CN103063216B - A kind of inertia based on star image coordinates modeling and celestial combined navigation method - Google Patents

Abstract

The present invention proposes a kind of inertia based on star image coordinates modeling and celestial combined navigation method, described method is according to the difference of observed fixed star number, inertia when automatically realizing many star observations combines with astronomical, improve the dirigibility that fixed star starlight measurement information uses, when starlight configuration significantly worsens, the observation noise characteristic of input card Kalman Filtering still keeps stable, improve the navigation performance in available navigation fixed star quantity significantly minimizing situation in high dynamic flying, do not adopt conventional inertia of the present invention compared with astronomical combined system, the situation that the inventive method starlight configuration worsens has better adaptability, be applicable to engineer applied.

Description

A kind of inertia based on star image coordinates modeling and celestial combined navigation method

Technical field

The invention belongs to integrated navigation technology field, specifically refer to a kind of inertia based on star image coordinates modeling and celestial combined navigation method.

Background technology

Integrated navigation is the effective way improving aircraft guidance system reliability and precision, and current inertia and combinations of satellites are navigated with good positioning performance, are widely applied in the navigation of all kinds of aircraft, but its attitude accuracy is limited; In order to meet the high-acruracy survey demand of control system to attitude, starlight information combination can be observed to revise attitude error by star sensor by celestial navigation.

Along with the development of course of new aircraft, the application of pole rugged surroundings to celestial navigation system caused by Aerodynamic Heating proposes new problem.The aero-optical effect that high-speed flight causes will have a strong impact on the imaging of star sensor to star chart, and part starlight information will be caused to utilize.Comparatively strong in Vehicle nose according to the impact of plasma sheath and aero-optical effect, the characteristic that afterbody is comparatively weak, is similar to and thinks that visible satellite and navigation fixed star roughly constrain in the scope of a circular cone window.This makes the quantity of visible nautical star significantly reduce, and visible star is gathered in narrow its visibility window, and geometric configuration is poor.

Therefore, based on star image coordinate Direct Modeling, set up the air navigation aid that inertial navigation and celestial navigation more closely combine, the measurement noise modeling of inertia and celestial combined navigation can be simplified, effectively improve adaptability and the navigation performance of inertia and celestial combined navigation, will outstanding using value be had.

Conventional inertia and celestial combined navigation observe starlight azimuth information mainly through star sensor, and according to the attitude information of TRIAD, QUEST scheduling algorithm determination carrier under inertial system, recycling junction filter and inertial navigation system combine.During by star sensor determination attitude of flight vehicle, the geometric configuration of nautical star has larger impact to attitude accuracy.When the aero-optical effect of hypersonic flight causes part starlight information to utilize, the geometric configuration of visible nautical star significantly worsens, the attitude accuracy generation acute variation that star sensor exports, attitude information noisiness does not meet the requirement that Kalman filtering measurement noise is white noise, adopts conventional array mode will affect combined filter performance.

Summary of the invention

The object of the invention is to overcome the deficiencies in the prior art, avoid conventional inertia and celestial combined navigation method to the demand becoming statistical property modeling during celestial navigation system error characteristics, and provide assisting continuously inertial navigation system when star number of navigating is less, provide a kind of inertia based on star image coordinates modeling and celestial combined navigation method.

For achieving the above object, the technical solution adopted in the present invention is:

Based on inertia and the celestial combined navigation method of star image coordinates modeling, comprise the following steps:

Steps A, according to inertia and celestial combined navigation error characteristics, by the mathematical description of airborne INS errors, sets up inertia and celestial combined navigation error state amount equation; Inertia and celestial combined navigation error state amount X are defined as:

$X={[{\mathrm{\φ}}_E,{\mathrm{\φ}}_N,{\mathrm{\φ}}_U,{\mathrm{\δv}}_E,{\mathrm{\δv}}_N,{\mathrm{\δv}}_U,\mathrm{\δL},\mathrm{\δ\λ},\mathrm{\δh},{\mathrm{\ϵ}}_{\mathrm{bx}},{\mathrm{\ϵ}}_{\mathrm{by}},{\mathrm{\ϵ}}_{\mathrm{bz}},{\mathrm{\ϵ}}_{\mathrm{rx}},{\mathrm{\ϵ}}_{\mathrm{ry}},{\mathrm{\ϵ}}_{\mathrm{rz}},{\▿}_x,{\▿}_y,{\▿}_z]}^T$

Wherein,

φ _e, φ _n, φ _ueast orientation platform error angle quantity of state, north orientation platform error angle quantity of state and sky respectively in expression airborne INS errors quantity of state are to platform error angle quantity of state;

δ v _e, δ v _n, δ v _ueast orientation velocity error quantity of state, north orientation velocity error quantity of state and sky respectively in expression airborne INS errors quantity of state are to velocity error quantity of state;

δ L, δ λ, δ h represent latitude error quantity of state, longitude error quantity of state and height error quantity of state in airborne INS errors quantity of state respectively;

