CN104296781A - Real-time one-dimensional positioning method for inertia measurement system based on rocket sledge orbital coordinate system - Google Patents

Abstract

The invention discloses a real-time one-dimensional positioning method for an inertia measurement system based on a rocket sledge orbital coordinate system. Based on the rocket sledge orbital coordinate system, the speed and positional information of the inertia measurement system can be calculated in real time at every moment. According to the invention, navigation calculating is carried out through the method, so that the navigation distance value in the actual moving direction can be directly obtained; through error compensation, the X-axis speed and the Z-axis speed of the rail coordinate system and the positional navigation error can be reduced, so that the navigation accuracy can be improved.

Description

Based on the real-time one-dimensional positioning method of inertial measurement system of rocket sledge orbital coordinate system

Technical field

The present invention relates to the real-time one-dimensional positioning method of a kind of inertial measurement system based on rocket sledge orbital coordinate system, can be used in the inertial navigation of Rocket sled test.

Background technology

Rocket sled test has the ability producing the integrated conditions such as large overload, high speed, strong vibration and impact, can simulated missile Live Flying environment the most realistically.By testing the property indices and precision that can examine inertial measurement system under integrated environment condition, the correctness of checking inertial measuring system error model under high dynamic condition, particularly under large overload situations, high-order term amplification, can determine that inertial measurement system higher order error item is on the impact of navigation performance, be the optimal path realizing the checking of inertial measurement system dynamic property.

In inertial measurement system Rocket sled test, the main navigation computing method adopted based on geographic coordinate system at present.General navigation results comprises the attitude information of inertial measurement system (with attitude transfer matrix represent), velocity information (east orientation speed v _e, north orientation speed v _nwith sky to speed v _u) and positional information (latitude h), its navigation calculation formula is for longitude λ and height

$\left[\begin{array}{c}{\stackrel{\·}{r}}^L\\ {\stackrel{\·}{V}}^L\\ {\stackrel{\·}{R}}_b^L\end{array}\right]=\left[\begin{array}{c}{D}^{-1}{V}^L\\ R_b^L{\stackrel{\→}{f}}^b-(2{\mathrm{\Ω}}_{\mathrm{ie}}^L+{\mathrm{\Ω}}_{\mathrm{eL}}^L)V^L+{\stackrel{\→}{g}}^L\\ R_b^L({\mathrm{\Ω}}_{\mathrm{ib}}^b-{\mathrm{\Ω}}_{\mathrm{ie}}^b-{\mathrm{\Ω}}_{\mathrm{eL}}^b)\end{array}\right]$

Wherein, v ^l=(v _e, v _n, v _u).

For Rocket sled test, when calculating rocket sledge skid body running orbit, needing east orientation speed and north orientation velocity composite is orbital velocity, namely

$v=\sqrt{v_e^2+v_n^2+v_u^2}$

When asking for skid body range ability, have

$S={\∫}_0^{t}v\left(t\right)\mathrm{dt}={\∫}_0^t\sqrt{v_e^2+v_n^2}\mathrm{dt}$

As can be seen from above computation process, when inertial measurement system Rocket sled test, there is following shortcoming in the navigation computing method based on geographic coordinate system:

(1) because sky is to speed v _udisperse, so when calculating inertial measurement system speed, adopt following short-cut method

$v=\sqrt{v_e^2+v_n^2}$

The track that this method is parallel with earth level surface after being applicable to considering radius-of-curvature, but height error is there is concerning rectilinear orbit.

(2) because velocity calculated exists error, site error can be caused.In addition, owing to being scalar operation, without directional information, solve the position that obtains and velocity information is all one-dimension information, lack three-dimensional site error, velocity error and attitude error information.

In addition, be only use orbital coordinate system to carry out navigation calculating, because there is error, the speed of orbital coordinate system Y, Z axis and position navigation value can be caused and non-vanishing, and this do not conform to the actual conditions.Therefore, need to study a kind of inertial measurement system navigation calculation method being suitable for Rocket sled test newly.

Summary of the invention

Technology of the present invention is dealt with problems: overcome the deficiencies in the prior art, the real-time one-dimensional positioning method of inertial measurement system based on rocket sledge orbital coordinate system is provided, attitude when accurately can resolve inertial measurement system orbiting, position and velocity information, for the accuracy assessment and the assessment of inertial navigation impact accuracy finally carrying out inertial measurement system provides accurate navigation results.

