:
wherein h iss(X (t), t) is hs(X,t)，hI(X (t), t) is hI(X,t)。
Compared with the prior art, the invention has the advantages that:
(1) compared with the existing pulsar and Doppler combined navigation method, the method can still work normally and stably under unstable solar spectrum;
(2) compared with a pulsar navigation method and a Doppler navigation method, the method makes full use of various navigation information, has complete observability, and can provide positioning information with higher precision.
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FIG. 1: the Doppler differential velocity measurement principle schematic diagram of the embodiment of the invention.
Detailed Description
In order to facilitate the understanding and implementation of the present invention for those of ordinary skill in the art, the present invention is further described in detail with reference to the accompanying drawings and examples, it is to be understood that the embodiments described herein are merely illustrative and explanatory of the present invention and are not restrictive thereof.
This embodiment first presents a Mars probe trajectory as shown in Table 1.
TABLE 1 starting orbital parameters
Referring to fig. 1, the embodiment provides a doppler difference velocity measurement model, first, suppose that the deep space probe is at t1The positions of time and t are r1And r, Mars at t1The position and velocity of the time are rMAnd vMTwo spectrometers are carried on the deep space probe, the first spectrometer is at t1The spectral frequency shift of the direct solar light is measured at the moment, the spectral frequency shift of the solar light reflected by the mars is measured by the second spectrometer at the moment t, and t1The relationship of t to t is as follows:
wherein c is the speed of light;
based on the above assumptions, the establishment of the doppler difference velocity model comprises the following steps:
step A1: at t1Before the moment, t is determined according to t and formula one1A value of (d);
step A2: at t1At the moment, the Doppler velocity v in the solar radial direction is acquired by using a first spectrometerD1(ii) a At the time t, a second spectrometer is used for acquiring the Doppler velocity v in the radial direction of the MarsD2；
Step A3: establishing a Doppler difference velocity measurement model:
Ys(t)＝hs(X,t)+ωv(two)
Wherein, ω isvFor Doppler measurement of noise, YsAnd hsRespectively representing the measured values and the measurement equation, Ys＝vD2－vD1，
The present embodiment provides a method for combined navigation of a doppler difference velocity measurement model and an X-ray pulsar based on the doppler difference velocity measurement model, which includes the following steps:
step B1: establishing a track dynamics model of the deep space probe; the specific implementation comprises the following substeps:
step 1.1: determining the state vector X of the deep space probe as follows:
wherein r ═ x, y, z]TAnd v ═ vx,vy,vz]TRespectively the position and velocity vector of the deep space probe, x, y, z are the components of the position of the deep space probe in three axes, respectively, vx,vy,vzThe components of the speed of the deep space probe on three axes are respectively;
step 1.2: determining the orbit dynamics model of the deep space probe as follows:
wherein,are respectively x, y, z, vx,vy,vzThe derivative of (a) of (b),
formula four can be expressed as:
wherein,is the derivative of X and is the sum of,at a time tf (X, t) is the state transition model of the deep space probe, [ X ]1,y1,z1]And [ x ]2,y2,z2]The relative position vectors, μ, of Mars and Earth, respectively, with respect to the center of mass of the solar systems,μm,μeThe sun, the spark and the earth respectivelyG constant of attraction, rps,rpm,rpeThe distances from the deep space probe to the sun centroid, the mars centroid and the earth centroid respectively have the calculation formula: respectively the distances from the Mars centroid and the earth centroid to the sun centroid; navigation system noise omega of deep space probe is [0,0, 0, delta F ═x,ΔFy,ΔFz]TWherein, Δ Fx，ΔFyAnd Δ FzIs the pickup force, and omega (t) is the system noise of the deep space probe at the moment t.
Step B2: establishing an X-ray pulsar navigation ranging model; the specific implementation comprises the following substeps:
step 2.1: determining the number of X-ray pulsar used for navigation and orientation parameters thereof;
the pulsar of the present embodiment employs three pulsars, and the pulsars and their orientation parameters are shown in table 2.
TABLE 2 pulsar azimuth parameters
Step 2.2: establishing an X-ray pulse arrival time conversion model as follows:
wherein,the projection of the distance between the deep space detector and the solar system centroid in the direction of the jth pulsar; n isjIs the direction vector of the jth pulsar, j is 1,2, … I, I is the number of X-ray pulsar employed, I is 3, α in this examplejAndjthe right ascension and the declination of the jth pulsar respectively,andthe time of the pulse reaching the deep space detector and the time of the pulse reaching the center of mass of the solar system are respectively, c is the speed of light,the distance from the jth pulsar to the solar system centroid is shown, b is the position vector of the solar system centroid relative to the sun, and | b | is the length of the position vector b; mu.sSunThe constant is a solar attraction constant, r is a position vector of the deep space detector relative to the center of mass of the solar system, and | r | is the length of the position vector r;
step 2.3: determining X-ray pulsar navigation observation model hX(X(t),t)；
First, suppose X-ray pulsar navigation observed quantity YXComprises the following steps:
and the corresponding measurement noise is V, the X-ray pulsar navigation observation model can be expressed as follows:
YX＝hX(X (t), t) + V (t) (formula Jiu)
Wherein V (t) is the measurement noise at time t, and observation model hX(X (t), t) is as follows:
wherein, the corresponding term h of the jth pulsarj(X (t), t) is as follows:
step B3: establishing a Doppler differential velocity measurement model;
step B4: and filtering by using an extended Kalman filter. The specific implementation process is as follows: firstly, establishing a measurement model of a pulsar middle filter, wherein during pulsar observation, the measurement model h (X, t) and a measurement value Y are as follows:
h(X,t)＝hs(X, t) (formula twelve)
Y＝Ys(thirteen formula)
Once the pulse arrival time is obtained, the measurement model h (X, t) and the measurement value Y are then expressed as:
wherein h iss(X (t), t) is hs(X,t)，hI(X (t), t) is hI(X,t)。
The filter parameters for this example are shown in table 3:
TABLE 3 Filter parameters
Wherein X (0) is the state initial error of the deep space detector, P (0) is the initial state error matrix, Q is the state noise covariance,i.e. q1The square of the square,i.e. q2Square of (d).
