CN106932804A - Inertia/the Big Dipper tight integration navigation system and its air navigation aid of astronomy auxiliary - Google Patents

Abstract

The present invention discloses a kind of inertia/Big Dipper tight integration navigation system of astronomical auxiliary, data are sent into navigation computer module by inertance element, Beidou receiver and star sensor, and navigation computer module shows navigation calculation result feeding host computer display module after being processed in real time.Invention additionally discloses a kind of inertia of astronomical auxiliary/Big Dipper tight integration air navigation aid, first calculating speed, position, with the attitude motion of quaternion representation carrier；Set up the navigation system state equation of astronomical auxiliary；Different operating characteristic according to each navigation system, sets up the measurement equation of each subsystem；Geometric configuration construction adaptive Kalman filter according to visible star and visible star, so as to the navigation error to inertial navigation system is modified.This kind of technical scheme can efficiently real-time implementation inertia/astronomy/Big Dipper integrated navigation system subsystem resolve and use processing, obtain high accuracy, the navigation results of high reliability.

Description

Inertia/the Big Dipper tight integration navigation system and its air navigation aid of astronomy auxiliary

Technical field

The invention belongs to aircraft integrated navigation technology field, the inertia/Big Dipper tight integration of astronomical auxiliary is more particularly to planted Navigation system and its air navigation aid.

Background technology

The GPS in the current U.S. is the most widely used satellite navigation system, satellite navigation system country national defence and Economically play and its important effect.In U.S.'s hand, this national defense safety to China causes one to the dominant right of gps system Fixed threat, therefore the development of domestic triones navigation system is inexorable trend.Because China's triones navigation system is still in development Stage, it is seen that star is few, and satellite-signal easily influences by landform, building etc., also it is vulnerable to electromagnetic interference and ineffective, because The research of this inertia/BD tight integration navigation algorithms has positive effect.In recent years aerospace technology quickly grows for China, re-entry space vehicle With the flight characteristics when empty day, high maneuver, the boat hypersonic, long, the integrated navigation system of inertia/Big Dipper two cannot meet it To high accuracy, the demand of high reliability navigation system.Astronomy determines appearance, positioning has the advantages that high precision and not by electromagnetic interference, Therefore inertia/the Big Dipper tight integration navigation system of astronomical auxiliary be when realizing long-range boat long, motor-driven, hypersonic aircraft circle high Completely complete the guarantee of task.

In view of visible star number mesh and satellite information the quality dynamic change over time of Beidou satellite navigation system, because This, needs the trustworthiness problem of analysis triones navigation system measurement information in the inertia/triones navigation system of astronomical auxiliary. The kalman filter method mainly taken in information fusion process in inertia, astronomy, Big Dipper integrated navigation system, system The setting of parameter has strong influence to whole system, and the accuracy of the inaccurate not only influence system of parameter setting is also easily led Whole system diverging is caused until collapse.In view of the situation of triones navigation system measurement information penetration quality dynamic change, astronomy auxiliary The adaptive filter method of inertia/Big Dipper tight integration navigation system needs further research.

The content of the invention

The purpose of the present invention, is inertia/Big Dipper tight integration navigation system and its navigation side for providing a kind of astronomical auxiliary Method, it can solve aircraft when motor-driven, hypersonic, length high is navigated, can be with height to navigation system high accuracy, the demand of high reliability The subsystem of effect real-time implementation inertia/astronomy/Big Dipper integrated navigation system is resolved and use processing, obtains high accuracy, height The navigation results of reliability, while for the engineering realization and application of the inertia/Big Dipper tight integration navigation system of astronomical auxiliary are carried Effective support is supplied, with prominent practical value.

In order to reach above-mentioned purpose, solution of the invention is：

A kind of inertia/Big Dipper tight integration navigation system of astronomical auxiliary, including navigation computer module, inertance element, north Bucket receiver, star sensor and host computer display module, data are sent into and navigated by inertance element, Beidou receiver and star sensor Computer module, navigation computer module shows navigation calculation result feeding host computer display module after being processed in real time.

Above-mentioned navigation computer module includes inertial reference calculation module, measurement conversion module and Kalman filtering module, inertial navigation The output end of resolving module and measurement conversion module is all connected with the input of Kalman filtering module.

Above-mentioned Kalman filtering module includes SINS/CNS wave filters and SINS/BD sef-adapting filters, SINS/CNS filters The input of ripple device connects the output end of inertial reference calculation module and measurement conversion module respectively, SINS/BD sef-adapting filters Input connects the output end of inertial reference calculation module and measurement conversion module respectively.

Above-mentioned navigation computer module is using PC, work station, embedded based on WINDOWS systems or LINUX system Platform.