ε _bx, ε _by, L _bz, ε _rx, ε _ry, ε _rzrepresent X-axis, Y-axis, Z-direction gyroscope constant value drift error state amount and X-axis in airborne INS errors quantity of state, Y-axis, Z-direction gyro first order Markov drift error quantity of state respectively;

represent X-axis, Y-axis and the Z-direction accelerometer bias in airborne INS errors quantity of state respectively, T is transposition;

Step B, according to celestial navigation system Observation principle and INS errors model, analyzes the transitive relation between celestial navigation system starlight picpointed coordinate error and inertial navigation system position, attitude error, sets up star image error of coordinate TRANSFER MODEL;

Step C, adopt the linearization observation procedure under airborne Department of Geography, according to the observation modeling result based on celestial navigation system starlight picpointed coordinate error and inertial navigation system position, attitude error of step B, measurement equation is combined in the linearization between the celestial navigation system measured value of foundation and airborne INS errors quantity of state X;

Step D, carries out inertial navigation and resolves, and obtains airborne inertial navigation system Output rusults;

Step e, has judged whether celestial navigation system measured value, if so, then records the star image coordinates measurements of celestial navigation system and performs step F, otherwise performs step H;

Step F, the airborne inertial navigation system Output rusults utilizing step D to calculate, calculates the star image coordinate calculated value calculated by airborne inertial navigation system;

Step G, the star image coordinate that the star image coordinate recorded according to celestial navigation system in step e and step F airborne inertial navigation system are calculated, linearization between the celestial navigation system measured value utilizing step C to set up and airborne INS errors quantity of state X is combined measurement equation and is carried out combined filter, estimate airborne inertial navigation system evaluated error quantity of state and for revising navigation error;

Step H, exports navigation results, and judges whether navigation procedure terminates, and if it is stops navigation, otherwise re-executes step D.

Transitive relation between analysis celestial navigation system starlight picpointed coordinate error described in step B and inertial navigation system position, attitude error, set up the process of star image error of coordinate TRANSFER MODEL, comprise following sub-step:

Step B-1, under definition celestial navigation system coordinate system, starlight picture point error is δ x, δ y, then:

$\left.\begin{array}{c}\mathrm{\δx}=x-x_I\\ \mathrm{\δy}=y-y_I\end{array}\right\}$

Wherein x, y are star image coordinate actual value, x _i, y _ifor star image coordinate calculated value;

Step B-2, definition starlight deviation of directivity angle vector Ψ=[Ψ _xΨ _yΨ _z] ^t, Ψ _x, Ψ _y, Ψ _zrepresent the deviation angle of the spaced winding X-axis in starlight direction and the actual starlight direction calculated by airborne inertial navigation system, Y-axis, Z axis respectively;

Step B-3, definition airborne inertial navigation system platform error angle vector φ=[φ E φ N φ U] ^t, φ _e, φ _n, φ _ueast orientation platform error angle quantity of state, north orientation platform error angle quantity of state and sky respectively in expression airborne INS errors quantity of state are to platform error angle quantity of state; Definition airborne inertial navigation system site error vector delta P=[-δ L δ λ cosL δ λ sinL] ^t, δ L, δ λ represents airborne inertial navigation system latitude error quantity of state, longitude error quantity of state respectively, and L represents latitude;

Step B-4, according to celestial navigation system Observation principle, set up the linearization measurement model between starlight picpointed coordinate error and starlight deviation of directivity angle vector Ψ under celestial navigation system coordinate system, its expression formula is

$\left[\begin{array}{c}\mathrm{\δx}\\ \mathrm{\δy}\end{array}\right]=H_{\mathrm{\ψ}}\mathrm{\ψ}$

Wherein, $H_{\mathrm{\ψ}}=\left[\begin{array}{ccc}0& f& {-y}_I\\ -f& 0& x_I\end{array}\right],$ F is the focal length of celestial navigation system star sensor;

Step B-5, according to INS errors principle, set up starlight deviation of directivity angle vector Ψ and the linearization measurement model between airborne inertial navigation system platform error angle vector φ, site error vector delta P, its expression formula is

$\mathrm{\ψ}=C_b^s{\tilde{C}}_n^b(\mathrm{\φ}-\mathrm{\δP})$

Wherein, represent that aircraft body coordinate is tied to the coordinate conversion matrix of celestial navigation system coordinate system, represent that geographic coordinate is tied to the coordinate conversion matrix of aircraft body coordinate system;

Step B-6, to set up based on celestial navigation system starlight picpointed coordinate error the observation model of inertial navigation system position, attitude error:

$\left[\begin{array}{c}\mathrm{\δx}\\ \mathrm{\δy}\end{array}\right]=H_{\mathrm{\ψ}}{C}_b^s{\tilde{C}}_n^b(\mathrm{\φ}-\mathrm{\δP})$

Wherein, the celestial navigation system measured value described in step C and the linearization between INS errors quantity of state X are combined and are measured equation form and be:

