CN103471613A - Parameter simulation method for inertial navigation system of aircraft - Google Patents

Abstract

The invention relates to a parameter simulation method for an inertial navigation system of an aircraft. The method can effectively realize separation of dynamic calculation errors in the process of dynamic simulation of the inertial navigation system, eliminates influence of the dynamic calculation errors in simulation on inertial navigation simulation precision, corrects and compensates the dynamic calculation errors of navigation parameters in the navigation simulation process at a simulation output terminal of the inertial navigation system, improves navigation simulation precision of the inertial navigation system, provides bases for type selection of inertial navigation sensors and has a good engineering application value.

Description

A kind of aircraft inertial navigation system parameters simulation method

Technical field

The present invention relates to a kind of aircraft inertial navigation system parameters simulation method.

Background technology

Inertial navigation system is the navigational system of autonomous type, and wherein, strap-down inertial navigation system has replaced the mechanical platform inertial navigation system with " mathematical platform ", have simple in structure, cost is low, volume is little, the characteristics such as low in energy consumption.Along with the development of inertance element, and the raising day by day of computer technology level, the application of strap-down inertial navigation system is more and more extensive, also more and more higher to the accuracy requirement of strap-down inertial navigation system.The error component that affects strap-down inertial navigation system is mainly derived from the error characteristics of inertia measurement sensor, and still, existing analysis inertia measurement sensor error characteristic also very lacks the simulation analysis means of inertia system dynamic property impact, present stage is mainly carried out inertia measurement sensor performance index type selecting by the mode of test, still lack the effective analysis and the verification method that under the selected index condition of inertia measurement sensor, the inertial navigation system dynamic property are affected, usually need to take to hang the mode flown is verified, the manpower that need to expend, material resources and financial resources are larger, and in the acquisition of flight inertial navigation result, can produce larger dynamic calculation error, if this dynamic calculation error is not effectively separated, the precision of inertial navigation system will be affected, also be difficult to the impact of simulation study inertia measurement sensor error characteristic on inertial navigation system dynamic calculation error performance simultaneously.

Summary of the invention

For above-mentioned technical matters, technical matters to be solved by this invention is to provide a kind ofly to be resolved based on traditional inertial navigation, for inertial navigation system dynamic simulation process, can effectively separate and eliminate the aircraft inertial navigation system parameters simulation method of dynamic calculation error.

The present invention is in order to solve the problems of the technologies described above by the following technical solutions: the present invention has designed a kind of aircraft inertial navigation system parameters simulation method, comprises following method:

Step 01. is obtained flight benchmark flight path data;

Step 02., according to flight benchmark flight path data, is obtained inertial navigation sensors output data by the inertial navigation sensors output model;

Step 03., according to inertial navigation sensors output data, is obtained inertial navigation sensors model error data by the inertial navigation sensors error model;

Step 04. is carried out inertial navigation for inertial navigation sensors output data and is resolved acquisition the first inertial navigation data;

Inertial navigation sensors is exported to data and inertial navigation sensors model error data are superposeed, and carry out inertial navigation for stack result and resolve and obtain the second inertial navigation data;

Step 05. contrasts the first inertial navigation data to ask poor with flight benchmark flight path data, obtains the dynamic calculation error;

Step 06., for the second inertial navigation data, is removed the dynamic calculation error, obtains the inertial navigation result.

As a preferred technical solution of the present invention: described step 01 comprises the steps:

Step 011. adopts the vehicle dynamics model to obtain space vehicle dynamic flight path data;

Step 012. is carried out the data pre-service for space vehicle dynamic flight path data, obtains flight benchmark flight path data.

As a preferred technical solution of the present invention: in described step 012, the data pre-service comprises markers conversion, physical quantity conversion and, by the navigational parameter threshold value is set, data is carried out to validity check and reparation.

As a preferred technical solution of the present invention: in described step 02, the inertial navigation sensors output model comprises gyro sensor output model and acceleration transducer output model; The inertial navigation sensors error model comprises gyro sensor error model and acceleration transducer error model.

As a preferred technical solution of the present invention: described gyro sensor output model is as shown in the formula shown in (1):

$W=\left[\begin{array}{ccc}\cos {\mathrm{\&gamma;}}_0& 0& \sin {\mathrm{\&gamma;}}_0\cos {\mathrm{\&theta;}}_0\\ 0& 1& -\sin {\mathrm{\&theta;}}_0\\ \sin {\mathrm{\&gamma;}}_0& 0& -\cos {\mathrm{\&gamma;}}_0\cos {\mathrm{\&theta;}}_0\end{array}\right]\left[\begin{array}{c}\stackrel{\&CenterDot;}{{\mathrm{\&theta;}}_0}\\ \stackrel{\&CenterDot;}{{\mathrm{\&gamma;}}_0}\\ \stackrel{\&CenterDot;}{{\mathrm{\&psi;}}_0}\end{array}\right]+C_n^b\&times;(\left[\begin{array}{c}0\\ {\mathrm{\&omega;}}_{\mathrm{ie}}\cos {\mathrm{<figure-callout\; id="0"\; label="L"\; filenames="HDA00003583760600012.png,HDA00003583760600021.png"\; state="\{\{state\}\}">L</figure-callout>}}_0\\ {\mathrm{\&omega;}}_{\mathrm{ie}}\sin {\mathrm{<figure-callout\; id="0"\; label="L"\; filenames="HDA00003583760600012.png,HDA00003583760600021.png"\; state="\{\{state\}\}">L</figure-callout>}}_0\end{array}\right]+\left[\begin{array}{c}-\frac{V_{\mathrm{eny}}^n}{(R_e+h_0)}\\ \frac{V_{\mathrm{enx}}^n}{(R_e+h_0)}\\ \frac{V_{\mathrm{enx}}^n}{(R_e+h_0)}\tan L_0\end{array}\right])---\left(1\right)$

In formula, W is gyroscope output data, θ ₀roll angle, γ for aircraft in flight benchmark flight path data ₀the angle of pitch, ψ for aircraft in flight benchmark flight path data ₀for the course angle of aircraft in flight benchmark flight path data, L ₀for the latitude of aircraft in flight benchmark flight path data, h ₀for the height of aircraft in flight benchmark flight path data,

be respectively aircraft speed component on x axle and y axle in navigation coordinate system,

for the attitude matrix between navigation coordinate system and aircraft coordinate system, n means navigation coordinate system, and b means the aircraft coordinate system, and the expression of adding some points on above letter is carried out differentiate to this letter.

As a preferred technical solution of the present invention: described acceleration transducer output model is as shown in the formula shown in (2):

$\left\{\begin{array}{c}{f}_n=\stackrel{\&CenterDot;}{V}+({2\mathrm{\&omega;}}_{\mathrm{ie}}^n+{\mathrm{\&omega;}}_{\mathrm{en}}^n)\&times;V-G\\ f_b=C_n^b{f}_n\end{array}\right.---\left(2\right)$

In formula, f _bfor acceleration transducer output data, f _nfor the specific force under navigation coordinate system,

for the attitude matrix between navigation coordinate system and aircraft coordinate system, ω _iefor earth rotation angular speed, ω _enfor the angular speed of the relative earth of aircraft, the vector that the projection on V be aircraft speed in navigation coordinate system three coordinate axis forms, and add some points on above letter and mean this letter is carried out to differentiate.

As a preferred technical solution of the present invention: described gyro sensor error model is as shown in the formula shown in (3):

$\mathrm{\&Delta;W}=\left[\begin{array}{c}{\&dtri;\mathrm{<figure-callout\; id="0"\; label="W\; x"\; filenames="HDA00003583760600012.png,HDA00003583760600021.png"\; state="\{\{state\}\}">W</figure-callout>}}_x\\ {\&dtri;\mathrm{<figure-callout\; id="0"\; label="W\; y"\; filenames="HDA00003583760600012.png,HDA00003583760600021.png"\; state="\{\{state\}\}">W</figure-callout>}}_y\\ {\&dtri;\mathrm{<figure-callout\; id="0"\; label="W\; z"\; filenames="HDA00003583760600012.png,HDA00003583760600021.png"\; state="\{\{state\}\}">W</figure-callout>}}_z\end{array}\right]+\mathrm{diag}[K_{\mathrm{qx}},K_{\mathrm{qy}},K_{\mathrm{qz}}]W+\left[\begin{array}{ccc}1& -{\mathrm{\&theta;}}_{\mathrm{yz}}& -{\mathrm{\&theta;}}_{\mathrm{zy}}\\ {\mathrm{\&theta;}}_{\mathrm{xz}}& 1& -{\mathrm{\&theta;}}_{\mathrm{zx}}\\ -{\mathrm{\&theta;}}_{\mathrm{xy}}& {-\mathrm{\&theta;}}_{\mathrm{yx}}& 1\end{array}\right]W+\left[\begin{array}{c}{\mathrm{\&epsiv;}}_{\mathrm{bwx}}\\ {\mathrm{\&epsiv;}}_{\mathrm{bwy}}\\ {\mathrm{\&epsiv;}}_{\mathrm{bwz}}\end{array}\right]+\left[\begin{array}{c}{\mathrm{\&epsiv;}}_{\mathrm{rwx}}\\ {\mathrm{\&epsiv;}}_{\mathrm{rwy}}\\ {\mathrm{\&epsiv;}}_{\mathrm{rwz}}\end{array}\right]+\left[\begin{array}{c}{w}_{\mathrm{gwx}}\\ w_{\mathrm{gwy}}\\ w_{\mathrm{gwz}}\end{array}\right]---\left(3\right)$