A kind of inertia/Big Dipper tight integration air navigation aid of astronomical auxiliary, comprises the following steps：

Step 1, for the inertia/Big Dipper tight integration navigation system of astronomical auxiliary, speed computing formula is：

In formula,Projection of the acceleration on carrier for carrier equivalent to Department of Geography,It is carrier equivalent to Department of Geography Projection of the speed on carrier,The attitude transfer matrix of navigational coordinate system is tied to for body,It is carrier equivalent to geography The projection that the speed of coordinate system is fastened in navigation coordinate, geographic coordinate system therein is navigational coordinate system；

Position computing formula is：

With the attitude motion of quaternion representation carrier, computing formula is：

It is expressed in matrix as

In formula, q is attitude quaternion,It is q to the derivative of time,Vector is quaternary number form formula, represents carrier coordinate It is projection of the Relative Navigation coordinate system in carrier coordinate system；

Step 2, on the basis of the above, the SINS/BD tight integration navigation system state equations for setting up astronomical auxiliary are：

Wherein, state variable is：

Represent strap-down inertial coordinate system Xia Dong, north, day direction platform error angle, δ v in the ground_E,δv_N,δ v_URepresent inertial navigation system geographic coordinate system Xia Dong, north, day direction velocity error；δ L, δ λ, δ h represent inertial navigation system System latitude, longitude, the error of height under coordinate system in the ground；ε_bx,ε_by,ε_bzRepresent Gyro Random constant error；ε_rx,ε_ry,ε_rz Represent gyro first-order Markov process random error；Represent the first-order Markov process of accelerometer with chance error Difference；δt_u,δt_ruThe clock correction and frequency difference between Beidou receiver and satellite are represented, is embodied with distance and speed respectively；A(t)_20×20 It is the state-transition matrix of system；G(t)_20×11It is noise coefficient matrix；W(t)_11×1It is the white noise vector of system；

Step 3, the different operating characteristic according to each navigation system, sets up the measurement equation of each subsystem；

Step 4, the geometric configuration construction adaptive Kalman filter according to visible star and visible star, so as to be led to inertia The navigation error of boat system is modified.

In above-mentioned steps 3, the measurement equation of SINS/BD subsystems is divided into pseudo range measurement part and pseudorange rates measure part, The pseudorange letter that the pseudo-range information that wherein pseudo range measurement is gone out for the positional information calculation provided using inertial navigation is provided with Beidou receiver The difference of breath；Pseudorange rates measurement information is the speed of the velocity information, satellite Doppler shift information and satellite that are provided by inertial navigation Degree information is calculated；

If the receiver moment observes n usable satellite, then pseudo range measurement equation：

Z_ρ(t)=H_ρ(t)X(t)+v_ρ(t)

Wherein H_ρ(t)=[0_n×6 H_ρ1 0_n×6 H_ρ2],e_i1、e_i2、 e_i3It is i-th direction cosines between satellite and carrier, v_ρT () is pseudo range measurement noise, R_NIt is earth reference ellipsoid prime vertical Radius of curvature；

Pseudorange rates measurement equation is：

Wherein

For pseudorange rates measure noise.

The detailed content of above-mentioned steps 4 is：

(41) when visible star is less than 4, setting measures noise and is gradually reduced with visible increasing for star, you can see that star is got over At most more trust the measurement information of triones navigation system, the measurement noise of pseudorange and pseudorange rates is expressed as follows：

N represents visible star number mesh, v in formula_ρ0,Pseudorange, the initial measurement noise of pseudorange rates are represented respectively, and α represents one Constant coefficient；

(42) when the visible star of the Big Dipper be more than 4 when, first the elevation angle according to navigation position and satellite position calculation satellite and Azimuth, by the elevation angle and azimuthal angle calculation GDOP values of satellite, finally the measurement noise to pseudorange and pseudorange rates is adjusted Section, process is as follows：

A, elevation of satellite, azimuthal angle calculation

Position of user's navigation position under body-fixed coordinate system is：

P_u=[p_ux p_uy p_uz]

I-th satellite marks the position under being admittedly on ground：

P_s=[p_sx p_sy p_sz]

If

D=[d₁ d₂ d₃]=(P_s-P_u)E

Then elevation angle is：

Azimuth is：

The calculating of b, geometric dilution of precision GDOP

If the visible star number mesh of certain moment Beidou satellite navigation system is n, if matrix Q is as follows：

Then the value of GDOP is calculated by following formula：

C, satellite measure the setting of noise to receiver pseudorange, pseudorange rates

Wherein v_ρ0,Pseudorange, the initial measurement noise of pseudorange rates, GDOP are represented respectively₀Represent the first of triones navigation system Beginning geometric dilution of precision, GDOP_kRepresent the geometric dilution of precision at triones navigation system kth moment.