It should be understood that the above description of the preferred embodiments is given for clarity and not for any purpose of limitation, and that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (4)
1. A method for combined navigation by using a Doppler differential velocity measurement model and an X-ray pulsar comprises the steps of firstly, assuming that a deep space detector is at t1The positions of time and t are r1And r, Mars at t1The position and velocity of the time are rMAnd vMTwo spectrometers are carried on the deep space probe, the first spectrometer is at t1The spectral frequency shift of the direct solar light is measured at the moment, the spectral frequency shift of the solar light reflected by the mars is measured by the second spectrometer at the moment t, and t1The relationship of t to t is as follows:
wherein c is the speed of light;
based on the above assumptions, the establishment of the doppler difference velocity model comprises the following steps:
step A1: at t1Before the moment, t is determined according to t and formula one1A value of (d);
step A2: at t1At the moment, the Doppler velocity v in the solar radial direction is acquired by using a first spectrometerD1(ii) a At the time t, a second spectrometer is used for acquiring the Doppler velocity v in the radial direction of the MarsD2；
Step A3: establishing a Doppler difference velocity measurement model:
Ys(t)＝hs(X,t)+ωv(two)
Wherein, ω isvFor Doppler measurement of noise, YsAnd hsRespectively representing the measured values and the measurement equation, Ys＝vD2－vD1，
The method is characterized by comprising the following steps:
step B1: establishing a track dynamics model of the deep space probe;
step B2: establishing an X-ray pulsar navigation ranging model;
step B3: establishing a Doppler differential velocity measurement model;
step B4: and filtering by using an extended Kalman filter.
2. The combined navigation method of the Doppler differential velocity model and the X-ray pulsar of claim 1, wherein: the track dynamics model of the deep space probe established in the step B1 is specifically realized by the following steps:
because the state vector X of the deep space probe is:
wherein r ═ x, y, z]TAnd v ═ vx,vy,vz]TRespectively the position and velocity vector of the deep space probe, x, y, z are the components of the position of the deep space probe in three axes, respectively, vx,vy,vzThe components of the speed of the deep space probe on three axes are respectively;
the orbit dynamics model of the deep space probe is then:
wherein,are respectively x, y, z, vx,vy,vzThe derivative of (a) of (b),
formula four can be expressed as:
wherein,is the derivative of X and is the sum of,at a time tf (X, t) is the state transition model of the deep space probe, [ X ]1,y1,z1]And [ x ]2,y2,z2]The relative position vectors, μ, of Mars and Earth, respectively, with respect to the center of mass of the solar systems,μm,μeThe gravitational constants, r, of the sun, Mars and Earth, respectivelyps,rpm,rpeThe distances from the deep space probe to the sun centroid, the mars centroid and the earth centroid respectively have the calculation formula: the distances from the Mars mass center and the Earth mass center to the Sun mass center respectively, and the navigation system noise omega of the deep space probe is [0,0, 0, △ Fx,△Fy,△Fz]TWherein, △ Fx，△FyAnd △ FzIs a perturbation force, and omega (t) is the noise of a navigation system of the deep space probe at the moment t.
3. The combined navigation method of the Doppler differential velocity model and the X-ray pulsar of claim 2, wherein: the establishing of the X-ray pulsar navigation ranging model in the step B2 includes the following specific steps:
step 2.1: determining the number of X-ray pulsar used for navigation and orientation parameters thereof;
step 2.2: establishing an X-ray pulse arrival time conversion model as follows:
wherein,the projection of the distance between the deep space detector and the solar system centroid in the direction of the jth pulsar; n isjIs the direction vector of the jth pulsar, j is 1,2, … I, I is the number of X-ray pulsar employed, αjAndjthe right ascension and the declination of the jth pulsar respectively,andthe time of the pulse reaching the deep space detector and the time of the pulse reaching the center of mass of the solar system are respectively, c is the speed of light,the distance from the jth pulsar to the solar system centroid is shown, b is the position vector of the solar system centroid relative to the sun, and | b | is the length of the position vector b; mu.sSunThe constant is a solar attraction constant, r is a position vector of the deep space detector relative to the center of mass of the solar system, and | r | is the length of the position vector r;
step 2.3: determining X-ray pulsar navigation observation model hX(X(t),t)；
First, suppose X-ray pulsar navigation observed quantity YXComprises the following steps:
and the corresponding measurement noise is V, the X-ray pulsar navigation observation model can be expressed as follows:
YX＝hX(X (t), t) + V (t) (formula Jiu)
Wherein V (t) is the measurement noise at time t, and observation model hX(X (t), t) is as follows:
wherein, the corresponding term h of the jth pulsarj(X (t), t) is as follows:
4. the combined navigation method of the Doppler differential velocity model and the X-ray pulsar of claim 3, wherein: the filtering in the step B4 by using the extended kalman filter is specifically implemented by: firstly, establishing a measurement model of a pulsar middle filter, wherein during pulsar observation, the measurement model h (X, t) and a measurement value Y are as follows:
h(X,t)＝hs(X, t) (formula twelve)
Y＝Ys(thirteen formula)
Once the pulse arrival time is obtained, the measurement model h (X, t) and the measurement value Y are then expressed as:
wherein h iss(X (t), t) is hs(X,t)，hI(X (t), t) is hI(X,t)。
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