$\left[\begin{array}{c}{Z}_1\\ Z_2\\ .\\ .\\ .\\ Z_m\end{array}\right..=\left[\begin{array}{c}{H}_{\mathrm{\ψ}1}\\ H_{\mathrm{\ψ}2}\\ .\\ .\\ .\\ H_{\mathrm{\ψm}}\end{array}\right]H_{X}X+{\mathrm{Vi}}_{m\×1}$

In formula, m is the fixed star number simultaneously observed, I _{m × 1}represent complete 1 column vector of m dimension, V represents celestial navigation system measurement noise, Z _i(i=1 ... m) be observed quantity, Z _iexpression formula be

$Z_i=\left[\begin{array}{c}{x}_{\mathrm{Ii}}-x_{\mathrm{Ci}}\\ y_{\mathrm{Ii}}-y_{\mathrm{Ci}}\end{array}\right]$

Wherein, x _ii, y _iibe the X-axis of i-th fixed star and the star image coordinate calculated value of Y-axis; x _ci, y _cifor celestial navigation system records the star image coordinate of i-th fixed star X-axis and Y-axis;

In formula, H _{Ψ i}(i=1 ... m) expression formula is

$H_{\mathrm{\ψi}}=\left[\begin{array}{ccc}0& f& {-y}_{\mathrm{Ii}}\\ -f& 0& x_{\mathrm{Ii}}\end{array}\right]$

Wherein, f is the focal length of celestial navigation system;

In formula, H _xexpression formula be

$H_X=C_b^s{\tilde{C}}_n^b\left[\begin{array}{cccc}{I}_{3\×3}& 0_{3\×3}& M& 0_{3\×9}\end{array}\right]$

Wherein, represent that aircraft body coordinate is tied to the coordinate conversion matrix of celestial navigation system coordinate system, represent that geographic coordinate is tied to the coordinate conversion matrix of aircraft body coordinate system; I _{3 × 3}represent the unit matrix that 3 row 3 arrange, 0 _{3 × 3}represent the full null matrix that 3 row 3 arrange, 0 _{3 × 9}represent the full 0 matrix that 3 row 9 arrange, Metzler matrix expression formula is

$M=\left[\begin{array}{ccc}1& 0& 0\\ 0& -\cos L& 0\\ 0& -\sin L& 0\end{array}\right].$

The star image coordinate that calculating described in step F is calculated by airborne inertial navigation system comprises following sub-step:

Step F-1, from right ascension α, the declination δ of navigation fixed star library inquiry fixed star, according to starlight direction vector r under formula calculating inertial system _i:

$r_i=\left[\begin{array}{c}\cos \mathrm{\α}\cos \mathrm{\δ}\\ \sin \mathrm{\α}\cos \mathrm{\δ}\\ \sin \mathrm{\δ}\end{array}\right]$

Step F-2, according to airborne inertial navigation system Output rusults, and starlight direction vector r under the inertial system of sub-step F-1 calculating _i, starlight direction vector r under calculating star sensor coordinate system _i:

$r_I=C_b^s{\tilde{C}}_n^b{\tilde{C}}_e^n{C}_i^e{r}_i$

Wherein, represent that aircraft body coordinate is tied to the coordinate conversion matrix of celestial navigation system coordinate system, represent that the geographic coordinate of airborne inertial navigation system calculating is tied to the coordinate conversion matrix of aircraft body coordinate system; represent that the terrestrial coordinates of airborne inertial navigation system calculating is tied to the coordinate conversion matrix of geographic coordinate system; represent that inertial coordinate is tied to the coordinate conversion matrix of terrestrial coordinate system;

Step F-3, starlight direction vector r under the star sensor coordinate system calculated by sub-step F-2 _i, be calculated as star image coordinate calculated value x _i, y _i

$\left.\begin{array}{c}{x}_I=f\frac{r_{\mathrm{Ix}}}{r_{\mathrm{Iz}}}\\ y_I=f\frac{r_{\mathrm{Iy}}}{r_{\mathrm{Iz}}}\end{array}\right\}$

Wherein, f represents the focal length of celestial navigation system star sensor, r _ixstarlight direction vector r under expression star sensor coordinate system _icomponent in X-axis, r _iystarlight direction vector r under expression star sensor coordinate system _icomponent in Y-axis, r _izstarlight direction vector r under expression star sensor coordinate system _icomponent on Z axis.

The invention has the beneficial effects as follows: the present invention proposes a kind of inertia based on star image coordinates modeling and celestial combined navigation method, described method is according to the difference of observed fixed star number, inertia when automatically realizing many star observations combines with astronomical, improve the dirigibility that fixed star starlight measurement information uses, when starlight configuration significantly worsens, the observation noise characteristic of input card Kalman Filtering still keeps stable, improve the navigation performance in available navigation fixed star quantity significantly minimizing situation in high dynamic flying, do not adopt conventional inertia of the present invention compared with astronomical combined system, the situation that the inventive method starlight configuration worsens has better adaptability, be applicable to engineer applied.