In above-mentioned steps 3, SINS/CNS subsystems measure the attitude angle and the astronomical attitude angle letter for providing provided for inertial navigation The difference of breath, defines the difference of the attitude angle of attitude of carrier angle that observed quantity measured for star sensor and inertial navigation, and measurement equation is such as Under：

Z_s(t)=H_s(t)X(t)+v_s(t)

Because the error angle quantity of state in integrated navigation system state equation is Inertial Navigation Platform error angle, what it was described It is the error angular dependence between mathematical platform and ground the inside coordinate system, it is therefore desirable to inertial attitude error angle is transformed into platform and is missed Declinate；When platform error angle is a small amount of, measurement matrix is represented by below equation：

Therefore, measurement equation is expressed as：

In formula, γ, θ, ψ are respectively roll angle, the angle of pitch and course angle, v_sT () is attitude error angle measurements noise.

In above-mentioned steps 4, filtering is as follows：

In above formula,Represent t_k-1The state at moment is to t_kThe optimal estimation value of the state at moment, Φ_k/k-1Represent t_k-1 Moment is to t_kWhen etching system state-transition matrix,Represent t_k-1The system state estimation value at moment, K_kRepresent gain square Battle array, H_kRepresent filtration module t_kThe observed differential matrix at moment, P_k/k-1Represent optimum prediction evaluated error covariance matrix, P_k/kTable Show filtration module t_kThe systematic error covariance matrix at moment, Q_k-1Represent t_k-1The noise variance matrix at moment, Γ_k/k-1Represent t_k-1 The noise vector at moment is to t_kThe noise coefficient matrix of moment state vector influence, R_kRepresent t_kThe measurement variance matrix at moment, I It is unit matrix.

After such scheme, beneficial effects of the present invention are as follows：

(1) in whole navigation system, inertia and triones navigation system use tight integration mode, improve system can Applicability when seeing that star is few, the auxiliary of ephemeris information significantly improves the precision of navigation system attitude angle.It is tight for inertia/Big Dipper Composite module, it is proposed that based on elevation of satellite and azimuthal adaptive filter method, greatly strengthen the self adaptation of system Property.

(2) on hardware view, whole navigation system transplantability is very strong, can be in the module such as work station, PC, embedded Work.Belong to coordination on sensor logic in system, sensor and navigational computer, navigational computer and host computer it Between can be communicated by USB serial ports or RS232 serial ports, improve the flexibility of system, be easy to the extension of system and cut.

(3) on software view, whole navigation system uses multithread mode, and whole navigation system is carried out between different task High-speed cruising and rotation, task concurrently carries out ensure that the real-time of system, the extension beneficial to system in task with cut.

Brief description of the drawings

Fig. 1 is schematic diagram of the invention；

Fig. 2 is navigation system hardware modularity pie graph of the present invention；

Fig. 3 is the attitude error curve comparison figure for whetheing there is astronomical auxiliary；

Fig. 4 and Fig. 5 are respectively the speed-error curve contrasts of the site error curve comparison figure of AKF and KF, AKF and KF Figure；

In this experiment, by be manually set make the visible star of satellite every 25 seconds real-time transforms once, Fig. 4's and Fig. 5 The waveform of non-self-adapting filtering can reflect the situation of visible star change.

Specific embodiment

Below with reference to accompanying drawing, technical scheme is described in detail.

The present invention provides a kind of inertia/Big Dipper tight integration navigation system and its air navigation aid of astronomical auxiliary, using removable Plant property very strong cross-platform Navigator and navigational hardware device, Navigator are write by Qt Creator, it is contemplated that navigation system The real-time and modular arrangements of system, whole Navigator take multithreading scheme, respectively including inertial navigation thread, SINS/ BD tight integrations filtering thread, the astronomical filtering threads of SINS/, serial data read decoding and navigation periodic Control thread, host computer Display and navigation pattern configurations thread；Navigational hardware device by star sensor emulator, Beidou receiver, MEMS inertance elements, Navigation computer module, host computer display module composition, wherein navigation computer module can by PC, work station, be based on The embedded platform of WINDOWS systems or LINUX system undertakes.

As shown in figure 1, a kind of principle of the inertia/Big Dipper tight integration air navigation aid of astronomical auxiliary of the present invention is：For used Property/Big Dipper tight integration module, elevation angle and azimuth according to visible star obtain dilution of precision GDOP, further according to dilution of precision reality When adjustment measure noise, improve filtration module adaptivity.In addition, using starlight information to the appearance of whole navigation system State angle is modified.Specific implementation method is as follows：

1st, the inertia of astronomical auxiliary/Big Dipper tight integration navigation system modeling

1) integrated navigation system ins error quantity of state equation Modeling

For the inertia/Big Dipper tight integration navigation system of astronomical auxiliary, its inertial navigation solution process is as follows, and speed is calculated Formula is：

In formula,Projection of the acceleration on carrier for carrier equivalent to Department of Geography,It is carrier equivalent to Department of Geography Projection of the speed on carrier,The attitude transfer matrix of navigational coordinate system is tied to for body,It is carrier equivalent to geography The projection that the speed of coordinate system is fastened in navigation coordinate, the geographic coordinate system of this model is navigational coordinate system.