Technical solution of the present invention: based on the real-time one-dimensional positioning method of inertial measurement system of rocket sledge orbital coordinate system, step is as follows:

(1) inertial measurement system is mounted on rocket sledge, with rocket sledge track starting point for initial point sets up rocket sledge orbital coordinate system OX _ly _lz _l, wherein OX _laxle points to rocket sledge skid body direction of motion, OZ _laxle upward perpendicular to track, OY _laxle in surface level perpendicular to track, and OX _laxle, OY _laxle and OZ _laxle meets right-handed coordinate system;

(2) inertial measurement system carries out autoregistration or Transfer Alignment, obtains t ₀moment, inertial measurement system was at OX _laxle, OY _laxle and OZ _lattitude angle on axle, and calculate t according to the attitude angle obtained ₀moment rocket sledge orbit coordinate is tied to the posture changing matrix of strapdown body coordinate system; Wherein strapdown body coordinate system initial point is the center of inertial measurement system, and x, y, z axle defines according to inertial measurement system prescribed direction;

(3) after rocket sledge ignition trigger, at the t of rocket sledge motion _n+1moment, the acceleration recorded according to inertial measurement system and angular velocity, and t _nmoment, inertial measurement system was at OY _laxle and OZ _lthe speed of axle and positional information, calculate following parameter:

A () inertial measurement system is at OX _laxle, OY _laxle and OZ _lattitude error value on axle;

B () inertial measurement system is at OY _laxle and OZ _lspeed error value on axle;

C () inertial measurement system is at OY _laxle and OZ _lsite error value on axle;

D () inertial measurement system is at OX _lone dimension acceleration error value on direction of principal axis;

(4) according to the t that step (3) obtains _n+1moment, inertial measurement system was at OX _laxle, OY _laxle and OZ _lattitude error value on axle, obtains t _n+1moment, inertial measurement system was at OX _laxle, OY _laxle and OZ _lattitude angle on direction of principal axis;

(5) t is utilized _n+1moment, inertial measurement system was at OX _laxle, OY _laxle and OZ _lattitude angle on direction of principal axis calculates t _n+1moment rocket sledge orbit coordinate is tied to the posture changing matrix of strapdown body coordinate system;

(6) component of acceleration of gravity under rocket sledge orbital coordinate system is utilized, and t _n+1moment rocket sledge orbit coordinate is tied to the posture changing matrix of strapdown body coordinate system, the acceleration of inertial measurement system, inertial measurement system at OX _lone dimension acceleration error value on direction of principal axis, inertial measurement system are at OY _laxle and OZ _lspeed error value on axle and site error value, carry out navigation calculation and obtain t _n+1moment, inertial measurement system was at OX _laxle, OY _laxle and OZ _lspeed on axle and positional information, thus the real-time one dimension location realizing inertial measurement system;

Wherein n=0,1,2 ... N, N are natural number.

The implementation of described step (2) is:

(2.1) when inertial measurement system carries out autoregistration, following formula is utilized to obtain t ₀moment, inertial measurement system was at OX _laxle, OY _laxle and OZ _lattitude angle φ on axle _x, φ _y, φ _z:

Wherein, a _x, a _y, a _zbe respectively t ₀time be engraved in the accekeration that on strapdown body coordinate system three axles, inertial measurement system measurement obtains, ω _x, ω _y, ω _zfor t ₀time be engraved in the magnitude of angular velocity that on strapdown body coordinate system three axles, inertial measurement system measurement obtains, ω _iefor earth rate, for test site latitude;

When carrying out Transfer Alignment, t ₀moment, inertial measurement system was at OX _laxle, OY _laxle and OZ _lattitude angle φ on axle _x, φ _yand φ _zprovided by external system;

(2.2) following formulae discovery t is utilized according to the attitude angle obtained ₀moment rocket sledge orbit coordinate is tied to the posture changing matrix of strapdown body coordinate system

$R_l^b=\left[\begin{array}{ccc}\cos {\mathrm{\φ}}_y& 0& -\sin {\mathrm{\φ}}_y\\ 0& 1& 0\\ \sin {\mathrm{\φ}}_y& 0& \cos {\mathrm{\φ}}_y\end{array}\right]\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos {\mathrm{\φ}}_x& \sin {\mathrm{\φ}}_x\\ 0& -\sin {\mathrm{\φ}}_x& \cos {\mathrm{\φ}}_x\end{array}\right]\left[\begin{array}{ccc}\cos {\mathrm{\φ}}_z& \sin {\mathrm{\φ}}_z& 0\\ -\sin {\mathrm{\φ}}_z& \cos {\mathrm{\φ}}_z& 0\\ 0& 0& 1\end{array}\right].$