Accompanying drawing explanation

Fig. 1 is a kind of inertia based on star image coordinates modeling of the present invention and celestial combined navigation method flow diagram;

Navigation angle of pitch graph of errors comparison diagram when Fig. 2 is different visible navigation fixed star number;

Fig. 3 is the visible navigation fixed star curve map under dynamic track flight taper constraint;

Fig. 4 is for nothing astronomy is auxiliary and assembled gesture graph of errors comparison diagram under having astronomical aided case;

Fig. 5 is for nothing astronomy is auxiliary and gyro single order Markov drift estimate error to standard deviation curve comparison figure under having astronomical aided case.

Embodiment

Below in conjunction with accompanying drawing, a kind of inertia based on star image coordinates modeling propose the present invention and celestial combined navigation method are described in detail:

Based on inertia and the celestial combined navigation method of star image coordinates modeling, this method flow process as shown in Figure 1, the steps include:

1) inertia and celestial combined navigation error state amount equation is set up

According to inertia and celestial combined navigation error characteristics, by the mathematical description of airborne INS errors, set up inertia and celestial combined navigation error state amount equation, inertia and celestial combined navigation error state amount X are defined as:

$X={[{\mathrm{\φ}}_E,{\mathrm{\φ}}_N,{\mathrm{\φ}}_U,{\mathrm{\δv}}_E,{\mathrm{\δv}}_N,{\mathrm{\δv}}_U,\mathrm{\δL},\mathrm{\δ\λ},\mathrm{\δh},{\mathrm{\ϵ}}_{\mathrm{bx}},{\mathrm{\ϵ}}_{\mathrm{by}},{\mathrm{\ϵ}}_{\mathrm{bz}},{\mathrm{\ϵ}}_{\mathrm{rx}},{\mathrm{\ϵ}}_{\mathrm{ry}},{\mathrm{\ϵ}}_{\mathrm{rz}},{\▿}_x,{\▿}_y,{\▿}_z]}^T,$ φ _e, φ _n, φ _ueast orientation platform error angle quantity of state, north orientation platform error angle quantity of state and sky respectively in expression airborne INS errors quantity of state are to platform error angle quantity of state; δ v _e, δ v _n, δ v _ueast orientation velocity error quantity of state, north orientation velocity error quantity of state and sky respectively in expression airborne INS errors quantity of state are to velocity error quantity of state; δ L, δ λ, δ h represent latitude error quantity of state, longitude error quantity of state and height error quantity of state in airborne INS errors quantity of state respectively; ε _bx, ε _by, ε _bz, ε _rx, ε _ry, ε _rzrepresent X-axis, Y-axis, Z-direction gyroscope constant value drift error state amount and X-axis in airborne INS errors quantity of state, Y-axis, Z-direction gyro first order Markov drift error quantity of state respectively; represent X-axis, Y-axis and the Z-direction accelerometer bias in airborne INS errors quantity of state respectively, T is transposition;

2) star image error of coordinate TRANSFER MODEL is set up

According to celestial navigation system Observation principle and INS errors model, set up the TRANSFER MODEL between celestial navigation system starlight picpointed coordinate error and inertial navigation system position, attitude error, concrete steps are as follows:

2.1) according to starlight picture point error delta x, δ y under formula definition celestial navigation system coordinate system

$\left.\begin{array}{c}\mathrm{\δx}=x-x_I\\ \mathrm{\δy}=y-y_I\end{array}\right\}$

Wherein x, y are star image coordinate actual value, x _i, y _ifor star image coordinate calculated value;

2.2) starlight deviation of directivity angle vector Ψ=[Ψ is defined _xΨ _yΨ _z] ^t, Ψ _x, Ψ _y, Ψ _zrepresent the deviation angle of the spaced winding X-axis in starlight direction and the actual starlight direction calculated by airborne inertial navigation system, Y-axis, Z axis respectively;

2.3) airborne inertial navigation system platform error angle vector φ=[φ is defined _eφ _nφ _u] ^t, φ _e, φ _n, φ _ueast orientation platform error angle quantity of state, north orientation platform error angle quantity of state and sky respectively in expression airborne INS errors quantity of state are to platform error angle quantity of state; Definition airborne inertial navigation system site error vector delta P=[-δ L δ λ cosL δ λ sinL] ^t, δ L, δ λ represents airborne inertial navigation system latitude error quantity of state, longitude error quantity of state respectively, and L represents latitude;

2.4) according to celestial navigation system Observation principle, set up the linearization measurement model between starlight picpointed coordinate error and starlight deviation of directivity angle vector Ψ under celestial navigation system coordinate system, its expression formula is

$\left[\begin{array}{c}\mathrm{\δx}\\ \mathrm{\δy}\end{array}\right]=H_{\mathrm{\ψ}}\mathrm{\ψ}$

Wherein $H_{\mathrm{\ψ}}=\left[\begin{array}{ccc}0& f& {-y}_I\\ -f& 0& x_I\end{array}\right],$ F is the focal length of celestial navigation system star sensor;

2.5) according to INS errors principle, set up starlight deviation of directivity angle vector Ψ and the linearization measurement model between airborne inertial navigation system platform error angle vector φ, site error vector delta P, its expression formula is