Position computing formula is：

With the attitude motion of quaternion representation carrier, computing formula is：

It is expressed in matrix as

In formula, q is attitude quaternion,It is q to the derivative of time,Vector is quaternary number form formula, represents carrier coordinate It is projection of the Relative Navigation coordinate system in carrier coordinate system.

On the basis of the above, setting up the astronomical SINS/BD tight integration navigation system state equations for aiding in is：

Wherein, state variable is：

Represent strap-down inertial coordinate system Xia Dong, north, day direction platform error angle, δ v in the ground_E,δv_N,δ v_URepresent inertial navigation system geographic coordinate system Xia Dong, north, day direction velocity error；δ L, δ λ, δ h represent inertial navigation system System latitude, longitude, the error of height under coordinate system in the ground；ε_bx,ε_by,ε_bzRepresent Gyro Random constant error；ε_rx,ε_ry,ε_rz Represent gyro first-order Markov process random error；Represent the first-order Markov process of accelerometer with chance error Difference；δt_u,δt_ruThe clock correction and frequency difference between Beidou receiver and satellite are represented, is embodied with distance and speed respectively.A(t)_20×20 It is the state-transition matrix of system；G(t)_20×11It is noise coefficient matrix；W(t)_11×1It is the white noise vector of system；

2) integrated navigation system measurement equation modeling

It is to used using astronomical attitude information in astronomical supplementary inertial/Big Dipper tight integration navigation system that this is described The attitude information led is filtered estimation, the pseudorange that is provided using triones navigation system and doppler information to the position of inertial navigation and Velocity information is filtered estimation.Different operating characteristic according to each navigation system, sets up the measurement equation of each subsystem. SINS/CNS subsystems measure the difference of the attitude angle information that the attitude angle provided for inertial navigation is provided with astronomy.SINS/BD subsystems Measurement equation be divided into pseudo range measurement part and pseudorange rates and measure part, wherein pseudo range measurement is that the position provided using inertial navigation is believed The difference of the pseudo-range information that the pseudo-range information and Beidou receiver that breath is calculated are provided；Pseudorange rates measurement information is provided by inertial navigation The velocity information of velocity information, satellite Doppler shift information and satellite calculate.

A, SINS/BD tight integration system

If the receiver moment observes n usable satellite, then pseudo range measurement equation：

Z_ρ(t)=H_ρ(t)X(t)+v_ρ(t) (10)

Wherein H_ρ(t)=[0_n×6 H_ρ1 0_n×6 H_ρ2],e_i1、e_i2、 e_i3It is i-th direction cosines between satellite and carrier, v_ρT () is pseudo range measurement noise, R_NIt is earth reference ellipsoid prime vertical Radius of curvature.

Pseudorange rates measurement equation is：

Wherein

For pseudorange rates measure noise.

B, SINS/CNS combined system

In SINS/CNS subsystems, the appearance at attitude of carrier angle that observed quantity measured for star sensor and inertial navigation is defined The difference at state angle, measurement equation is as follows：

Z_s(t)=H_s(t)X(t)+v_s(t) (12)

Because the error angle quantity of state in integrated navigation system state equation is Inertial Navigation Platform error angle, what it was described It is the error angular dependence between mathematical platform and ground the inside coordinate system, it is therefore desirable to inertial attitude error angle is transformed into platform and is missed Declinate.When platform error angle is a small amount of, measurement matrix can be represented by below equation：

Therefore, measurement equation can be expressed as：

In formula, γ, θ, ψ are respectively roll angle, the angle of pitch and course angle, v_sT () is attitude error angle measurements noise.

2nd, inertia/Big Dipper tight integration navigation system adaptive filter method

For SINS/BD subsystems, because the visible star number mesh of triones navigation system changes over time, it is seen that star number mesh And the configuration of visible star can cause the dynamic change of pseudorange and pseudorange rates information quality, therefore according to the several of visible star and visible star What configuration adaptive Kalman filter, so as to the navigation error to inertial navigation system is modified.