The implementation of described step (3) is:

(3.1) at the t of rocket sledge motion _n+1in the moment, utilize following formulae discovery inertial measurement system at OX _laxle, OY _laxle and OZ _lattitude error value on axle, at OY _laxle and OZ _lspeed error value on axle, at OY _laxle and OZ _lsite error value on axle:

(1)X(t _n|t _n+1)＝Φ(t _n)X(t _n)

(2)P(t _n|t _n+1)＝Φ(t _n)P(t _n)Φ(t _n) ^T+Q·ΔT

(3)Κ(t _n)＝P(t _n|t _n+1)H ^T[HP(t _n|t _n+1)H ^T+R] ^-1

(4)X(t _n+1)＝X(t _n|t _n+1)+K(t _n)[Y(t _n)-HX(t _n)]

(5)P(t _n+1)＝[I ₇-K(t _n)H]P(t _n|t _n+1)[I ₇-K(t _n)H] ^T+K(t _n)RK(t _n) ^T

Wherein, $X\left(t_n\right)=\left[\begin{array}{c}\mathrm{\δ}{\mathrm{\φ}}_x\left(t_n\right)\\ \mathrm{\δ}{\mathrm{\φ}}_y\left(t_n\right)\\ \mathrm{\δ}{\mathrm{\φ}}_z\left(t_n\right)\\ \mathrm{\δ}{v}_y\left(t_n\right)\\ \mathrm{\δ}{v}_z\left(t_n\right)\\ \mathrm{\δ}{r}_y\left(t_n\right)\\ \mathrm{\δ}{r}_z\left(t_n\right)\end{array}\right]$ For t _nthe vector of moment each error coefficient composition, δ φ _x, δ φ _y, δ φ _zfor inertial measurement system is at OX _laxle, OY _laxle and OZ _lattitude error on axle, δ v _y, δ v _zfor inertial measurement system is at OY _laxle and OZ _lvelocity error on axle, δ r _y, δ r _zfor inertial measurement system is at OY _laxle and OZ _lsite error value on axle, at t ₀moment, X (t ₀)=[0 00000 0] ^t;

$X\left(t_n\right|t_{n+1})=\left[\begin{array}{c}\mathrm{\δ}{\mathrm{\φ}}_x\left(t_n\right|t_{n+1})\\ \mathrm{\δ}{\mathrm{\φ}}_y\left(t_n\right|t_{n+1})\\ \mathrm{\δ}{\mathrm{\φ}}_z\left(t_n\right|t_{n+1})\\ \mathrm{\δ}{v}_y\left(t_n\right|t_{n+1})\\ \mathrm{\δ}{v}_z\left(t_n\right|t_{n+1})\\ \mathrm{\δ}{r}_y\left(t_n\right|t_{n+1})\\ \mathrm{\δ}{r}_z\left(t_n\right|t_{n+1})\end{array}\right],$ For t _nmoment is to t _n+1the vector of moment each error coefficient one-step prediction value composition; $\mathrm{\Φ}\left(t_n\right)=I_7+\left[\begin{array}{ccccccc}0& A_{12}& A_{13}& 0& 0& 0& 0\\ A_{21}& A_{22}& A_{23}& 0& 0& 0& 0\\ A_{31}& A_{32}& A_{33}& 0& 0& 0& 0\\ A_{41}& A_{42}& A_{43}& 0& 2{\mathrm{\ω}}_{\mathrm{ie},x}^l& 0& 0\\ A_{51}& A_{52}& 0& -2{\mathrm{\ω}}_{\mathrm{ie},x}^l& 0& 0& 0\\ 0& 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 1& 0& 0\end{array}\right]\·\mathrm{\ΔT},$ For state transfer matrix, and

A ₁₂＝-ω _x(t _n)sinφ _y(t _n)+ω _z(t _n)cosφ _y(t _n)

$A_{13}={\mathrm{\ω}}_{\mathrm{ie},x}^l\sin {\mathrm{\φ}}_z\left(t_n\right)-{\mathrm{\ω}}_{\mathrm{ie},y}^l\cos {\mathrm{\φ}}_z\left(t_n\right)$