$\mathrm{\ψ}=C_b^s{\tilde{C}}_n^b(\mathrm{\φ}-\mathrm{\δP})$

Wherein represent that aircraft body coordinate is tied to the coordinate conversion matrix of celestial navigation system coordinate system, represent that geographic coordinate is tied to the coordinate conversion matrix of aircraft body coordinate system;

2.6) according to step 2.4) linearization measurement model under the celestial navigation system coordinate system set up between starlight picpointed coordinate error and starlight direction vector misalignment Ψ, and step 2.5) the starlight direction vector misalignment Ψ that sets up and airborne inertial navigation system platform error angle vector φ, site error vector delta P, set up based on celestial navigation system starlight picpointed coordinate error the observation model of inertial navigation system position, attitude error

$\left[\begin{array}{c}\mathrm{\δx}\\ \mathrm{\δy}\end{array}\right]=H_{\mathrm{\ψ}}{C}_b^s{\tilde{C}}_n^b(\mathrm{\φ}-\mathrm{\δP})$

3) inertia based on star image coordinates modeling and celestial combined navigation measurement equation is set up

Adopt the linearization observation procedure under airborne Department of Geography, according to the observation modeling result based on celestial navigation system starlight picpointed coordinate error and inertial navigation system position, attitude error of step (2), the linearization between the celestial navigation system measured value of foundation and airborne INS errors quantity of state X is combined and is measured equation form and be:

$\left[\begin{array}{c}{Z}_1\\ Z_2\\ .\\ .\\ .\\ Z_m\end{array}\right..=\left[\begin{array}{c}{H}_{\mathrm{\ψ}1}\\ H_{\mathrm{\ψ}2}\\ .\\ .\\ .\\ H_{\mathrm{\ψm}}\end{array}\right]H_{X}X+{\mathrm{Vi}}_{m\×1}$

In formula, m is the fixed star number simultaneously observed, I _{m × 1}represent complete 1 column vector of m dimension, V represents celestial navigation system measurement noise, Z _i(i=1 ... m) be observed quantity, Z _iexpression formula be

$Z_i=\left[\begin{array}{c}{x}_{\mathrm{Ii}}-x_{\mathrm{Ci}}\\ y_{\mathrm{Ii}}-y_{\mathrm{Ci}}\end{array}\right]$

Wherein x _ii, y _iibe the X-axis of i-th fixed star and the star image coordinate calculated value of Y-axis; x _ci, y _cifor celestial navigation system records the star image coordinate of i-th fixed star X-axis and Y-axis;

In formula, H _{Ψ i}(i=1 ... m) expression formula is

$H_{\mathrm{\ψi}}=\left[\begin{array}{ccc}0& f& {-y}_{\mathrm{Ii}}\\ -f& 0& x_{\mathrm{Ii}}\end{array}\right]$

Wherein f is the focal length of celestial navigation system;

In formula, H _xexpression formula be

$H_X=C_b^s{\tilde{C}}_n^b\left[\begin{array}{cccc}{I}_{3\×3}& 0_{3\×3}& M& 0_{3\×9}\end{array}\right]$

Wherein, represent that aircraft body coordinate is tied to the coordinate conversion matrix of celestial navigation system coordinate system, represent that geographic coordinate is tied to the coordinate conversion matrix of aircraft body coordinate system; I _{3 × 3}represent the unit matrix that 3 row 3 arrange, 0 _{3 × 3}represent the full null matrix that 3 row 3 arrange, 0 _{3 × 9}represent the full 0 matrix that 3 row 9 arrange, Metzler matrix expression formula is

$M=\left[\begin{array}{ccc}1& 0& 0\\ 0& -\cos L& 0\\ 0& -\sin L& 0\end{array}\right]$

4) carry out inertial navigation to resolve, obtain airborne inertial navigation system Output rusults

5) judge whether that carrying out inertia combines with astronomical, obtains star image coordinates measurements

Judge whether celestial navigation system measurement data, if so, then recorded the star image coordinates measurements of celestial navigation system and perform step (6), otherwise perform step (8);

6) star image coordinate calculated value is obtained

Utilize the airborne inertial navigation system Output rusults that step (4) is calculated, calculate the star image coordinate calculated value calculated by airborne inertial navigation system, specifically comprise following sub-step:

6.1) from right ascension α, the declination δ of navigation star database inquiry fixed star, according to starlight direction vector r under formula calculating inertial system _i:

$r_i=\left[\begin{array}{c}\cos \mathrm{\α}\cos \mathrm{\δ}\\ \sin \mathrm{\α}\cos \mathrm{\δ}\\ \sin \mathrm{\δ}\end{array}\right]$

6.2) according to airborne inertial navigation system Output rusults, with sub-step 6.1) starlight direction vector r under the inertial system that calculates _i, starlight direction vector r under calculating star sensor coordinate system _i