When the visible star of the Big Dipper be more than 4 when, can by the elevation angle of visible star and declinometer calculate geometric accuracy because Sub (GDOP) value, GDOP is the critically important coefficient for weighing positioning precision, and it represents the reception that Big Dipper range error is caused Distance vector amplification factor between machine and Aerospace Satellite.It is actual to characterize the unit from receiver to Aerospace Satellite for participating in positioning solution Body volume and the GDOP that vector is sketched the contours are inversely proportional, and the smaller then positioning precisions of GDOP are higher.In inertia/Big Dipper tight integration navigation In system, can be according to the elevation angle and azimuth of navigation position and satellite position calculation each satellite, and then according to elevation angle With the geometric positioning accuracy factor GDOP that azimuthal angle calculation describes satellite fix precision, finally by the size real-time adjustment of GDOP The measurement noise of pseudorange, pseudorange rates, so that whole combined system reaches the performance of self-adaptative adjustment.Its transfer process is as follows：

(1) when visible star is less than 4, setting measures noise and is gradually reduced with visible increasing for star, you can see that star is got over At most more trust the measurement information of triones navigation system.The measurement noise of pseudorange and pseudorange rates is expressed as follows：

N represents visible star number mesh (less than 4), v in formula_ρ0,Pseudorange, the initial measurement noise of pseudorange rates, α are represented respectively A constant coefficient is represented, typically to be set according to the actual measurement situation of system.

(2) when the visible star of the Big Dipper is more than 4, first according to the elevation angle and side of navigation position and satellite position calculation satellite Parallactic angle, by the elevation angle and azimuthal angle calculation GDOP values of satellite, finally the measurement noise to pseudorange and pseudorange rates is adjusted, Process is as follows：

A, elevation of satellite, azimuthal angle calculation

Position of user's navigation position under body-fixed coordinate system is：

P_u=[p_ux p_uy p_uz] (17)

I-th satellite marks the position under being admittedly on ground：

P_s=[p_sx p_sy p_sz] (18)

If

D=[d₁ d₂ d₃]=(P_s-P_u)E (20)

Then elevation angle is：

Azimuth is：

The calculating of b, geometric dilution of precision GDOP

If the visible star number mesh of certain moment Beidou satellite navigation system is n, if matrix Q is as follows：

Then the value of GDOP can be calculated by following formula：

C, satellite measure the setting of noise to receiver pseudorange, pseudorange rates

Wherein v_ρ0,Pseudorange, the initial measurement noise of pseudorange rates, GDOP are represented respectively₀Represent the first of triones navigation system Beginning geometric dilution of precision, GDOP_kRepresent the geometric dilution of precision at triones navigation system kth moment.

(3) in the inertia/Big Dipper tight integration navigation system of astronomical auxiliary, for CNS/SINS and SINS/BD subsystems, respectively Filtration module process is as follows：

In above formula,Represent t_k-1The state at moment is to t_kThe optimal estimation value of the state at moment, Φ_k/k-1Represent t_k-1When Carve to t_kWhen etching system state-transition matrix,Represent t_k-1The system state estimation value at moment, K_kRepresent gain matrix, H_kRepresent filtration module t_kThe observed differential matrix at moment, P_k/k-1Represent optimum prediction evaluated error covariance matrix, P_k/kRepresent filter Ripple module t_kThe systematic error covariance matrix at moment, Q_k-1Represent t_k-1The noise variance matrix at moment, Γ_k/k-1Represent t_k-1Moment Noise vector to t_kThe noise coefficient matrix of moment state vector influence, R_kRepresent t_kThe measurement variance matrix at moment, I is single Bit matrix.

Summary, inertia/Big Dipper tight integration navigation system and its navigation side the invention discloses a kind of astronomical auxiliary Method, whole Navigator is write by Qt, using multi-thread concurrent pattern, with ensure the real-time of whole Navigator with it is expansible Property.Navigator is read by inertial navigation thread, SINS/BD tight integrations filtering thread, the astronomical filtering threads of SINS/, serial data Take decoding and navigation periodic Control thread, host computer show and navigate that pattern configurations thread is constituted.Navigational hardware device is quick by star Sensor emulator, Beidou receiver, MEMS inertance elements, navigational computer, host computer display module composition, wherein navigation is calculated Machine can be undertaken by PC, work station, the embedded platform based on WINDOWS systems or LINUX system.Air navigation aid include with Lower step：Inertia/Big Dipper tight integration model, inertia/astronomy built-up pattern are set up respectively under geographic coordinate system first, used Property/Big Dipper tight integration on the basis of research be based on elevation of satellite and azimuthal adaptive filter method.Big-dipper satellite is visible The change of star number purpose dynamic change and satellite geometry configuration, not only influences the accuracy of whole system, in extreme circumstances also System can be caused to dissipate even collapse.The present invention can effectively solve this problem, and obtain high-precision navigation results, while For the Project Realization of the inertia/Big Dipper tight integration navigation system of astronomical auxiliary and application provide effective support.

Above example is only explanation technological thought of the invention, it is impossible to limit protection scope of the present invention with this, every According to technological thought proposed by the present invention, any change done on the basis of technical scheme each falls within the scope of the present invention Within.

Claims (9)

1. inertia/Big Dipper tight integration navigation system that a kind of astronomy is aided in, it is characterised in that：Including navigation computer module, it is used to Property element, Beidou receiver, star sensor and host computer display module, inertance element, Beidou receiver and star sensor are by number According to feeding navigation computer module, navigation calculation result is sent into host computer display module by navigation computer module after being processed Display in real time.