In formula, the error output that Δ W is gyro sensor, ▽ W _x0, ▽ W _y0, ▽ W _z0be respectively gyro sensor corresponding its axially, normal direction, horizontal three-dimensional zero error; Diag[K _qx, K _qy, K _qz] be the three-dimensional scale coefficient error matrix of gyro sensor, $\left[\begin{array}{ccc}1& {-\mathrm{\&theta;}}_{\mathrm{yz}}& {-\mathrm{\&theta;}}_{\mathrm{zy}}\\ {\mathrm{\&theta;}}_{\mathrm{xz}}& 1& {-\mathrm{\&theta;}}_{\mathrm{zx}}\\ {-\mathrm{\&theta;}}_{\mathrm{xy}}& {-\mathrm{\&theta;}}_{\mathrm{<figure-callout\; id="1"\; label="yx"\; filenames="HDA00003583760600012.png,HDA00003583760600021.png"\; state="\{\{state\}\}">yx</figure-callout>}}& 1\end{array}\right]$ For three-dimensional alignment error.ε _bwx, ε _bwy, ε _bwzfor arbitrary constant, ε _rwx, ε _rwy, ε _rwzfor single order Markov noise, ε _gwx, ε _gwy, ε _gwzfor white noise, W is gyroscope output data.

As a preferred technical solution of the present invention: described acceleration transducer error model is as shown in the formula shown in (4):

${\&dtri;f}_b=\left[\begin{array}{c}{\&dtri;\mathrm{<figure-callout\; id="0"\; label="f\; bx"\; filenames="HDA00003583760600012.png,HDA00003583760600021.png"\; state="\{\{state\}\}">f</figure-callout>}}_{\mathrm{bx}}\\ {\&dtri;f}_{\mathrm{by}0}\\ {\&dtri;\mathrm{<figure-callout\; id="0"\; label="f\; bz"\; filenames="HDA00003583760600012.png,HDA00003583760600021.png"\; state="\{\{state\}\}">f</figure-callout>}}_{\mathrm{bz}}\end{array}\right]+\mathrm{diag}[K_{\mathrm{px}},K_{\mathrm{py}},K_{\mathrm{pz}}]f_b+\left[\begin{array}{ccc}1& {-\mathrm{\&theta;}}_{\mathrm{yz}}& -{\mathrm{\&theta;}}_{\mathrm{zy}}\\ {\mathrm{\&theta;}}_{\mathrm{xz}}& 1& {-\mathrm{\&theta;}}_{\mathrm{zx}}\\ {-\mathrm{\&theta;}}_{\mathrm{xy}}& -{\mathrm{\&theta;}}_{\mathrm{yx}}& 1\end{array}\right]f_b+\left[\begin{array}{c}{\mathrm{\&epsiv;}}_{\mathrm{rax}}\\ {\mathrm{\&epsiv;}}_{\mathrm{ray}}\\ {\mathrm{\&epsiv;}}_{\mathrm{raz}}\end{array}\right]---\left(4\right)$

In formula, Δ f _bfor the error output of acceleration transducer, ▽ f _bx0, ▽ f _by0, ▽ f _bz0be respectively acceleration transducer corresponding its axially, normal direction, horizontal three-dimensional zero error; Diag[K _px, K _py, K _pz] be the three-dimensional scale coefficient error matrix of acceleration transducer, $\left[\begin{array}{ccc}1& {-\mathrm{\&theta;}}_{\mathrm{yz}}& {-\mathrm{\&theta;}}_{\mathrm{zy}}\\ {\mathrm{\&theta;}}_{\mathrm{xz}}& 1& {-\mathrm{\&theta;}}_{\mathrm{zx}}\\ {-\mathrm{\&theta;}}_{\mathrm{xy}}& {-\mathrm{\&theta;}}_{\mathrm{<figure-callout\; id="1"\; label="yx"\; filenames="HDA00003583760600012.png,HDA00003583760600021.png"\; state="\{\{state\}\}">yx</figure-callout>}}& 1\end{array}\right]$ For three-dimensional alignment error, ε _rax, ε _ray, ε _razfor single order Markov drift error, f _bfor acceleration transducer output data.

As a preferred technical solution of the present invention: described dynamic calculation error comprises site error, velocity error and attitude error.

A kind of aircraft inertial navigation system parameters simulation method of the present invention adopts above technical scheme compared with prior art, has following technique effect:

(1) the aircraft inertial navigation system parameters simulation method of the present invention's design, at traditional inertial navigation, resolve on basis, in resolving ultimate principle without prejudice to inertial navigation and not affecting simulation process under the prerequisite of inertial navigation sensors error Propagation Property, efficiently solve the dynamic calculation error that the difference due to algorithm principle causes, the effective separation of realization to navigational parameter dynamic calculation error in inertial navigation system dynamic simulation process, the error of calculation of navigational parameter in inertial navigation system simulation data end is revised the navigation simulation process to the navigational parameter of simulation data, improved the precision of inertial navigation system dynamic simulation, and can effectively realize the dynamic simulation effect of inertial navigation sensors error characteristics to the inertial navigation system performance impact, be applicable to the engineering application,

(2) in the aircraft inertial navigation system parameters simulation method of the present invention's design, adopt the vehicle dynamics model to obtain space vehicle dynamic flight path data, and carry out the data pre-service for space vehicle dynamic flight path data, obtain flight benchmark flight path data, effectively improved the convenience of computing in inertial navigation system dynamic simulation process.

The accompanying drawing explanation

Fig. 1 is the conceptual scheme of the aircraft inertial navigation system parameters simulation method that designs of the present invention;

Concrete flight benchmark flight path schematic diagram data in the aircraft inertial navigation system parameters simulation method that Fig. 2 designs for the present invention;

Fig. 3 a is not for adopting the contrast schematic diagram of the inventive method and the corresponding longitude of employing the inventive method and standard longitude;

Fig. 3 b is not for adopting the corresponding longitude error schematic diagram of the inventive method and employing the inventive method;

Fig. 3 c is for adopting the corresponding longitude error enlarged diagram of the inventive method;

Fig. 4 a is not for adopting the contrast schematic diagram of the inventive method and employing the inventive method corresponding latitude and normal latitude;

Fig. 4 b is not for adopting the corresponding latitude error schematic diagram of the inventive method and employing the inventive method;

Fig. 4 c is for adopting the corresponding latitude error enlarged diagram of the inventive method;

Fig. 5 a is not for adopting the contrast schematic diagram of the inventive method and employing the inventive method respective heights and calibrated altitude;

Fig. 5 b is not for adopting the respective heights error schematic diagram of the inventive method and employing the inventive method;

Fig. 5 c is for adopting the respective heights error enlarged diagram of the inventive method;

Fig. 6 specifically adds three groups of embodiment inertial navigation sensors error models, the inertial navigation system dynamic simulation position corresponding latitude graph of errors contrast schematic diagram that gained is different in the present invention;

Fig. 7 specifically adds three groups of embodiment inertial navigation sensors error models, the inertial navigation system dynamic simulation position corresponding longitude error curve comparison schematic diagram that gained is different in the present invention;

Fig. 8 specifically adds three groups of embodiment inertial navigation sensors error models, the inertial navigation system dynamic simulation position respective heights graph of errors contrast schematic diagram that gained is different in the present invention.

Embodiment

Below in conjunction with Figure of description, the specific embodiment of the present invention is described in further detail.

As shown in Figure 1, the present invention has designed a kind of aircraft inertial navigation system parameters simulation method, comprises following method:

Step 01. is obtained flight benchmark flight path data;

Step 02., according to flight benchmark flight path data, is obtained inertial navigation sensors output data by the inertial navigation sensors output model;

Step 03., according to inertial navigation sensors output data, is obtained inertial navigation sensors model error data by the inertial navigation sensors error model;

Step 04. is carried out inertial navigation for inertial navigation sensors output data and is resolved acquisition the first inertial navigation data;

Inertial navigation sensors is exported to data and inertial navigation sensors model error data are superposeed, and carry out inertial navigation for stack result and resolve and obtain the second inertial navigation data;

Step 05. contrasts the first inertial navigation data to ask poor with flight benchmark flight path data, obtains the dynamic calculation error;

Step 06., for the second inertial navigation data, is removed the dynamic calculation error, obtains the inertial navigation result.