$r_I=C_b^s{\tilde{C}}_n^b{\tilde{C}}_e^n{C}_i^e{r}_i$

Wherein represent that aircraft body coordinate is tied to the coordinate conversion matrix of celestial navigation system coordinate system, represent that the geographic coordinate of airborne inertial navigation system calculating is tied to the coordinate conversion matrix of aircraft body coordinate system; represent that the terrestrial coordinates of airborne inertial navigation system calculating is tied to the coordinate conversion matrix of geographic coordinate system; represent that inertial coordinate is tied to the coordinate conversion matrix of terrestrial coordinate system;

6.3) by sub-step 6.2) starlight direction vector r under the star sensor coordinate system that calculates _i, calculate star image coordinate calculated value x _i, y _i

$\left.\begin{array}{c}{x}_I=f\frac{r_{\mathrm{Ix}}}{r_{\mathrm{Iz}}}\\ y_I=f\frac{r_{\mathrm{Iy}}}{r_{\mathrm{Iz}}}\end{array}\right\}$

Wherein f represents the focal length of celestial navigation system star sensor, r _ixstarlight direction vector r under expression star sensor coordinate system _icomponent in X-axis, r _iystarlight direction vector r under expression star sensor coordinate system _icomponent in Y-axis, r _izstarlight direction vector r under expression star sensor coordinate system _icomponent on Z axis.

7) inertia and astronomical combined filter and error correction is carried out

The star image coordinate that the star image coordinate recorded according to celestial navigation system in step (5) and step (6) airborne inertial navigation system are calculated, the celestial navigation system measured value utilizing step (3) to set up and airborne INS errors quantity of state x _ibetween linearization combination measurement equation carry out combined filter, estimate airborne inertial navigation system evaluated error quantity of state and for revising navigation error;

8) navigation results is exported

Export navigation results, and judge whether navigation procedure terminates, if it is stop navigation, otherwise re-execute step (4).

In order to verify a kind of inertia based on star image coordinates modeling proposed by the invention and the performance of celestial combined navigation method, in order to analyze the inertia and astronomical tight integration model set up herein, first carry out simulation analysis in conjunction with the attitude determination performance of dynamic flight path to astronomical tight integration aided inertial navigation.Constant to the omnidistance fixed star that navigates as seen of flight is respectively that the situation of 1 ~ 6 carries out dynamic simulation, and corresponding angle of pitch graph of errors as shown in Figure 2.

As can be seen from Figure 2, when not having astronomical sight information to assist, the angle of pitch error of inertial navigation system presents the trend of rapid divergence, and after adding astronomical sight, angle of pitch precision has clear improvement.In the long run, for the situation of observation 1 nautical star, angle of pitch error is still slowly dispersed, but its divergence speed has received obvious suppression with compared with during astronomical assisting.It should be noted that, determine appearance algorithm because TRIAD etc. is astronomical at least needs two fixed stars that navigate could determine the attitude of carrier under inertial system, and therefore conventional first to determine appearance, the inertia of recombinant and the loose assembled scheme of astronomy be inoperable when only having 1 nautical star.Therefore, tight integration method of the present invention has better applicability in contrast.

Consider when high-speed flight, the impact of aero-optical effect is stronger in Vehicle nose, the characteristic that afterbody is comparatively weak, setting navigation fixed star is only visible in the conical range constraint that coning angle is 60 °, and in dynamic flying process, the change of the navigation fixed star number that celestial navigation system can observe as shown in Figure 3.As can be seen from Figure 3, when considering celestial navigation system observational constraints, the quantity of visible star remains lower level, for the ease of contrast, emulates respectively here for conventional inertia and combinations of satellites and astronomical inertia of assisting and combinations of satellites scheme.Fig. 4 is for nothing astronomy is auxiliary and combine the contrast of course angle graph of errors under having astronomical aided case, and Fig. 5 is for nothing astronomy is auxiliary and gyro single order Markov drift estimate error to standard deviation curve comparison under having astronomical aided case.

As can be seen from Figure 4, add celestial navigation system fixed star picpointed coordinate observation information auxiliary after, the precision of course angle has had and has significantly improved.As can be seen from the gyro single order Markov drift estimate error to standard deviation curve comparison of Fig. 5, add fixed star picpointed coordinate observation information auxiliary after, the speed of convergence of the inertia more conventional for the error estimation accuracy of gyro and combinations of satellites filtering is accelerated, and steady state estimation errors reduces.

Can be found out by the simulation result of Fig. 2, Fig. 4 and Fig. 5, the present invention effectively can improve the attitude accuracy of integrated navigation system, and provide assisting continuously inertial navigation system when star number of navigating is less, effectively improve adaptability and the navigation performance of inertia and celestial combined navigation, there is useful engineer applied and be worth.