2. inertia/Big Dipper tight integration navigation system that astronomy as claimed in claim 1 is aided in, it is characterised in that：The navigation Computer module includes inertial reference calculation module, measurement conversion module and Kalman filtering module, and inertial reference calculation module and measurement turn The output end for changing the mold block is all connected with the input of Kalman filtering module.

3. inertia/Big Dipper tight integration navigation system that astronomy as claimed in claim 2 is aided in, it is characterised in that：The karr Graceful filtration module includes SINS/CNS wave filters and SINS/BD sef-adapting filters, and the input of SINS/CNS wave filters is distinguished The output end of connection inertial reference calculation module and measurement conversion module, the input of SINS/BD sef-adapting filters connects used respectively Lead the output end for resolving module and measurement conversion module.

4. inertia/Big Dipper tight integration navigation system that astronomy as claimed in claim 1 is aided in, it is characterised in that：The navigation Computer module uses PC, work station, the embedded platform based on WINDOWS systems or LINUX system.

5. inertia/Big Dipper tight integration air navigation aid that a kind of astronomy is aided in, it is characterised in that comprise the following steps：

Step 1, for the inertia/Big Dipper tight integration navigation system of astronomical auxiliary, speed computing formula is：

$v_{en}^b=v_{en0}^b+{\∫}_0^t{\stackrel{\·}{v}}_{en}^{b}dt$

$v_{en}^n=C_b^n{v}_{en}^b$

In formula,Projection of the acceleration on carrier for carrier equivalent to Department of Geography,Speed for carrier equivalent to Department of Geography The projection on carrier is spent,The attitude transfer matrix of navigational coordinate system is tied to for body,It is carrier equivalent to geographical coordinate The projection that the speed of system is fastened in navigation coordinate, geographic coordinate system therein is navigational coordinate system；

Position computing formula is：

$L=L_0+{\∫}_0^t\frac{v_y^n}{R_m}dt$

$\mathrm{\λ}={\mathrm{\λ}}_0+{\∫}_0^t\frac{v_x^n}{R_n}\sec Ldt$

$h=h_0+{\∫}_0^t{v}_z^{n}dt$

With the attitude motion of quaternion representation carrier, computing formula is：

It is expressed in matrix as

$\left[\begin{array}{c}{\stackrel{\·}{q}}_0\\ {\stackrel{\·}{q}}_1\\ {\stackrel{\·}{q}}_2\\ {\stackrel{\·}{q}}_3\end{array}\right]=0.5\×\left[\begin{array}{cccc}0& -{\mathrm{\ω}}_{nbx}^b& -{\mathrm{\ω}}_{nby}^b& -{\mathrm{\ω}}_{nbz}^b\\ {\mathrm{\ω}}_{nbx}^b& 0& {\mathrm{\ω}}_{nbz}^b& -{\mathrm{\ω}}_{nby}^b\\ {\mathrm{\ω}}_{nby}^b& -{\mathrm{\ω}}_{nbz}^b& 0& {\mathrm{\ω}}_{nbx}^b\\ {\mathrm{\ω}}_{nbz}^b& {\mathrm{\ω}}_{nby}^b& {\mathrm{\ω}}_{nbz}^b& 0\end{array}\right]$

In formula, q is attitude quaternion,It is q to the derivative of time,Vector is quaternary number form formula, represents carrier coordinate system phase The projection in carrier coordinate system is tied up to navigation coordinate；

Step 2, on the basis of the above, the navigation system state equation for setting up astronomical auxiliary is：

$\left[\begin{array}{c}{\stackrel{\·}{X}}_I\left(t\right)\\ {\stackrel{\·}{X}}_G\left(t\right)\end{array}\right]=\left[\begin{array}{cc}{F}_I\left(t\right)& 0\\ 0& F_G\left(t\right)\end{array}\right]\left[\begin{array}{c}{X}_I\left(t\right)\\ X_G\left(t\right)\end{array}\right]+\left[\begin{array}{cc}{G}_I\left(t\right)& 0\\ 0& G_G\left(t\right)\end{array}\right]\left[\begin{array}{c}{W}_I\left(t\right)\\ W_G\left(t\right)\end{array}\right]$

$\stackrel{\·}{X}{\left(t\right)}_{20\×1}=A{\left(t\right)}_{20\×20}X\left(t\right)+G{\left(t\right)}_{20\×11}W{\left(t\right)}_{11\×1}$