$\begin{array}{c}{A}_{21}=[{\mathrm{\ω}}_x\left(t_n\right)\sin {\mathrm{\φ}}_y\left(t_n\right)-{\mathrm{\ω}}_z\left(t_n\right)\cos {\mathrm{\φ}}_y{\left(t_n\right)]\sec }^2{\mathrm{\φ}}_x\left(t_n\right)\\ +[{\mathrm{\ω}}_{\mathrm{ie},x}^l\sin {\mathrm{\φ}}_z\left(t_n\right)-{\mathrm{\ω}}_{\mathrm{ie},y}^l\cos {\mathrm{\φ}}_z\left(t_n\right)]\tan {\mathrm{\φ}}_x\left(t_n\right)\sec {\mathrm{\φ}}_x\left(t_n\right)\end{array}$

A ₂₂＝[ω _x(t _n)cosφ _y(t _n)+ω _z(t _n)sinφ _y(t _n)]tanφ _x(t _n)

$A_{23}=[{\mathrm{\ω}}_{\mathrm{ie},x}^l\cos {\mathrm{\φ}}_z\left(t_n\right)+{\mathrm{\ω}}_{\mathrm{ie},y}^l\sin {\mathrm{\φ}}_z\left(t_n\right)]\sec {\mathrm{\φ}}_x\left(t_n\right)$

$\begin{array}{c}{A}_{31}=-[{\mathrm{\ω}}_x\left(t_n\right)\sin {\mathrm{\φ}}_y\left(t_n\right)-{\mathrm{\ω}}_z\left(t_n\right)\cos {\mathrm{\φ}}_y\left(t_n\right)]\tan {\mathrm{\φ}}_x\left(t_n\right)\sec {\mathrm{\φ}}_x\left(t_n\right)\\ +[{\mathrm{\ω}}_{\mathrm{ie},x}^l\sin {\mathrm{\φ}}_z\left(t_n\right)-{\mathrm{\ω}}_{\mathrm{ie},y}^l\cos {\mathrm{\φ}}_z\left(t_n\right)]{\sec }^2{\mathrm{\φ}}_x\left(t_n\right)\end{array}$

A ₃₂＝-[ω _x(t _n)cosφ _y(t _n)+ω _z(t _n)sinφ _y(t _n)]secφ _x(t _n)

$A_{33}=-[{\mathrm{\ω}}_{\mathrm{ie},x}^l\cos {\mathrm{\φ}}_z\left(t_n\right)+{\mathrm{\ω}}_{\mathrm{ie},y}^l\sin {\mathrm{\φ}}_z\left(t_n\right)]\tan {\mathrm{\φ}}_x\left(t_n\right)$

A ₄₁＝a _x(t _n)sinφ _y(t _n)cosφ _x(t _n)cosφ _z(t _n)-a _y(t _n)sinφ _x(t _n)cosφ _z(t _n)

-a _z(t _n)cosφ _y(t _n)cosφ _x(t _n)cosφ _z(t _n)

A ₄₂＝a _x(t _n)[-sinφ _y(t _n)sinφ _z(t _n)+cosφ _y(t _n)sinφ _x(t _n)cosφ _z(t _n)]

+a _z(t _n)[cosφ _y(t _n)sinφ _z(t _n)+sinφ _y(t _n)sinφ _x(t _n)cosφ _z(t _n)]

A ₄₃＝a _x(t _n)[cosφ _y(t _n)cosφ _z(t _n)-sinφ _y(t _n)sinφ _x(t _n)sinφ _z(t _n)]-a _y(t _n)cosφ _x(t _n)sinφ _z(t _n)

+a _z(t _n)[sinφ _y(t _n)cosφ _z(t _n)+cosφ _y(t _n)sinφ _x(t _n)sinφ _z(t _n)]

A ₅₁＝a _x(t _n)sinφ _y(t _n)sinφ _x(t _n)+a _y(t _n)cosφ _x(t _n)-a _z(t _n)cosφ _y(t _n)sinφ _x(t _n)

A ₅₂＝-a _x(t _n)cosφ _y(t _n)cosφ _x(t _n)-a _z(t _n)sinφ _y(t _n)cosφ _x(t _n)

Wherein, Δ T is the update cycle, Δ T=t _n+1-t _n; for at rocket sledge orbital coordinate system OX _laxle, OY _laxle and OZ _lcomponent on axle; φ _x(t _n), φ _y(t _n), φ _z(t _n) be respectively t _nmoment, inertial measurement system was at OX _laxle, OY _laxle and OZ _lattitude angle on axle; a _x(t _n), a _y(t _n), a _z(t _n) be respectively t _nmoment inertial measurement system measures the accekeration obtained on strapdown body coordinate system three axles; ω _x(t _n), ω _y(t _n), ω _z(t _n) be that rocket sledge skid body is through the angular velocity of over-compensation on strapdown body coordinate system three axles, computing formula is:

$\left[\begin{array}{c}{\mathrm{\ω}}_x\left(t_n\right)\\ {\mathrm{\ω}}_y\left(t_n\right)\\ {\mathrm{\ω}}_z\left(t_n\right)\end{array}\right]={\stackrel{\→}{\mathrm{\ω}}}_{\mathrm{ib}}^b\left(t_n\right)-R_l^b\left(t_{n-1}\right){\stackrel{\→}{\mathrm{\ω}}}_{\mathrm{ie}}^l$

For t ₀moment, $\left[\begin{array}{c}{\mathrm{\ω}}_x\left(t_0\right)\\ {\mathrm{\ω}}_y\left(t_0\right)\\ {\mathrm{\ω}}_z\left(t_0\right)\end{array}\right]={\stackrel{\→}{\mathrm{\ω}}}_{\mathrm{ib}}^b\left(t_0\right);$ for t _nthe magnitude of angular velocity that moment inertial measurement system gyroscope measures on strapdown body coordinate system three axles, form is the column vector that X, Y, Z axis forms to angular velocity; for the projection components of earth rate in orbital coordinate system, be fixed value in navigation calculates; for t _n-1moment rocket sledge orbit coordinate is tied to the posture changing matrix of strapdown body coordinate system; P (t _n| t _n+1) be one-step prediction square error; P (t _n) for estimating square error; Q is noise sequence variance matrix, is fixed value in navigation calculation process; Κ (t _n) be filter gain; $H=\left[\begin{array}{ccccccc}0& 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 0& 1\end{array}\right],$ For measuring battle array; R is the variance matrix of measurement noise sequence, is fixed value in navigation calculation; $Y\left(t_n\right)=\left[\begin{array}{c}{v}_y\left(t_n\right)\\ v_z\left(t_n\right)\\ r_y\left(t_n\right)\\ r_z\left(t_n\right)\end{array}\right],$ Wherein, v _y(t _n), v _z(t _n) be respectively t _nmoment, inertial navigation system was at OY _l, OZ _lthe velocity information of axle, r _y(t _n), r _z(t _n) be respectively t _nmoment, inertial navigation system was at OY _l, OZ _lthe positional information of axle; I ₇be 7 rank unit matrix.

(3.2) at the t of rocket sledge motion _n+1in the moment, utilize following formulae discovery inertial measurement system at OX _lone dimension acceleration error value Δ a on direction of principal axis _x(t _n+1):

Δa _x(t _n+1)

＝[-a _x(t _n+1)sinφ _y(t _n+1)cosφ _x(t _n+1)sinφ _z(t _n+1)+a _y(t _n+1)sinφ _x(t _n+1)sinφ _z(t _n+1)

+a _z(t _n+1)cosφ _y(t _n+1)cosφ _x(t _n+1)sinφ _z(t _n+1)]δφ _x(t _n+1)

+[-a _x(t _n+1)(sinφ _y(t _n+1)cosφ _z(t _n+1)+cosφ _y(t _n+1)sinφ _x(t _n+1)sinφ _z(t _n+1))

+a _z(t _n+1)(cosφ _y(t _n+1)cosφ _z(t _n+1)-sinφ _y(t _n+1)sinφ _x(t _n+1)sinφ _z(t _n+1))]δφ _y(t _n+1)

+[-a _x(t _n+1)(cosφ _y(t _n+1)sinφ _z(t _n+1)+sinφ _y(t _n+1)sinφ _x(t _n+1)cosφ _z(t _n+1))

-a _y(t _n+1)cosφ _x(t _n+1)cosφ _z(t _n+1)

+a _z(t _n+1)(-sinφ _y(t _n+1)sinφ _z(t _n+1)+cosφ _y(t _n+1)sinφ _x(t _n+1)cosφ _z(t _n+1))]δφ _z(t _n+1)

Wherein, be respectively t _n+1moment, inertial measurement system was at OX _laxle, OY _laxle and OZ _lattitude angle on axle; a _x(t _n+1), a _y(t _n+1), a _z(t _n+1) be respectively t _n+1moment inertial measurement system measures the accekeration obtained on strapdown body coordinate system three axles.