Claims (3)

1., based on inertia and the celestial combined navigation method of star image coordinates modeling, it is characterized in that comprising the following steps:

Steps A, according to inertia and celestial combined navigation error characteristics, by the mathematical description of airborne INS errors, sets up inertia and celestial combined navigation error state amount equation; Airborne INS errors quantity of state X is defined as:

$X={[{\mathrm{\φ}}_E,{\mathrm{\φ}}_N,{\mathrm{\φ}}_U,{\mathrm{\δv}}_E,{\mathrm{\δv}}_N,{\mathrm{\δv}}_U,\mathrm{\δL},\mathrm{\δ\λ},\mathrm{\δh},{\mathrm{\ϵ}}_{\mathrm{bx}},{\mathrm{\ϵ}}_{\mathrm{by}},{\mathrm{\ϵ}}_{\mathrm{bz}},{\mathrm{\ϵ}}_{\mathrm{rx}},{\mathrm{\ϵ}}_{\mathrm{ry}},{\mathrm{\ϵ}}_{\mathrm{rz}},{\▿}_x,{\▿}_y,{\▿}_z]}^T$

Wherein, φ _e, φ _n, φ _ueast orientation platform error angle quantity of state, north orientation platform error angle quantity of state and sky respectively in expression airborne INS errors quantity of state are to platform error angle quantity of state;

δ v _e, δ v _n, δ v _ueast orientation velocity error quantity of state, north orientation velocity error quantity of state and sky respectively in expression airborne INS errors quantity of state are to velocity error quantity of state;

δ L, δ λ, δ h represent latitude error quantity of state, longitude error quantity of state and height error quantity of state in airborne INS errors quantity of state respectively;

ε _bx, ε _by, ε _bzrepresent X-axis, Y-axis, the Z-direction gyroscope constant value drift error state amount in airborne INS errors quantity of state respectively;

ε _rx, ε _ry, ε _rzrepresent X-axis, Y-axis, the Z-direction gyro first order Markov drift error quantity of state in airborne INS errors quantity of state respectively;

represent X-axis, Y-axis and the Z-direction accelerometer bias in airborne INS errors quantity of state respectively, T is transposition;

Step B, according to celestial navigation system Observation principle and INS errors model, analyze the transitive relation between celestial navigation system starlight picpointed coordinate error and inertial navigation system position, attitude error, set up star image error of coordinate TRANSFER MODEL, comprise following sub-step:

Step B-1, under definition celestial navigation system coordinate system, starlight picpointed coordinate error is δ x, δ y, then:

$\left.\begin{array}{c}\mathrm{\δx}=x-x_I\\ \mathrm{\δy}=y-y_I\end{array}\right\}$

Wherein x, y are star image coordinate actual value, x _i, y _ifor star image coordinate calculated value;

Step B-2, definition starlight deviation of directivity angle vector ψ=[ψ _xψ _yψ _z] ^t, ψ _x, ψ _y, ψ _zrepresent the deviation angle of the spaced winding X-axis in starlight direction and the actual starlight direction calculated by airborne inertial navigation system, Y-axis, Z axis respectively;

Step B-3, definition airborne inertial navigation system platform error angle vector φ=[φ _eφ _nφ _u] ^t, definition airborne inertial navigation system site error vector delta P=[-δ L δ λ cosL δ λ sinL] ^t, L represents latitude;

Step B-4, according to celestial navigation system Observation principle, set up the linearization measurement model between starlight picpointed coordinate error and starlight deviation of directivity angle vector ψ under celestial navigation system coordinate system, its expression formula is

$\left[\begin{array}{c}\mathrm{\δx}\\ \mathrm{\δy}\end{array}\right]=H_{\mathrm{\ψ}}\mathrm{\ψ}$

Wherein, $H_{\mathrm{\ψ}}=\left[\begin{array}{ccc}0& f& -y_I\\ -f& 0& x_I\end{array}\right],$ F is the focal length of celestial navigation system star sensor;

Step B-5, according to INS errors principle, set up starlight deviation of directivity angle vector ψ and the linearization measurement model between airborne inertial navigation system platform error angle vector φ, site error vector delta P, its expression formula is

$\mathrm{\ψ}=C_b^s{\tilde{C}}_n^b(\mathrm{\φ}-\mathrm{\δP})$

Wherein, represent that aircraft body coordinate is tied to the coordinate conversion matrix of celestial navigation system coordinate system, represent that geographic coordinate is tied to the coordinate conversion matrix of aircraft body coordinate system;

Step B-6, to set up based on celestial navigation system starlight picpointed coordinate error the observation model of inertial navigation system position, attitude error:

$\left[\begin{array}{c}\mathrm{\δx}\\ \mathrm{\δy}\end{array}\right]=H_{\mathrm{\ψ}}{C}_b^s{\tilde{C}}_n^b(\mathrm{\φ}-\mathrm{\δP});$

Step C, adopt the linearization observation procedure under airborne Department of Geography, according to the observation modeling result based on celestial navigation system starlight picpointed coordinate error and inertial navigation system position, attitude error of step B, measurement equation is combined in the linearization of setting up between celestial navigation system measured value and airborne INS errors quantity of state X;

Step D, carries out inertial navigation and resolves, and obtains airborne inertial navigation system Output rusults;

Step e, has judged whether celestial navigation system measured value, if so, then records the star image coordinates measurements of celestial navigation system and performs step F, otherwise performs step H;

Step F, the airborne inertial navigation system Output rusults utilizing step D to calculate, calculates the star image coordinate calculated value calculated by airborne inertial navigation system;

Step G, the star image coordinate that the star image coordinate recorded according to celestial navigation system in step e and step F airborne inertial navigation system are calculated, linearization between the celestial navigation system measured value utilizing step C to set up and airborne INS errors quantity of state X is combined measurement equation and is carried out combined filter, estimate airborne inertial navigation system evaluated error quantity of state and for revising navigation error;

Step H, exports navigation results, and judges whether navigation procedure terminates, and if it is stops navigation, otherwise re-executes step D.