Wherein, state variable is：

Represent strap-down inertial coordinate system Xia Dong, north, day direction platform error angle, δ v in the ground_E,δv_N,δv_UTable Show inertial navigation system geographic coordinate system Xia Dong, north, day direction velocity error；δ L, δ λ, δ h represent that inertial navigation system exists In ground under coordinate system latitude, longitude, height error；ε_bx,ε_by,ε_bzRepresent Gyro Random constant error；ε_rx,ε_ry,ε_rzRepresent Gyro first-order Markov process random error；▽_x,▽_y,▽_zRepresent the first-order Markov process of accelerometer with chance error Difference；δt_u,δt_ruThe clock correction and frequency difference between Beidou receiver and satellite are represented, is embodied with distance and speed respectively；A(t)_20×20 It is the state-transition matrix of system；G(t)_20×11It is noise coefficient matrix；W(t)_11×1It is the white noise vector of system；

Step 3, the different operating characteristic according to each navigation system, sets up the measurement equation of each subsystem；

Step 4, the geometric configuration construction adaptive Kalman filter according to visible star and visible star, so as to inertial navigation system The navigation error of system is modified.

6. inertia/Big Dipper tight integration air navigation aid that astronomy as claimed in claim 5 is aided in, it is characterised in that：The step 3 In, the measurement equation of SINS/BD subsystems is divided into pseudo range measurement part and pseudorange rates measure part, and wherein pseudo range measurement is utilization The difference of the pseudo-range information that the pseudo-range information and Beidou receiver that the positional information calculation that inertial navigation is provided goes out are provided；Pseudorange rates measure letter Breath is that the velocity information of the velocity information, satellite Doppler shift information and satellite that are provided by inertial navigation is calculated；

If the receiver moment observes n usable satellite, then pseudo range measurement equation：

Z_ρ(t)=H_ρ(t)X(t)+v_ρ(t)

Wherein H_ρ(t)=[0_n×6 H_ρ1 0_n×6 H_ρ2],e_i1、e_i2、e_i3For I-th direction cosines between satellite and carrier, v_ρT () is pseudo range measurement noise, R_NIt is earth reference ellipsoid prime vertical curvature half Footpath；

Pseudorange rates measurement equation is：

$Z_{\stackrel{\·}{\mathrm{\ρ}}}\left(t\right)=H_{\stackrel{\·}{\mathrm{\ρ}}}\left(t\right)X\left(t\right)+v_{\stackrel{\·}{\mathrm{\ρ}}}\left(t\right)$

Wherein For pseudorange rates measure noise.

7. inertia/Big Dipper tight integration air navigation aid that astronomy as claimed in claim 6 is aided in, it is characterised in that：The step 4 Detailed content be：

(41) when visible star is less than 4, setting measures noise and is gradually reduced with visible increasing for star, you can see star more at most More trust the measurement information of triones navigation system, the measurement noise of pseudorange and pseudorange rates is expressed as follows：

$v_{\mathrm{\ρ}}\left(t\right)=\frac{\mathrm{\α}}{n}\×v_{\mathrm{\ρ}0}$

$v_{\stackrel{\·}{\mathrm{\ρ}}}\left(t\right)=\frac{\mathrm{\α}}{n}\×v_{\stackrel{\·}{\mathrm{\ρ}}0}$

N represents visible star number mesh, v in formula_ρ0,Pseudorange, the initial measurement noise of pseudorange rates are represented respectively, and α represents an often system Number；

(42) when the visible star of the Big Dipper is more than 4, first according to navigation position and the elevation angle and orientation of satellite position calculation satellite Angle, by the elevation angle and azimuthal angle calculation GDOP values of satellite, finally the measurement noise to pseudorange and pseudorange rates is adjusted, mistake Journey is as follows：

A, elevation of satellite, azimuthal angle calculation

Position of user's navigation position under body-fixed coordinate system is：

P_u=[p_ux p_uy p_uz]

I-th satellite marks the position under being admittedly on ground：

P_s=[p_sx p_sy p_sz]

If

$E=\left[\begin{array}{ccc}-\frac{p_{ux}}{p_1}& \frac{p_{ux}}{p_1}& 0\\ -\frac{x_{ux}{x}_{uz}}{p_1{p}_2}& -\frac{x_{uy}{x}_{uz}}{p_1{p}_2}& \frac{p_1}{p_2}\\ \frac{x_{ux}}{p_2}& \frac{x_{uy}}{p_2}& \frac{x_{uz}}{p_2}\end{array}\right]$

D=[d₁ d₂ d₃]=(P_s-P_u)E

$s=\frac{d_2}{\sqrt{d_1^2+d_2^2+d_3^2}}$

Then elevation angle is：

$El=\left\{\begin{array}{cc}\frac{\mathrm{\π}}{2},& s=1\\ a\tan \frac{s}{\sqrt{1-s^2}},& s\≠1\end{array}\right.$

Azimuth is：

The calculating of b, geometric dilution of precision GDOP

If the visible star number mesh of certain moment Beidou satellite navigation system is n, if matrix Q is as follows：