The aircraft inertial navigation system parameters simulation method of the present invention's design, at traditional inertial navigation, resolve on basis, in resolving ultimate principle without prejudice to inertial navigation and not affecting simulation process under the prerequisite of inertial navigation sensors error Propagation Property, efficiently solve the dynamic calculation error that the difference due to algorithm principle causes, the effective separation of realization to navigational parameter dynamic calculation error in inertial navigation system dynamic simulation process, the error of calculation of navigational parameter in inertial navigation system simulation data end is revised the navigation simulation process to the navigational parameter of simulation data, improved the precision of inertial navigation system dynamic simulation, and can effectively realize the dynamic simulation effect of inertial navigation sensors error characteristics to the inertial navigation system performance impact, be applicable to the engineering application.

As a preferred technical solution of the present invention: described step 01 comprises the steps:

Step 011. adopts the vehicle dynamics model to obtain space vehicle dynamic flight path data;

Step 012. is carried out the data pre-service for space vehicle dynamic flight path data, obtains flight benchmark flight path data.

As a preferred technical solution of the present invention: in described step 012, the data pre-service comprises markers conversion, physical quantity conversion and, by the navigational parameter threshold value is set, data is carried out to validity check and reparation.

In the aircraft inertial navigation system parameters simulation method of the present invention's design, adopt the vehicle dynamics model to obtain space vehicle dynamic flight path data, and carry out the data pre-service for space vehicle dynamic flight path data, obtain flight benchmark flight path data, effectively improved the convenience of computing in inertial navigation system dynamic simulation process.

As a preferred technical solution of the present invention: in described step 02, the inertial navigation sensors output model comprises gyro sensor output model and acceleration transducer output model; The inertial navigation sensors error model comprises gyro sensor error model and acceleration transducer error model.

As a preferred technical solution of the present invention: described gyro sensor output model is as shown in the formula shown in (1):

$W=\left[\begin{array}{ccc}\cos {\mathrm{\&gamma;}}_0& 0& \sin {\mathrm{\&gamma;}}_0\cos {\mathrm{\&theta;}}_0\\ 0& 1& -\sin {\mathrm{\&theta;}}_0\\ \sin {\mathrm{\&gamma;}}_0& 0& -\cos {\mathrm{\&gamma;}}_0\cos {\mathrm{\&theta;}}_0\end{array}\right]\left[\begin{array}{c}\stackrel{\&CenterDot;}{{\mathrm{\&theta;}}_0}\\ \stackrel{\&CenterDot;}{{\mathrm{\&gamma;}}_0}\\ \stackrel{\&CenterDot;}{{\mathrm{\&psi;}}_0}\end{array}\right]+C_n^b\&times;(\left[\begin{array}{c}0\\ {\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="0"\; label="ie\; cos\; L"\; filenames="HDA00003583760600012.png,HDA00003583760600021.png"\; state="\{\{state\}\}">ie</figure-callout>}}\cos L_{}{}_0\\ {\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="0"\; label="ie\; sin\; L"\; filenames="HDA00003583760600012.png,HDA00003583760600021.png"\; state="\{\{state\}\}">ie</figure-callout>}}\sin L_{}{}_0\end{array}\right]+\left[\begin{array}{c}-\frac{V_{\mathrm{eny}}^n}{(R_e+h_0)}\\ \frac{V_{\mathrm{enx}}^n}{(R_e+h_0)}\\ \frac{V_{\mathrm{enx}}^n}{(R_e+h_0)}\tan L_0\end{array}\right])---\left(1\right)$

In formula, W is gyroscope output data, θ ₀roll angle, γ for aircraft in flight benchmark flight path data ₀the angle of pitch, ψ for aircraft in flight benchmark flight path data ₀for the course angle of aircraft in flight benchmark flight path data, L ₀for the latitude of aircraft in flight benchmark flight path data, h ₀for the height of aircraft in flight benchmark flight path data, be respectively aircraft speed component on x axle and y axle in navigation coordinate system,

for the attitude matrix between navigation coordinate system and aircraft coordinate system, n means navigation coordinate system, and b means the aircraft coordinate system, and the expression of adding some points on above letter is carried out differentiate to this letter.

As a preferred technical solution of the present invention: described acceleration transducer output model is as shown in the formula shown in (2):

$\left\{\begin{array}{c}{f}_n=\stackrel{\&CenterDot;}{V}+({2\mathrm{\&omega;}}_{\mathrm{ie}}^n+{\mathrm{\&omega;}}_{\mathrm{en}}^n)\&times;V-G\\ f_b=C_n^b{f}_n\end{array}\right.---\left(2\right)$

In formula, f _bfor acceleration transducer output data, f _nfor the specific force under navigation coordinate system,

for the attitude matrix between navigation coordinate system and aircraft coordinate system, ω _iefor earth rotation angular speed, ω _enfor the angular speed of the relative earth of aircraft, the vector that the projection on V be aircraft speed in navigation coordinate system three coordinate axis forms, and add some points on above letter and mean this letter is carried out to differentiate.

As a preferred technical solution of the present invention: described gyro sensor error model is as shown in the formula shown in (3):

$\mathrm{\&Delta;W}=\left[\begin{array}{c}{\&dtri;W}_{x0}\\ {\&dtri;\mathrm{<figure-callout\; id="0"\; label="W\; y"\; filenames="HDA00003583760600012.png,HDA00003583760600021.png"\; state="\{\{state\}\}">W</figure-callout>}}_y\\ {\&dtri;\mathrm{<figure-callout\; id="0"\; label="W\; z"\; filenames="HDA00003583760600012.png,HDA00003583760600021.png"\; state="\{\{state\}\}">W</figure-callout>}}_z\end{array}\right]+\mathrm{diag}[K_{\mathrm{qx}},K_{\mathrm{qy}},K_{\mathrm{qz}}]W+\left[\begin{array}{ccc}1& -{\mathrm{\&theta;}}_{\mathrm{yz}}& -{\mathrm{\&theta;}}_{\mathrm{zy}}\\ {\mathrm{\&theta;}}_{\mathrm{xz}}& 1& -{\mathrm{\&theta;}}_{\mathrm{zx}}\\ -{\mathrm{\&theta;}}_{\mathrm{xy}}& {-\mathrm{\&theta;}}_{\mathrm{yx}}& 1\end{array}\right]W+\left[\begin{array}{c}{\mathrm{\&epsiv;}}_{\mathrm{bwx}}\\ {\mathrm{\&epsiv;}}_{\mathrm{bwy}}\\ {\mathrm{\&epsiv;}}_{\mathrm{bwz}}\end{array}\right]+\left[\begin{array}{c}{\mathrm{\&epsiv;}}_{\mathrm{rwx}}\\ {\mathrm{\&epsiv;}}_{\mathrm{rwy}}\\ {\mathrm{\&epsiv;}}_{\mathrm{rwz}}\end{array}\right]+\left[\begin{array}{c}{w}_{\mathrm{gwx}}\\ w_{\mathrm{gwy}}\\ w_{\mathrm{gwz}}\end{array}\right]---\left(3\right)$

In formula, the error output that Δ W is gyro sensor, ▽ W _x0, ▽ W _y0, ▽ W _z0be respectively gyro sensor corresponding its axially, normal direction, horizontal three-dimensional zero error; Diag[K _qx, K _qy, K _qz] be the three-dimensional scale coefficient error matrix of gyro sensor, $\left[\begin{array}{ccc}1& {-\mathrm{\&theta;}}_{\mathrm{yz}}& {-\mathrm{\&theta;}}_{\mathrm{zy}}\\ {\mathrm{\&theta;}}_{\mathrm{xz}}& 1& {-\mathrm{\&theta;}}_{\mathrm{zx}}\\ {-\mathrm{\&theta;}}_{\mathrm{xy}}& {-\mathrm{\&theta;}}_{\mathrm{yx}}& 1\end{array}\right]$ For three-dimensional alignment error.ε _bwx, ε _bwy, ε _bwzfor arbitrary constant, ε _rwx, ε _rwy, ε _rwzfor single order Markov noise, ε _gwx, ε _gwy, ε _gwzfor white noise, W is gyroscope output data.