2. the inertia based on star image coordinates modeling according to claim 1 and celestial combined navigation method, it is characterized in that, the celestial navigation system measured value described in step C and the linearization between airborne INS errors quantity of state X are combined and are measured equation form and be:

$\left[\begin{array}{c}{Z}_1\\ Z_2\\ .\\ .\\ .\\ Z_m\end{array}\right]=\left[\begin{array}{c}{H}_{\mathrm{\ψ}1}\\ H_{\mathrm{\ψ}2}\\ .\\ .\\ .\\ H_{\mathrm{\ψm}}\end{array}\right]H_{X}X+{\mathrm{VI}}_{m\×1}$

In formula, m is the fixed star number simultaneously observed, I _{m × 1}represent complete 1 column vector of m dimension, V represents celestial navigation system measurement noise, Z _i(i=1 ... m) be observed quantity, Z _iexpression formula be

$Z_i=\left[\begin{array}{c}{x}_{\mathrm{Ii}}-x_{\mathrm{Ci}}\\ y_{\mathrm{Ii}}-y_{\mathrm{Ci}}\end{array}\right]$

Wherein, x _ii, y _iibe respectively the X-axis of i-th fixed star and the star image coordinate calculated value of Y-axis; x _ci, y _cibe respectively the star image coordinate that celestial navigation system records i-th fixed star X-axis and Y-axis;

In formula, H _{ψ i}(i=1 ... m) expression formula is

$H_{\mathrm{\ψi}}=\left[\begin{array}{ccc}0& f& -y_{\mathrm{Ii}}\\ -f& 0& x_{\mathrm{Ii}}\end{array}\right]$

Wherein, f is the focal length of celestial navigation system star sensor;

In formula, H _xexpression formula be

$H_X=C_b^s{\tilde{C}}_n^b\left[\begin{array}{cccc}{I}_{3\×3}& 0_{3\×3}& M& 0_{3\×9}\end{array}\right]$

Wherein, represent that aircraft body coordinate is tied to the coordinate conversion matrix of celestial navigation system coordinate system, represent that geographic coordinate is tied to the coordinate conversion matrix of aircraft body coordinate system; I _{3 × 3}represent the unit matrix that 3 row 3 arrange, 0 _{3 × 3}represent the full null matrix that 3 row 3 arrange, 0 _{3 × 9}represent the full 0 matrix that 3 row 9 arrange, Metzler matrix expression formula is

$M=\left[\begin{array}{ccc}1& 0& 0\\ 0& -\cos L& 0\\ 0& -\sin L& 0\end{array}\right]$

Wherein, L represents latitude.

3. the inertia based on star image coordinates modeling according to claim 1 and celestial combined navigation method, is characterized in that the star image coordinate that the calculating described in step F is calculated by airborne inertial navigation system comprises following sub-step:

Step F-1, from right ascension α, the declination δ of navigation fixed star library inquiry fixed star, starlight direction vector r under calculating inertial system _i:

$r_i=\left[\begin{array}{c}\cos \mathrm{\α}\cos \mathrm{\δ}\\ \sin \mathrm{\α}\cos \mathrm{\δ}\\ \sin \mathrm{\δ}\end{array}\right]$

Step F-2, according to airborne inertial navigation system Output rusults, and starlight direction vector r under the inertial system of sub-step F-1 calculating _i, starlight direction vector r under calculating star sensor coordinate system _i:

$r_I=C_b^s{\tilde{C}}_n^b{\tilde{C}}_e^n{C}_i^e{r}_i$

Wherein, represent that aircraft body coordinate is tied to the coordinate conversion matrix of celestial navigation system coordinate system, represent that geographic coordinate is tied to the coordinate conversion matrix of aircraft body coordinate system; represent that the terrestrial coordinates of airborne inertial navigation system calculating is tied to the coordinate conversion matrix of geographic coordinate system; represent that inertial coordinate is tied to the coordinate conversion matrix of terrestrial coordinate system;

Step F-3, starlight direction vector r under the star sensor coordinate system calculated by sub-step F-2 _i, calculate star image coordinate calculated value x _i, y _i:

$\left.\begin{array}{c}{x}_I=f\frac{r_{\mathrm{Ix}}}{r_{\mathrm{Iz}}}\\ y_I=f\frac{r_{\mathrm{Iy}}}{r_{\mathrm{Iz}}}\end{array}\right\}$

Wherein, r _ixstarlight direction vector r under expression star sensor coordinate system _icomponent in X-axis, r _iystarlight direction vector r under expression star sensor coordinate system _icomponent in Y-axis, r _izstarlight direction vector r under expression star sensor coordinate system _icomponent on Z axis.