T in described step (4) _n+1moment, inertial measurement system was at OX _laxle, OY _laxle and OZ _lattitude angle φ on axle _x(t _n+1), φ _y(t _n+1) and φ _z(t _n+1) utilize following formulae discovery to obtain:

$\begin{array}{c}\left[\begin{array}{c}{\mathrm{\φ}}_x\left(t_{n+1}\right)\\ {\mathrm{\φ}}_y\left(t_{n+1}\right)\\ {\mathrm{\φ}}_z\left(t_{n+!}\right)\end{array}\right]=\left[\begin{array}{c}{\mathrm{\φ}}_x\left(t_n\right)\\ {\mathrm{\φ}}_y\left(t_n\right)\\ {\mathrm{\φ}}_z\left(t_n\right)\end{array}\right]+\left[\begin{array}{ccc}\cos {\mathrm{\φ}}_y\left(t_n\right)& 0& \sin {\mathrm{\φ}}_y\left(t_n\right)\\ \sin {\mathrm{\φ}}_y\left(t_n\right)\tan {\mathrm{\φ}}_x\left(t_n\right)& 1& -\cos {\mathrm{\φ}}_y\left(t_n\right)\tan {\mathrm{\φ}}_x\left(t_n\right)\\ -\sin {\mathrm{\φ}}_y\left(t_n\right)\sec {\mathrm{\φ}}_x\left(t_n\right)& 0& \cos {\mathrm{\φ}}_y\left(t_n\right)\sec {\mathrm{\φ}}_x\left(t_n\right)\end{array}\right]{\stackrel{\→}{\mathrm{\ω}}}_{\mathrm{ib}}^b\left(t_n\right)\·\mathrm{\ΔT}\\ -\left[\begin{array}{ccc}\cos {\mathrm{\φ}}_z\left(t_n\right)& \sin {\mathrm{\φ}}_z\left(t_n\right)& 0\\ -\sin {\mathrm{\φ}}_z\left(t_n\right)\sec {\mathrm{\φ}}_x\left(t_n\right)& \cos {\mathrm{\φ}}_z\left(t_n\right)\sec {\mathrm{\φ}}_x\left(t_n\right)& 0\\ \sin {\mathrm{\φ}}_z\left(t_n\right)\tan {\mathrm{\φ}}_x\left(t_n\right)& -\cos {\mathrm{\φ}}_z\left(t_n\right)\tan {\mathrm{\φ}}_x\left(t_n\right)& 1\end{array}\right]{\stackrel{\→}{\mathrm{\ω}}}_{\mathrm{ie}}^l\·\mathrm{\ΔT}-\left[\begin{array}{c}\mathrm{\δ}{\mathrm{\φ}}_x\left(t_{n+1}\right)\\ \mathrm{\δ}{\mathrm{\φ}}_y\left(t_{n+1}\right)\\ \mathrm{\δ}{\mathrm{\φ}}_z\left(t_{n+1}\right)\end{array}\right]\end{array}$

Wherein, φ _x(t _n), φ _y(t _n), φ _z(t _n) be respectively t _nmoment, inertial measurement system was at OX _laxle, OY _laxle and OZ _lattitude angle on axle, for t _nthe magnitude of angular velocity that moment inertial measurement system gyroscope measures on strapdown body coordinate system three axles, form is the column vector that X, Y, Z axis forms to angular velocity; for the projection components of earth rate in orbital coordinate system, be fixed value in navigation calculates; Δ T is the update cycle, Δ T=t _n+1-t _n; δ φ _x(t _n+1), δ φ _y(t _n+1), δ φ _z(t _n+1) be t _n+1moment, inertial measurement system was at OX _laxle, OY _laxle and OZ _lattitude error value on axle.

In described step (6), the component of acceleration of gravity under rocket sledge orbital coordinate system is as follows:

$\left[\begin{array}{c}{g}_x^l\\ g_y^l\\ g_z^l\end{array}\right]=\left[\begin{array}{c}-(g_0+b_1{r}_x+b_2{r}_x^2)\sin \frac{\left|P_{0}P\right|-r_x}{N+h_p}\\ 0\\ (g_0+b_1{r}_x+b_2{r}_x^2)\cos \frac{\left|P_{0}P\right|-r_x}{N+h_p}\end{array}\right]$

Wherein, a is semimajor axis of ellipsoid, e ²for eccentricity of the earth, for the latitude value of rocket sledge skid body point; h _pfor the height of the relative level surface of skid body; | P ₀p|=(N+h _p) β ', β ' be vector O ₀p ₀and O ₀the angle of P, wherein vector O ₀p ₀for earth center O ₀to track initial point P ₀vector, O ₀p is O ₀to the vector of P point, P is track and earth surface point of contact, for rocket sledge track acceleration of gravity model, wherein r _xfor the Orbiting distance of skid body; g ₀for the acceleration of gravity of launching site position, b ₁and b ₂for constant value.