As a preferred technical solution of the present invention: described acceleration transducer error model is as shown in the formula shown in (4):

${\&dtri;f}_b=\left[\begin{array}{c}{\&dtri;\mathrm{<figure-callout\; id="0"\; label="f\; bx"\; filenames="HDA00003583760600012.png,HDA00003583760600021.png"\; state="\{\{state\}\}">f</figure-callout>}}_{\mathrm{bx}}\\ {\&dtri;f}_{\mathrm{by}0}\\ {\&dtri;\mathrm{<figure-callout\; id="0"\; label="f\; bz"\; filenames="HDA00003583760600012.png,HDA00003583760600021.png"\; state="\{\{state\}\}">f</figure-callout>}}_{\mathrm{bz}}\end{array}\right]+\mathrm{diag}[K_{\mathrm{px}},K_{\mathrm{py}},K_{\mathrm{pz}}]f_b+\left[\begin{array}{ccc}1& {-\mathrm{\&theta;}}_{\mathrm{yz}}& -{\mathrm{\&theta;}}_{\mathrm{zy}}\\ {\mathrm{\&theta;}}_{\mathrm{xz}}& 1& {-\mathrm{\&theta;}}_{\mathrm{zx}}\\ {-\mathrm{\&theta;}}_{\mathrm{xy}}& -{\mathrm{\&theta;}}_{\mathrm{yx}}& 1\end{array}\right]f_b+\left[\begin{array}{c}{\mathrm{\&epsiv;}}_{\mathrm{rax}}\\ {\mathrm{\&epsiv;}}_{\mathrm{ray}}\\ {\mathrm{\&epsiv;}}_{\mathrm{raz}}\end{array}\right]---\left(4\right)$

In formula, Δ f _bfor the error output of acceleration transducer, ▽ f _bx0, ▽ f _by0, ▽ f _bz0be respectively acceleration transducer corresponding its axially, normal direction, horizontal three-dimensional zero error; Diag[K _px, K _py, K _pz] be the three-dimensional scale coefficient error matrix of acceleration transducer, $\left[\begin{array}{ccc}1& {-\mathrm{\&theta;}}_{\mathrm{yz}}& {-\mathrm{\&theta;}}_{\mathrm{zy}}\\ {\mathrm{\&theta;}}_{\mathrm{xz}}& 1& {-\mathrm{\&theta;}}_{\mathrm{zx}}\\ {-\mathrm{\&theta;}}_{\mathrm{xy}}& {-\mathrm{\&theta;}}_{\mathrm{yx}}& 1\end{array}\right]$ For three-dimensional alignment error, ε _rax, ε _ray, ε _razfor single order Markov drift error, f _bfor acceleration transducer output data.

The aircraft inertial navigation system parameters simulation method of the present invention's design is in actual application, and as a specific embodiment in practical application, in simulation process, navigation coordinate system adopts east northeast navigation coordinate system here, carries out in accordance with the following steps emulation:

Step 011. adopts the vehicle dynamics model to obtain space vehicle dynamic flight path data comparatively true to nature, mainly provides the basic navigation amount under aircraft coordinate system and inertial navigation coordinate system, as the basis that completes the strapdown inertial navigation system dynamic simulation;

Step 012. is carried out the data pre-service for space vehicle dynamic flight path data, obtains flight benchmark flight path data, and wherein, process of data preprocessing comprises as follows:

Physical quantity conversion and markers conversion, resolve the basis of emulation as follow-up inertial navigation sensors emulation and inertial navigation due to space vehicle dynamic flight path data, so the correctness of resolving in order to ensure inertial navigation sensors emulation and inertial navigation, need to carry out preprocessing process to space vehicle dynamic flight path data.

The physical quantity conversion mainly comprises the unification of each coordinate system and navigational parameter scope, if it is not corresponding with the corresponding coordinate system of inertial navigation to judge the coordinate system of space vehicle dynamic flight path data in the vehicle dynamics model, need to carry out the coordinate system conversion, by the coordinate system unification under the corresponding coordinate system of inertial navigation; If it is inconsistent to judge navigational parameter scope and the inertial navigation relevant parameter scope of space vehicle dynamic flight path data in the vehicle dynamics model, such as the attitude angle scope, need navigational parameter scope and inertial navigation parameter area unified.

If it is inharmonious to judge in the vehicle dynamics model in space vehicle dynamic flight path data markers markers corresponding to inertial navigation, need to carry out the markers conversion, markers is unified under the corresponding coordinate system of inertial navigation.

Set the inertial navigation parameter threshold, threshold value is set to the inertial navigation parameter, wherein part threshold value form is as shown in the formula shown in (5):

The longitude threshold value: | λ ₀|<λ _max(5)

The latitude threshold value: | L ₀|<L _max

In formula, L ₀for the latitude of aircraft in flight benchmark flight path data, λ ₀for the longitude of aircraft in flight benchmark flight path data, λ _max, L _maxbe respectively predefined longitude threshold value and latitude threshold values; Threshold value is set to each navigational parameter, if occur exceeding the data of threshold value in space vehicle dynamic flight path data, it is rejected to laggard line linearity Interpolation compensation.

After dynamics flight path data have been carried out above-mentioned data and processed, obtain flight benchmark flight path data, as shown in Figure 2.

Step 02., according to flight benchmark flight path data, is obtained inertial navigation sensors output data by the inertial navigation sensors output model; Wherein, the inertial navigation sensors output model comprises gyro sensor output model and acceleration transducer output model;

According to flight benchmark flight path data, by gyro sensor output model shown in following formula (1), obtain gyroscope output data W, the gyro sensor output model is as shown in the formula shown in (1):

$W=\left[\begin{array}{ccc}\cos {\mathrm{\&gamma;}}_0& 0& \sin {\mathrm{\&gamma;}}_0\cos {\mathrm{\&theta;}}_0\\ 0& 1& -\sin {\mathrm{\&theta;}}_0\\ \sin {\mathrm{\&gamma;}}_0& 0& -\cos {\mathrm{\&gamma;}}_0\cos {\mathrm{\&theta;}}_0\end{array}\right]\left[\begin{array}{c}\stackrel{\&CenterDot;}{{\mathrm{\&theta;}}_0}\\ \stackrel{\&CenterDot;}{{\mathrm{\&gamma;}}_0}\\ \stackrel{\&CenterDot;}{{\mathrm{\&psi;}}_0}\end{array}\right]+C_n^b\&times;(\left[\begin{array}{c}0\\ {\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="0"\; label="ie\; cos\; L"\; filenames="HDA00003583760600012.png,HDA00003583760600021.png"\; state="\{\{state\}\}">ie</figure-callout>}}\cos L_{}{}_0\\ {\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="0"\; label="ie\; sin\; L"\; filenames="HDA00003583760600012.png,HDA00003583760600021.png"\; state="\{\{state\}\}">ie</figure-callout>}}\sin L_{}{}_0\end{array}\right]+\left[\begin{array}{c}-\frac{V_{\mathrm{eny}}^n}{(R_e+h_0)}\\ \frac{V_{\mathrm{enx}}^n}{(R_e+h_0)}\\ \frac{V_{\mathrm{enx}}^n}{(R_e+h_0)}\tan L_0\end{array}\right])---\left(1\right)$

In formula, θ ₀roll angle, γ for aircraft in flight benchmark flight path data ₀the angle of pitch, ψ for aircraft in flight benchmark flight path data ₀for the course angle of aircraft in flight benchmark flight path data, L ₀for the latitude of aircraft in flight benchmark flight path data, h ₀for the height of aircraft in flight benchmark flight path data,

be respectively aircraft speed component on x axle and y axle in navigation coordinate system,

for the attitude matrix between navigation coordinate system and aircraft coordinate system, n means navigation coordinate system, and b means the aircraft coordinate system, and the expression of adding some points on above letter is carried out differentiate to this letter.

According to flight benchmark flight path data, by acceleration transducer output model shown in following formula (2), obtain acceleration transducer output data f _b, the acceleration transducer output model is as shown in the formula shown in (2):

$\left\{\begin{array}{c}{f}_n=\stackrel{\&CenterDot;}{V}+({2\mathrm{\&omega;}}_{\mathrm{ie}}^n+{\mathrm{\&omega;}}_{\mathrm{en}}^n)\&times;V-G\\ f_b=C_n^b{f}_n\end{array}\right.---\left(2\right)$

In formula, f _nfor the specific force under navigation coordinate system, for the attitude matrix between navigation coordinate system and aircraft coordinate system, ω _iefor earth rotation angular speed, ω _enfor the angular speed of the relative earth of aircraft, the vector that the projection on V be aircraft speed in navigation coordinate system three coordinate axis forms, and add some points on above letter and mean this letter is carried out to differentiate.