$Q=\left[\begin{array}{cccc}\sin {\mathrm{El}}_1& \cos {\mathrm{El}}_1\sin {\mathrm{Az}}_1& \cos {\mathrm{El}}_1\cos {\mathrm{Az}}_1& -1\\ \sin {\mathrm{El}}_2& \cos {\mathrm{El}}_1\sin {\mathrm{Az}}_1& \cos {\mathrm{El}}_1\cos {\mathrm{Az}}_1& -1\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ \sin {\mathrm{El}}_n& \cos {\mathrm{El}}_1\sin {\mathrm{Az}}_1& \cos {\mathrm{El}}_1\cos {\mathrm{Az}}_1& -1\end{array}\right]$

Then the value of GDOP is calculated by following formula：

$GDOP=\sqrt{trace{\left(Q^{T}Q\right)}^{-1}}$

C, satellite measure the setting of noise to receiver pseudorange, pseudorange rates

$v_{\mathrm{\ρ}}\left(t\right)=\frac{{\mathrm{GDOP}}_k}{{\mathrm{GDOP}}_0}\×v_{\mathrm{\ρ}0}$

$v_{\stackrel{\·}{\mathrm{\ρ}}}\left(t\right)=\frac{GDOP}{{\mathrm{GDOP}}_0}\×v_{\stackrel{\·}{\mathrm{\ρ}}0}$

Wherein v_ρ0,Pseudorange, the initial measurement noise of pseudorange rates, GDOP are represented respectively₀Represent the initial several of triones navigation system What dilution of precision, GDOP_kRepresent the geometric dilution of precision at triones navigation system kth moment.

8. inertia/Big Dipper tight integration air navigation aid that astronomy as claimed in claim 5 is aided in, it is characterised in that：The step 3 In, SINS/CNS subsystems measure the difference of the attitude angle and astronomical attitude angle information for providing provided for inertial navigation, definition observed quantity The attitude of carrier angle measured for star sensor and the difference of the attitude angle of inertial navigation, measurement equation are as follows：

Z_s(t)=H_s(t)X(t)+v_s(t)

Because the error angle quantity of state in integrated navigation system state equation is Inertial Navigation Platform error angle, it describes several Learn the error angular dependence between platform and ground the inside coordinate system, it is therefore desirable to which inertial attitude error angle is transformed into platform error Angle；When platform error angle is a small amount of, measurement matrix is represented by below equation：

$H_s=\frac{-1}{cos\mathrm{\θ}}\left[\begin{array}{ccc}sin\mathrm{\ψ}& cos\mathrm{\ψ}& 0\\ cos\mathrm{\ψ}cos\mathrm{\θ}& -sin\mathrm{\ψ}cos\mathrm{\θ}& 0\\ sin\mathrm{\ψ}sin\mathrm{\θ}& cos\mathrm{\ψ}sin\mathrm{\θ}& -\cos \mathrm{\θ}\end{array}\right]$

Therefore, measurement equation is expressed as：

In formula, γ, θ, ψ are respectively roll angle, the angle of pitch and course angle, v_sT () is attitude error angle measurements noise.

9. inertia/Big Dipper tight integration air navigation aid that astronomy as claimed in claim 5 is aided in, it is characterised in that：The step 4 In, filtering is as follows：

${\hat{X}}_{k/k-1}={\mathrm{\Φ}}_{k/k-1}{\hat{X}}_{k-1/k-1}$

$P_{k/k-1}={\mathrm{\Φ}}_{k/k-1}{P}_{k-1/k-1}{\mathrm{\Φ}}_{k/k-1}^T+{\mathrm{\Γ}}_{k/k-1}{Q}_{k-1}{\mathrm{\Γ}}_{k/k-1}^T$

$K_k=P_{k/k-1}{H}_k^T{(H_k{P}_{k/k-1}{H}_k^T+R_k)}^{-1}$

${\hat{X}}_{k/k}={\hat{X}}_{k/k-1}+K_k(Z_k-H_k{\hat{X}}_{k/k-1})$

$P_{k/k}=(I-K_k{H}_k)P_{k/k-1}{(I-K_k{H}_k)}^T+K_k{R}_k{K}_k^T$

In above formula,Represent t_k-1The state at moment is to t_kThe optimal estimation value of the state at moment, Φ_k/k-1Represent t_k-1Moment is extremely t_kWhen etching system state-transition matrix,Represent t_k-1The system state estimation value at moment, K_kRepresent gain matrix, H_kTable Show filtration module t_kThe observed differential matrix at moment, P_k/k-1Represent optimum prediction evaluated error covariance matrix, P_k/kRepresent filtering mould Block t_kThe systematic error covariance matrix at moment, Q_k-1Represent t_k-1The noise variance matrix at moment, Γ_k/k-1Represent t_k-1Moment makes an uproar Acoustic vector is to t_kThe noise coefficient matrix of moment state vector influence, R_kRepresent t_kThe measurement variance matrix at moment, I is unit square Battle array.