The implementation of described step (6) is:

(6.1) utilize following formula to carry out navigation calculation, obtain t _n+1moment, inertial measurement system was at OX _laxle, OY _laxle and OZ _lvelocity information v on axle _x(t _n+1), v _y(t _n+1) and v _z(t _n+1):

$\left[\begin{array}{c}{v}_x\left(t_{n+1}\right)\\ v_y\left(t_{n+1}\right)\\ v_z\left(t_{n+1}\right)\end{array}\right]=\left[\begin{array}{c}{v}_x\left(t_n\right)\\ v_y\left(t_n\right)\\ v_z\left(t_n\right)\end{array}\right]+(R_b^l\left(t_{n+1}\right)f^b\left(t_{n+1}\right)-2{\mathrm{\Ω}}_{\mathrm{ie}}^l\·\left[\begin{array}{c}{v}_x\left(t_n\right)\\ v_y\left(t_n\right)\\ v_z\left(t_n\right)\end{array}\right]+g^l-\left[\begin{array}{c}\mathrm{\Δ}{a}_x\left(t_{n+1}\right)\\ 0\\ 0\end{array}\right])\·\mathrm{\ΔT}-\left[\begin{array}{c}0\\ \mathrm{\δ}{v}_y\left(t_{n+1}\right)\\ \mathrm{\δ}{v}_z\left(t_{n+1}\right)\end{array}\right]$

Wherein, v _x(t _n), v _y(t _n), v _z(t _n) be t _nmoment, inertial measurement system was at OX _laxle, OY _laxle and OZ _lvelocity information on axle; for t _n+1moment rocket sledge orbit coordinate is tied to the posture changing matrix of strapdown body coordinate system; for earth rate is in orbital coordinate system projection components antisymmetric matrix; f ^b(t _n) be the measured value of inertial measurement system accelerometer, form is the column vector that X, Y, Z axis forms to acceleration; g ^lfor the component of acceleration of gravity under rocket sledge orbital coordinate system; Δ a _x(t _n+1) be t _n+1moment, inertial measurement system was at OX _lone dimension acceleration error value on direction of principal axis; Δ T is the update cycle, Δ T=t _n+1-t _n; δ v _y(t _n+1), δ v _z(t _n+1) be t _n+1moment, inertial measurement system was at OY _laxle and OZ _lspeed error value on axle;

(6.2) utilize following formula to carry out navigation calculation, obtain t _n+1moment, inertial measurement system was at OX _laxle, OY _laxle and OZ _lpositional information r on axle _x(t _n+1), r _y(t _n+1) and r _z(t _n+1):

$\left[\begin{array}{c}{r}_x\left(t_{n+1}\right)\\ r_y\left(t_{n+1}\right)\\ r_z\left(t_{n+1}\right)\end{array}\right]=\left[\begin{array}{c}{r}_x\left(t_n\right)\\ r_y\left(t_n\right)\\ r_z\left(t_n\right)\end{array}\right]+\left[\begin{array}{c}{v}_x\left(t_{n+1}\right)\\ v_y\left(t_{n+1}\right)\\ v_z\left(t_{n+1}\right)\end{array}\right]\·\mathrm{\ΔT}-\left[\begin{array}{c}0\\ \mathrm{\δ}{r}_y\left(t_{n+1}\right)\\ \mathrm{\δ}{r}_z\left(t_{n+1}\right)\end{array}\right]$

Wherein, r _x(t _n), r _y(t _n), r _z(t _n) be t _nmoment, inertial measurement system was at OX _laxle, OY _laxle and OZ _lpositional information on axle; δ r _y(t _n+1), δ r _z(t _n+1) be t _n+1moment, inertial measurement system was at OY _laxle and OZ _lsite error value on axle.

The present invention's advantage is compared with prior art as follows:

(1) in the navigation algorithm based on the orbital coordinate system of rocket sledge launching site, for rectilinear orbit, based on the orbital coordinate system OX of rocket sledge launching site _laxle and parallel track, therefore, directly can obtain skid body (inertial measurement system) Orbiting range information; For the warp rail with earth plane-parallel, just can at the orbital coordinate system OX based on rocket sledge launching site _lz _lin plane, skid body (inertial measurement system) Orbiting range information is described.These computing method are simple, and explicit physical meaning.