Step 03., according to inertial navigation sensors output data, is obtained inertial navigation sensors model error data by the inertial navigation sensors error model; Wherein, the inertial navigation sensors error model comprises gyro sensor error model and acceleration transducer error model, and detailed process is as follows:

According to gyroscope output data W, by gyro sensor error model shown in following formula (3), obtain the error output Δ W of gyro sensor, the gyro sensor error model is as shown in the formula shown in (3):

$\mathrm{\&Delta;W}=\left[\begin{array}{c}{\&dtri;W}_{x0}\\ {\&dtri;\mathrm{<figure-callout\; id="0"\; label="W\; y"\; filenames="HDA00003583760600012.png,HDA00003583760600021.png"\; state="\{\{state\}\}">W</figure-callout>}}_y\\ {\&dtri;\mathrm{<figure-callout\; id="0"\; label="W\; z"\; filenames="HDA00003583760600012.png,HDA00003583760600021.png"\; state="\{\{state\}\}">W</figure-callout>}}_z\end{array}\right]+\mathrm{diag}[K_{\mathrm{qx}},K_{\mathrm{qy}},K_{\mathrm{qz}}]W+\left[\begin{array}{ccc}1& -{\mathrm{\&theta;}}_{\mathrm{yz}}& -{\mathrm{\&theta;}}_{\mathrm{zy}}\\ {\mathrm{\&theta;}}_{\mathrm{xz}}& 1& -{\mathrm{\&theta;}}_{\mathrm{zx}}\\ -{\mathrm{\&theta;}}_{\mathrm{xy}}& {-\mathrm{\&theta;}}_{\mathrm{yx}}& 1\end{array}\right]W+\left[\begin{array}{c}{\mathrm{\&epsiv;}}_{\mathrm{bwx}}\\ {\mathrm{\&epsiv;}}_{\mathrm{bwy}}\\ {\mathrm{\&epsiv;}}_{\mathrm{bwz}}\end{array}\right]+\left[\begin{array}{c}{\mathrm{\&epsiv;}}_{\mathrm{rwx}}\\ {\mathrm{\&epsiv;}}_{\mathrm{rwy}}\\ {\mathrm{\&epsiv;}}_{\mathrm{rwz}}\end{array}\right]+\left[\begin{array}{c}{w}_{\mathrm{gwx}}\\ w_{\mathrm{gwy}}\\ w_{\mathrm{gwz}}\end{array}\right]---\left(3\right)$

In formula, ▽ W _x0, ▽ W _y0, ▽ W _z0be respectively gyro sensor corresponding its axially, normal direction, horizontal three-dimensional zero error; Diag[K _qx, K _qy, K _qz] be the three-dimensional scale coefficient error matrix of gyro sensor, $\left[\begin{array}{ccc}1& {-\mathrm{\&theta;}}_{\mathrm{yz}}& {-\mathrm{\&theta;}}_{\mathrm{zy}}\\ {\mathrm{\&theta;}}_{\mathrm{xz}}& 1& {-\mathrm{\&theta;}}_{\mathrm{zx}}\\ {-\mathrm{\&theta;}}_{\mathrm{xy}}& {-\mathrm{\&theta;}}_{\mathrm{yx}}& 1\end{array}\right]$ For three-dimensional alignment error.ε _bwx, ε _bwy, ε _bwzfor arbitrary constant, ε _rwx, ε _rwy, ε _rwzfor single order Markov noise, ε _gwx, ε _gwy, ε _gwzfor white noise.

Acceleration transducer output data f _b, by acceleration transducer error model shown in following formula (4), obtain the error output Δ f of acceleration transducer _b, the acceleration transducer error model is as shown in the formula shown in (4):

${\&dtri;f}_b=\left[\begin{array}{c}{\&dtri;\mathrm{<figure-callout\; id="0"\; label="f\; bx"\; filenames="HDA00003583760600012.png,HDA00003583760600021.png"\; state="\{\{state\}\}">f</figure-callout>}}_{\mathrm{bx}}\\ {\&dtri;f}_{\mathrm{by}0}\\ {\&dtri;\mathrm{<figure-callout\; id="0"\; label="f\; bz"\; filenames="HDA00003583760600012.png,HDA00003583760600021.png"\; state="\{\{state\}\}">f</figure-callout>}}_{\mathrm{bz}}\end{array}\right]+\mathrm{diag}[K_{\mathrm{px}},K_{\mathrm{py}},K_{\mathrm{pz}}]f_b+\left[\begin{array}{ccc}1& {-\mathrm{\&theta;}}_{\mathrm{yz}}& -{\mathrm{\&theta;}}_{\mathrm{zy}}\\ {\mathrm{\&theta;}}_{\mathrm{xz}}& 1& {-\mathrm{\&theta;}}_{\mathrm{zx}}\\ {-\mathrm{\&theta;}}_{\mathrm{xy}}& -{\mathrm{\&theta;}}_{\mathrm{yx}}& 1\end{array}\right]f_b+\left[\begin{array}{c}{\mathrm{\&epsiv;}}_{\mathrm{rax}}\\ {\mathrm{\&epsiv;}}_{\mathrm{ray}}\\ {\mathrm{\&epsiv;}}_{\mathrm{raz}}\end{array}\right]---\left(4\right)$

In formula, ▽ f _bx0, ▽ f _by0, ▽ f _bz0be respectively acceleration transducer corresponding its axially, normal direction, horizontal three-dimensional zero error; Diag[K _px, K _py, K _pz] be the three-dimensional scale coefficient error matrix of acceleration transducer, $\left[\begin{array}{ccc}1& {-\mathrm{\&theta;}}_{\mathrm{yz}}& {-\mathrm{\&theta;}}_{\mathrm{zy}}\\ {\mathrm{\&theta;}}_{\mathrm{xz}}& 1& {-\mathrm{\&theta;}}_{\mathrm{zx}}\\ {-\mathrm{\&theta;}}_{\mathrm{xy}}& {-\mathrm{\&theta;}}_{\mathrm{yx}}& 1\end{array}\right]$ For three-dimensional alignment error, ε _rax, ε _ray, ε _razfor single order Markov drift error.

Step 04. is carried out inertial navigation for inertial navigation sensors output data and is resolved acquisition the first inertial navigation data.

Inertial navigation sensors is exported to data and inertial navigation sensors model error data are superposeed, and carry out inertial navigation for stack result and resolve and obtain the second inertial navigation data.

Wherein, according to gyroscope output data W, acceleration transducer output data f _bcarry out inertial navigation and resolve acquisition the first inertial navigation data, inertial navigation resolves and comprises that attitude of flight vehicle solves, navigation speed solves and solve with position of aircraft, the first inertial navigation data comprises attitude of flight vehicle angle, navigation speed and position of aircraft, wherein, in the first inertial navigation data, the attitude of flight vehicle angle comprises aircraft roll angle θ ₁, aircraft angle of pitch γ ₁, aircraft course angle ψ ₁, because navigation coordinate system adopts east northeast navigation coordinate system, navigation speed comprises north orientation navigation speed V _n1, east orientation navigation speed V _e1, navigation speed V _d1, position of aircraft comprises aircraft longitude λ ₁, aircraft latitude L ₁, aircraft height h ₁.

By gyroscope output data W, the acceleration transducer output data f obtained _brespectively with the error output Δ W of gyro sensor, the error output Δ f of acceleration transducer _bsuperposeed, and carry out inertial navigation for stack result and resolve acquisition the second inertial navigation data, equally, inertial navigation resolves and comprises that attitude of flight vehicle solves, navigation speed solves and solve with position of aircraft, secondary navigation data comprises attitude of flight vehicle angle, navigation speed and position of aircraft, wherein, in the second inertial navigation data, the attitude of flight vehicle angle comprises aircraft roll angle θ ₂, aircraft angle of pitch γ ₂, aircraft course angle ψ ₂, because navigation coordinate system adopts east northeast navigation coordinate system, navigation speed comprises north orientation navigation speed V equally _n2, east orientation navigation speed V _e2, navigation speed V _d2, position of aircraft comprises aircraft longitude λ ₂, aircraft latitude L ₂, aircraft height h ₂.

In aforesaid operations, described inertial navigation resolves with reference to following process and algorithm and is resolved:

In the method design solved for attitude of flight vehicle, due to characteristics such as Quaternion Method have attitude work entirely, amount of calculation is little, error is little, therefore, in the present embodiment, for attitude, solve and use Quaternion Method to carry out solving of attitude angle.In conjunction with gyroscope output data W and flight benchmark flight path data initial value, according to the rotational motion of a rigid body with a fixed point theory, the form of the attitude quaternion differential equation is as shown in the formula shown in (6):

$\stackrel{.}{Q}\left(q\right)=\frac{1}{2}{M}^{*}\left({\mathrm{\&omega;}}_{\mathrm{nb}}^b\right)Q\left(q\right)---\left(6\right)$

In formula, $Q\left(q\right)=\left[\begin{array}{c}{q}_1\\ q_2\\ q_3\\ q_4\end{array}\right]$ For hypercomplex number, $M^{*}\left({\mathrm{\&omega;}}_{\mathrm{nb}}^b\right)=\left[\begin{array}{cccc}0& -{\mathrm{\&omega;}}_{\mathrm{nbx}}^b& -{\mathrm{\&omega;}}_{\mathrm{nby}}^b& -{\mathrm{\&omega;}}_{\mathrm{nbz}}^b\\ {\mathrm{\&omega;}}_{\mathrm{nbx}}^{\mathrm{<figure-callout\; id="0"\; label="b"\; filenames="HDA00003583760600012.png,HDA00003583760600021.png"\; state="\{\{state\}\}">b</figure-callout>}}& 0& {\mathrm{\&omega;}}_{\mathrm{nbz}}^b& {-\mathrm{\&omega;}}_{\mathrm{nby}}^b\\ {\mathrm{\&omega;}}_{\mathrm{nby}}^b& {-\mathrm{\&omega;}}_{\mathrm{nbz}}^{\mathrm{<figure-callout\; id="0"\; label="b"\; filenames="HDA00003583760600012.png,HDA00003583760600021.png"\; state="\{\{state\}\}">b</figure-callout>}}& 0& {\mathrm{\&omega;}}_{\mathrm{nbx}}^b\\ {\mathrm{\&omega;}}_{\mathrm{nbz}}^b& {\mathrm{\&omega;}}_{\mathrm{nby}}^b& -{\mathrm{\&omega;}}_{\mathrm{nbx}}^{\mathrm{<figure-callout\; id="0"\; label="b"\; filenames="HDA00003583760600012.png,HDA00003583760600021.png"\; state="\{\{state\}\}">b</figure-callout>}}& 0\end{array}\right]$ For the formula intermediate quantity, the angular speed that relatively rotates for aircraft coordinate system and navigation coordinate system

at each axial component of aircraft coordinate system, function for gyroscope output data W

by the attitude quaternion differential equation (6) discretize, obtain the equation analytic solution, and hypercomplex number is carried out to standardization, obtain hypercomplex number q _i(i=0,1,2,3), can obtain the attitude matrix between aircraft coordinate system and navigation coordinate system according to the relation of hypercomplex number and attitude matrix

, shown in (7):

$C_n^b=\left[\begin{array}{ccc}{{\mathrm{<figure-callout\; id="0"\; label="q"\; filenames="HDA00003583760600012.png,HDA00003583760600021.png"\; state="\{\{state\}\}">q</figure-callout>}}_0}^2+{{\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="HDA00003583760600012.png,HDA00003583760600021.png"\; state="\{\{state\}\}">q</figure-callout>}}_1}^2-{{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="HDA00003583760600012.png,HDA00003583760600021.png"\; state="\{\{state\}\}">q</figure-callout>}}_2}^2-{q_3}^2& 2(q_1{q}_2-q_0{q}_3)& 2(q_1{q}_3+q_0{q}_2)\\ 2(q_1{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="HDA00003583760600012.png,HDA00003583760600021.png"\; state="\{\{state\}\}">q</figure-callout>}}_2+q_0{q}_3)& {{\mathrm{<figure-callout\; id="0"\; label="q"\; filenames="HDA00003583760600012.png,HDA00003583760600021.png"\; state="\{\{state\}\}">q</figure-callout>}}_0}^2+{{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="HDA00003583760600012.png,HDA00003583760600021.png"\; state="\{\{state\}\}">q</figure-callout>}}_2}^2-{{\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="HDA00003583760600012.png,HDA00003583760600021.png"\; state="\{\{state\}\}">q</figure-callout>}}_1}^2-{q_3}^2& 2(q_2{q}_3+q_0{q}_1)\\ 2(q_1{q}_3-q_0{q}_2)& 2(q_2{q}_3-q_0{q}_1)& {{\mathrm{<figure-callout\; id="0"\; label="q"\; filenames="HDA00003583760600012.png,HDA00003583760600021.png"\; state="\{\{state\}\}">q</figure-callout>}}_0}^2+{q_3}^2-{{\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="HDA00003583760600012.png,HDA00003583760600021.png"\; state="\{\{state\}\}">q</figure-callout>}}_1}^2-{{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="HDA00003583760600012.png,HDA00003583760600021.png"\; state="\{\{state\}\}">q</figure-callout>}}_2}^2\end{array}\right]---\left(7\right)$

$={\left(C_{\mathrm{ij}}\right)}_{3\&times;3}$

Notice again

the orthogonality of matrix, just can obtain solving attitude angle

matrix, in simulation process, because navigation coordinate system adopts under east northeast navigation coordinate system, so the Eulerian angle definition of the attitude matrix under east northeast navigation coordinate system is as shown in the formula shown in (8)

$C_n^b=\left[\begin{array}{ccc}\cos {\mathrm{\&psi;}}^{\&prime;}\cos {\mathrm{\&theta;}}^{\&prime;}& \sin {\mathrm{\&psi;}}^{\&prime;}\cos {\mathrm{\&theta;}}^{\&prime;}& -\sin {\mathrm{\&theta;}}^{\&prime;}\\ \cos {\mathrm{\&psi;}}^{\&prime;}\sin {\mathrm{\&theta;}}^{\&prime;}\sin {\mathrm{\&gamma;}}^{\&prime;}-\sin {\mathrm{\&psi;}}^{\&prime;}\cos \mathrm{\&gamma;}& \sin {\mathrm{\&psi;}}^{\&prime;}\sin {\mathrm{\&theta;}}^{\&prime;}\sin {\mathrm{\&gamma;}}^{\&prime;}+\cos {\mathrm{\&psi;}}^{\&prime;}\cos {\mathrm{\&gamma;}}^{\&prime;}& \cos {\mathrm{\&theta;}}^{\&prime;}\sin {\mathrm{\&gamma;}}^{\&prime;}\\ \cos {\mathrm{\&psi;}}^{\&prime;}\sin {\mathrm{\&theta;}}^{\&prime;}\cos {\mathrm{\&gamma;}}^{\&prime;}+\sin {\mathrm{\&psi;}}^{\&prime;}\sin \mathrm{\&gamma;}& \sin {\mathrm{\&psi;}}^{\&prime;}\sin {\mathrm{\&theta;}}^{\&prime;}\cos {\mathrm{\&gamma;}}^{\&prime;}-\cos {\mathrm{\&psi;}}^{\&prime;}\sin {\mathrm{\&gamma;}}^{\&prime;}& \cos {\mathrm{\&theta;}}^{\&prime;}\cos {\mathrm{\&gamma;}}^{\&prime;}\end{array}\right]---\left(8\right)$

Wherein: θ ' is the aircraft roll angle, and γ ' is the aircraft angle of pitch, and ψ ' is the aircraft course angle.According to above formula, when obtained reciprocity attitude matrix by hypercomplex number after, by the corresponding relation of attitude matrix and attitude angle, can obtain three attitude angle aircraft roll angles, the aircraft angle of pitch, the aircraft course angle of aircraft.Use T _ijmean element (i, j=1,2,3) can obtain attitude angle as shown in the formula shown in (9):

$\left.\begin{array}{c}{\mathrm{\&psi;}}^{\text{'}}=\arctan \frac{T_{12}}{T_{11}}\\ {\mathrm{\&theta;}}^{\text{'}}=-\arcsin T_{13}\\ {\mathrm{\&gamma;}}^{\text{'}}=\arctan \frac{T_{23}}{T_{33}}\end{array}\right\}---\left(9\right)$

Wherein: the field of definition of course angle ψ ' is 0 °～360 °, and the field of definition of roll angle θ ' is-180 °～180 °, and the field of definition of angle of pitch γ ' is :-90 °～90 °.Except the angle of pitch, all there are the decision problem of quadrant in course angle and roll angle.

In the method design solved for navigation speed, because acceleration transducer is fixedly connected on aircraft, therefore, the output of acceleration transducer is the specific force output under the aircraft coordinate system, therefore needs with the attitude transition matrix the output specific force f under original aircraft coordinate system _bbe converted to the specific force f under navigation coordinate system _n, can obtain the speed differential equation of aircraft in east northeast navigation coordinate system as shown in the formula shown in (10):

$\left.\begin{array}{c}{\stackrel{\&CenterDot;}{V}}_n^{\&prime;}=f_n^n-(\frac{V_e^{\&prime;}}{(R_e+h^{\&prime;})\cos L^{\&prime;}}+2{\mathrm{\&omega;}}_{\mathrm{ie}})\sin L^{\&prime;}{V}_e^{\&prime;}+\frac{V_n^{\&prime;}}{(R_n+h^{\&prime;})}{V}_d^{\&prime;}\\ {\stackrel{\&CenterDot;}{V}}_e^{\&prime;}=f_e^n+(\frac{V_e^{\&prime;}}{(R_e+h^{\&prime;})\cos L^{\&prime;}}+2{\mathrm{\&omega;}}_{\mathrm{ie}})(\sin L^{\&prime;}{V}_n^{\&prime;}+\cos L{V}_d^{\&prime;})\\ {\stackrel{\&CenterDot;}{V}}_d=f_d^n-\frac{V_n^{\&prime;}}{(R_n+h)}{V}_n^{\&prime;}-(\frac{V_e^{\&prime;}}{(R_e+h)\cos L}+2{\mathrm{\&omega;}}_{\mathrm{ie}})\cos L{V}_e^{\&prime;}+G\end{array}\right\}---\left(10\right)$

By formula (10) can obtain the real-time speed of aircraft in navigation coordinate system (V ' _n, V ' _e, V ' _d).In formula, be respectively specific force f _neach component under navigation coordinate system on each coordinate axis, L' is the aircraft latitude, and λ ' is the aircraft longitude, and h' is the aircraft height, R _nfor the radius-of-curvature in earth meridian ellipse, R _mfor the radius-of-curvature in the plane normal perpendicular to meridian ellipse.The speed differential equation is the three-dimensional differential equation of single order, along with specific force f _nvariation, speed can constantly change.The acceleration of gravity computing formula is:

G=G ₀/ (1+L/R _e ²), G wherein ₀=9.78048878+0.051721512L-5.751576 * 10 ^-5* sin ²(2L), the m/s of unit ², R _efor the radius of earth equatorial plane, ω _iefor the earth rotation angular speed.

In the method design solved for position of aircraft, because aircraft moves at the earth's surface;on the face of the globe, therefore must consider the impact of earth curvature during Position-Solving, using longitude and latitude and height as the physical quantity of locating, can be tried to achieve the real time position (L', λ ', h') of aircraft by the following differential equation (11):

$\left.\begin{array}{c}{\stackrel{\&CenterDot;}{L}}^{\&prime;}=\frac{{V^{\&prime;}}_n}{(R_n+h^{\&prime;})}\\ {\stackrel{\&CenterDot;}{\mathrm{\&lambda;}}}^{\&prime;}=\frac{V_e^{\&prime;}}{(R_m+h^{\&prime;})\cos L}\\ {\stackrel{\&CenterDot;}{h}}^{\&prime;}=-V_d^{\&prime;}\end{array}\right\}---\left(11\right)$

R in formula _nfor the radius-of-curvature in earth meridian ellipse, R _mfor the radius-of-curvature in the plane normal perpendicular to meridian ellipse, V _n' be the north orientation navigation speed of aircraft, V _e' be the east orientation navigation speed of aircraft, V _d' be the ground navigation speed of aircraft.

Step 05. contrasts the first inertial navigation data to ask poor with flight benchmark flight path data, obtain the dynamic calculation error, comprise attitude of flight vehicle error, navigation speed error and position of aircraft error, wherein, the attitude of flight vehicle error comprises aircraft roll angle error ▽ θ, aircraft angle of pitch error ▽ γ, aircraft course angle error ▽ ψ, because navigation coordinate system adopts east northeast navigation coordinate system, the navigation speed error comprises north orientation navigation speed error ▽ V equally _n, east orientation navigation speed error ▽ V _e, navigation velocity error ▽ V _d, the position of aircraft error comprises aircraft longitude error ▽ λ, aircraft latitude error ▽ L, aircraft height error ▽ h.

Step 06., for the second inertial navigation data, is removed the dynamic calculation error, obtains the inertial navigation result, and detailed process is as follows:

For the second inertial navigation data, with reference to following formula (12), obtain the inertial navigation result, aircraft roll angle θ, aircraft angle of pitch γ, aircraft course angle ψ, equally because navigation coordinate system adopts east northeast navigation coordinate system, the north orientation navigation speed V of aircraft _n, aircraft east orientation navigation speed V _e, aircraft ground navigation speed V _d, aircraft longitude λ, aircraft latitude L, aircraft height h.

$\left\{\begin{array}{c}\mathrm{\&theta;}={\mathrm{\&theta;}}_2-\&dtri;\mathrm{\&theta;}\\ \mathrm{\&gamma;}={\mathrm{\&gamma;}}_2-\&dtri;\mathrm{\&gamma;}\\ \mathrm{\&psi;}={\mathrm{\&psi;}}_2-\&dtri;\mathrm{\&psi;}\end{array}\right.\left\{\begin{array}{c}{V}_n=V_{n2}-\&dtri;V_n\\ V_e=V_{e2}-\&dtri;V_e\\ V_d=V_{d2}-\&dtri;V_d\end{array}\right.\left\{\begin{array}{c}L=L_2-\&dtri;L\\ \mathrm{\&lambda;}={\mathrm{\&lambda;}}_2-\&dtri;\mathrm{\&lambda;}\\ h=h_2-\&dtri;h\end{array}\right.---\left(12\right)$

Obtain final inertial navigation result by above formula, by final inertial navigation result with do not use traditional strap inertial navigation algorithm emulation of the present invention to be contrasted, wherein the position part as shown in Figure 3.

In order to verify the performance of aircraft inertial navigation system parameters simulation method proposed by the invention, respectively traditional strapdown inertial navigation system and the system simulation method of the present invention that does not adopt the inventive method contrasted, the flight benchmark flight path data that obtain based on Fig. 2, two kinds of situation upper/lower positions graph of errors are respectively as shown in Fig. 3～Fig. 5.In addition for after verifying that the inventive method is eliminated the dynamic calculation error, validity for analytic inertial navigation sensor error characteristic on the impact of inertial navigation system dynamic property, adopt same flight benchmark flight path data to carry out emulation, add 3 groups of different inertial navigation sensors error models, wherein first group of inertial navigation sensors error be set to Gyro Random constant, gyro white noise error, gyro single order Markov drift error be 0.01 degree/hour; Accelerometer single order Markov biased error is 0.0001 * G meter per second 2, as shown in Figure 6; Second group of parameters is set to first group 5 times, as shown in Figure 7; The 3rd group of parameters is set to first group 1/5 times, as shown in Figure 8, utilizes above three grouping error models to carry out the simulating, verifying analysis, wherein adds the site error curve comparison figure of different inertial navigation sensors error models respectively as shown in Figure 6 to 8.

Simulation result by Fig. 3 a can find out, compensation and uncompensated inertial navigation emulation longitude curve and flight path benchmark longitude curvilinear trend are basically identical, so strap-down inertial dynamic simulation algorithm is reasonable.

Simulation result by Fig. 3 b, 3c can be found out, due to space vehicle dynamic flight path and inertial navigation, to resolve the different strap-down Inertial Navigation Simulation algorithm longitude errors of calculation that cause of principle excessive, the present invention can effectively realize the separation to longitude dynamic calculation error in inertial navigation system dynamic simulation process, longitude dynamic calculation error in the elimination simulation process is for the impact of inertial navigation simulation accuracy, and the dynamic calculation error of longitude in inertial navigation system simulation data end correction-compensation navigation simulation process, improved the longitude calculation accuracy of inertial navigation system.

Fig. 4 is identical with Fig. 3 conclusion with Fig. 5 conclusion, as shown in Fig. 4 a, Fig. 4 b, Fig. 4 c, Fig. 5 a, Fig. 5 b and Fig. 5 c, can find out that the present invention can effectively realize the separation to dynamic calculation error in inertial navigation system dynamic simulation process, dynamic calculation error in the elimination simulation process is for the impact of inertial navigation simulation accuracy, improve the navigation performance of inertial navigation system, there is good engineering using value.

By Fig. 6, Fig. 7 and Fig. 8 simulation result, can find out, the present invention can reflect that the error model magnitude that error model adds impact the fundamental sum of inertial navigation simulation result output is the consistance rule of conversion, effectively realize the dynamic simulation effect of inertial navigation sensors error characteristics to the inertial navigation system performance impact, can be actual inertial navigation sensors type selecting and index and select to provide support, be applicable to the engineering application.

To sum up, the aircraft inertial navigation system parameters simulation method of the present invention's design, on traditional inertial navigation algorithm basis, in resolving ultimate principle without prejudice to inertial navigation and not affecting simulation process under the prerequisite of inertial navigation sensors error Propagation Property, propose navigational parameter dynamic calculation error and separated compensation method, effective separation and elimination to the error of calculation in inertial navigation system dynamic simulation process have been realized, thereby for improving the inertial navigation system precision, for the type selecting of inertial navigation sensors has proposed foundation, will there is outstanding using value.

The above is explained in detail embodiments of the present invention by reference to the accompanying drawings, but the present invention is not limited to above-mentioned embodiment, in the ken possessed those of ordinary skills, can also under the prerequisite that does not break away from aim of the present invention, make a variety of changes.

Claims (9)

1. an aircraft inertial navigation system parameters simulation method, is characterized in that, comprises following method:

Step 01. is obtained flight benchmark flight path data;

Step 02., according to flight benchmark flight path data, is obtained inertial navigation sensors output data by the inertial navigation sensors output model;

Step 03., according to inertial navigation sensors output data, is obtained inertial navigation sensors model error data by the inertial navigation sensors error model;

Step 04. is carried out inertial navigation for inertial navigation sensors output data and is resolved acquisition the first inertial navigation data;

Inertial navigation sensors is exported to data and inertial navigation sensors model error data are superposeed, and carry out inertial navigation for stack result and resolve and obtain the second inertial navigation data;

Step 05. contrasts the first inertial navigation data to ask poor with flight benchmark flight path data, obtains the dynamic calculation error;

Step 06., for the second inertial navigation data, is removed the dynamic calculation error, obtains the inertial navigation result.

2. a kind of aircraft inertial navigation system parameters simulation method according to claim 1, it is characterized in that: described step 01 comprises the steps:

Step 011. adopts the vehicle dynamics model to obtain space vehicle dynamic flight path data;

Step 012. is carried out the data pre-service for space vehicle dynamic flight path data, obtains flight benchmark flight path data.

3. a kind of aircraft inertial navigation system parameters simulation method according to claim 2, it is characterized in that: in described step 012, the data pre-service comprises that markers converts, physical quantity is changed and, by the navigational parameter threshold value is set, data is carried out to validity check and reparation.

4. a kind of aircraft inertial navigation system parameters simulation method according to claim 1, it is characterized in that: in described step 02, the inertial navigation sensors output model comprises gyro sensor output model and acceleration transducer output model; The inertial navigation sensors error model comprises gyro sensor error model and acceleration transducer error model.

5. a kind of aircraft inertial navigation system parameters simulation method according to claim 4, it is characterized in that: described gyro sensor output model is as shown in the formula shown in (1):

$W=\left[\begin{array}{ccc}\cos {\mathrm{\&gamma;}}_0& 0& \sin {\mathrm{\&gamma;}}_0\cos {\mathrm{\&theta;}}_0\\ 0& 1& -{\sin \mathrm{\&theta;}}_0\\ {\sin \mathrm{\&gamma;}}_0& 0& -{\cos \mathrm{\&gamma;}}_0\cos {\mathrm{\&theta;}}_0\end{array}\right]\left[\begin{array}{c}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_0\\ {\stackrel{\&CenterDot;}{\mathrm{\&gamma;}}}_0\\ {\stackrel{\&CenterDot;}{\mathrm{\&psi;}}}_0\end{array}\right]+C_n^b\&times;(\left[\begin{array}{c}0\\ {\mathrm{\&omega;}}_{\mathrm{ie}}\cos L_0\\ {\mathrm{\&omega;}}_{\mathrm{ie}}\sin L_0\end{array}\right]+\left[\begin{array}{c}-\frac{V_{\mathrm{eny}}^n}{(R_e+h_0)}\\ \frac{V_{\mathrm{enx}}^n}{(R_e+h_0)}\\ \frac{V_{\mathrm{enx}}^n}{(R_e+h_0)}\tan L_0\end{array}\right])---\left(1\right)$

In formula, W is gyroscope output data, θ ₀roll angle, γ for aircraft in flight benchmark flight path data ₀the angle of pitch, ψ for aircraft in flight benchmark flight path data ₀for the course angle of aircraft in flight benchmark flight path data, L ₀for the latitude of aircraft in flight benchmark flight path data, h ₀for the height of aircraft in flight benchmark flight path data,

be respectively aircraft speed component on x axle and y axle in navigation coordinate system,

for the attitude matrix between navigation coordinate system and aircraft coordinate system, n means navigation coordinate system, and b means the aircraft coordinate system, and the expression of adding some points on above letter is carried out differentiate to this letter.

6. a kind of aircraft inertial navigation system parameters simulation method according to claim 4, it is characterized in that: described acceleration transducer output model is as shown in the formula shown in (2):

$\left\{\begin{array}{c}{f}_n=\stackrel{\&CenterDot;}{V}+({2\mathrm{\&omega;}}_{\mathrm{ie}}^n+{\mathrm{\&omega;}}_{\mathrm{en}}^n)\&times;V-G\\ f_b=C_n^b{f}_n\end{array}\right.---\left(2\right)$

In formula, f _bfor acceleration transducer output data, f _nfor the specific force under navigation coordinate system, for the attitude matrix between navigation coordinate system and aircraft coordinate system, ω _iefor earth rotation angular speed, ω _enfor the angular speed of the relative earth of aircraft, the vector that the projection on V be aircraft speed in navigation coordinate system three coordinate axis forms, and add some points on above letter and mean this letter is carried out to differentiate.

7. a kind of aircraft inertial navigation system parameters simulation method according to claim 4, it is characterized in that: described gyro sensor error model is as shown in the formula shown in (3):

$\mathrm{\&Delta;W}=\left[\begin{array}{c}{\&dtri;W}_{x0}\\ {\&dtri;W}_{y0}\\ {\&dtri;W}_{z0}\end{array}\right]+\mathrm{diag}[K_{\mathrm{qx}},K_{\mathrm{qy}},K_{\mathrm{qz}}]W+\left[\begin{array}{ccc}1& -{\mathrm{\&theta;}}_{\mathrm{yz}}& -{\mathrm{\&theta;}}_{\mathrm{zy}}\\ {\mathrm{\&theta;}}_{\mathrm{xz}}& 1& -{\mathrm{\&theta;}}_{\mathrm{zx}}\\ -{\mathrm{\&theta;}}_{\mathrm{xy}}& -{\mathrm{\&theta;}}_{\mathrm{yx}}& 1\end{array}\right]W+\left[\begin{array}{c}{\mathrm{\&epsiv;}}_{\mathrm{bwx}}\\ {\mathrm{\&epsiv;}}_{\mathrm{bwy}}\\ {\mathrm{\&epsiv;}}_{\mathrm{bwz}}\end{array}\right]+\left[\begin{array}{c}{\mathrm{\&epsiv;}}_{\mathrm{rwx}}\\ {\mathrm{\&epsiv;}}_{\mathrm{rwy}}\\ {\mathrm{\&epsiv;}}_{\mathrm{rwz}}\end{array}\right]+\left[\begin{array}{c}{w}_{\mathrm{gwx}}\\ w_{\mathrm{gwy}}\\ w_{\mathrm{gwz}}\end{array}\right]---\left(3\right)$

In formula, the error output that Δ W is gyro sensor,

be respectively gyro sensor corresponding its axially, normal direction, horizontal three-dimensional zero error; Diag[K _qx, K _qy, K _qz] be the three-dimensional scale coefficient error matrix of gyro sensor, $\left[\begin{array}{ccc}1& {-\mathrm{\&theta;}}_{\mathrm{yz}}& {-\mathrm{\&theta;}}_{\mathrm{zy}}\\ {\mathrm{\&theta;}}_{\mathrm{xz}}& 1& {-\mathrm{\&theta;}}_{\mathrm{zx}}\\ {-\mathrm{\&theta;}}_{\mathrm{xy}}& {-\mathrm{\&theta;}}_{\mathrm{yx}}& 1\end{array}\right]$ For three-dimensional alignment error.ε _bwx, ε _bwy, ε _bwzfor arbitrary constant, ε _rwx, ε _rwy, ε _rwzfor single order Markov noise, ε _gwx, ε _gwy, ε _gwzfor white noise, W is gyroscope output data.

8. a kind of aircraft inertial navigation system parameters simulation method according to claim 4, it is characterized in that: described acceleration transducer error model is as shown in the formula shown in (4):

${\mathrm{\&Delta;f}}_b=\left[\begin{array}{c}{\&dtri;f}_{\mathrm{bx}0}\\ {\&dtri;f}_{\mathrm{by}0}\\ {\&dtri;f}_{\mathrm{bz}0}\end{array}\right]+\mathrm{diag}[K_{\mathrm{px}},K_{\mathrm{py}},K_{\mathrm{pz}}]f_b+\left[\begin{array}{ccc}1& {-\mathrm{\&theta;}}_{\mathrm{yz}}& {-\mathrm{\&theta;}}_{\mathrm{zy}}\\ {\mathrm{\&theta;}}_{\mathrm{xz}}& 1& {-\mathrm{\&theta;}}_{\mathrm{zx}}\\ {-\mathrm{\&theta;}}_{\mathrm{xy}}& {-\mathrm{\&theta;}}_{\mathrm{yx}}& 1\end{array}\right]f_b+\left[\begin{array}{c}{\mathrm{\&epsiv;}}_{\mathrm{rax}}\\ {\mathrm{\&epsiv;}}_{\mathrm{ray}}\\ {\mathrm{\&epsiv;}}_{\mathrm{raz}}\end{array}\right]---\left(4\right)$

In formula, Δ f _bfor the error output of acceleration transducer,

be respectively acceleration transducer corresponding its axially, normal direction, horizontal three-dimensional zero error; Diag[K _px, K _py, K _pz] be the three-dimensional scale coefficient error matrix of acceleration transducer, $\left[\begin{array}{ccc}1& {-\mathrm{\&theta;}}_{\mathrm{yz}}& {-\mathrm{\&theta;}}_{\mathrm{zy}}\\ {\mathrm{\&theta;}}_{\mathrm{xz}}& 1& {-\mathrm{\&theta;}}_{\mathrm{zx}}\\ {-\mathrm{\&theta;}}_{\mathrm{xy}}& {-\mathrm{\&theta;}}_{\mathrm{yx}}& 1\end{array}\right]$ For three-dimensional alignment error, ε _rax, ε _ray, ε _razfor single order Markov drift error, f _bfor acceleration transducer output data.

9. a kind of aircraft inertial navigation system parameters simulation method according to claim 1, it is characterized in that: described dynamic calculation error comprises site error, velocity error and attitude error.

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