(2) to inertial measurement system OY _l, OZ _lafter axle navigation speed and site error are estimated, the offset of attitude angle, speed, position can be obtained, and can OX be obtained accordingly _lthe acceleration error offset of axle.Compensate after completing location, real-time compensation method can obtain higher navigation accuracy;

(3), in the navigation algorithm based on the orbital coordinate system of rocket sledge launching site, only need consider the measured value that gyroscope combines when inertial measurement system attitude angle upgrades, do not need the impact of consideration speed, algorithm is simple.

(4) relative to the method for carrying out again navigating after test, namely application the present invention in test can obtain navigation results, be convenient to analyze inertial measurement system state in test, effectively test interval can be shortened when needs carry out long run test, and, test can be stopped when there is defective mode in time, avoiding causing larger infringement, and provide foundation for failture evacuation.

Accompanying drawing explanation

Fig. 1 is realization flow figure of the present invention;

Fig. 2 is the schematic diagram of rocket sledge track in earth coordinates;

Fig. 3 is track crab angle and angle of pitch schematic diagram;

Fig. 4 is gravity acceleration simulation comparative result schematic diagram;

Fig. 5 is the navigation results without error deduction;

Fig. 6 is the navigation results through error deduction.

Embodiment

First the coordinate system related in method is described below.

Strapdown body coordinate system b and skid body are connected, and initial point is skid body center, and x-axis points to direction of motion, and z-axis refers to sky, and y-axis is vertical with x, z-axis respectively, and meets right hand rule.

Geographic coordinate system initial point is skid body center, and wherein x, y, z three axle meets sky, northeast criterion.

The inventive method step as shown in Figure 1, by based on the state-space model of orbital coordinate system, initial attitude is aimed at, attitude angle upgrades, transformation matrix of coordinates is asked for, error is asked for, speed and location updating and error deduction etc. form, concrete steps are as follows:

(1) inertial measurement system is mounted on rocket sledge, with rocket sledge track starting point for initial point sets up rocket sledge orbital coordinate system OX _ly _lz _l, wherein OX _laxle points to rocket sledge skid body direction of motion, OZ _laxle upward perpendicular to track, OY _laxle in surface level perpendicular to track, and OX _laxle, OY _laxle and OZ _laxle meets right-handed coordinate system;

(2) inertial measurement system carries out autoregistration or Transfer Alignment, obtains t ₀moment, inertial measurement system was at OX _laxle, OY _laxle and OZ _lattitude angle (being called attitude angle initial value) on axle, and calculate t according to the attitude angle obtained ₀moment rocket sledge orbit coordinate is tied to the posture changing matrix of strapdown body coordinate system; Wherein strapdown body coordinate system initial point is the center of inertial measurement system, and x, y, z axle defines according to inertial measurement system prescribed direction;

When inertial measurement system carries out autoregistration, following formula is utilized to obtain inertial measurement system at OX _laxle, OY _laxle and OZ _lattitude angle initial value on axle:

Wherein, φ _x, φ _y, φ _zbe respectively inertial measurement system at OX _laxle, OY _laxle and OZ _lattitude angle initial value on axle, a _x, a _y, a _zbe respectively the accekeration that inertial measurement system measurement obtains on strapdown body coordinate system three axles, ω _x, ω _y, ω _zfor the magnitude of angular velocity that inertial measurement system measurement on strapdown body coordinate system three axles obtains, ω _iefor earth rate, for test site latitude;

When carrying out Transfer Alignment, inertial measurement system is at OX _laxle, OY _laxle and OZ _lattitude angle initial value φ on axle _x, φ _yand φ _zprovided by external system;

Following formulae discovery t is utilized according to the attitude angle initial value obtained ₀moment rocket sledge orbit coordinate is tied to the posture changing matrix of strapdown body coordinate system

$R_l^b=\left[\begin{array}{ccc}\cos {\mathrm{\φ}}_y& 0& -\sin {\mathrm{\φ}}_y\\ 0& 1& 0\\ \sin {\mathrm{\φ}}_y& 0& \cos {\mathrm{\φ}}_y\end{array}\right]\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos {\mathrm{\φ}}_x& \sin {\mathrm{\φ}}_x\\ 0& -\sin {\mathrm{\φ}}_x& \cos {\mathrm{\φ}}_x\end{array}\right]\left[\begin{array}{ccc}\cos {\mathrm{\φ}}_z& \sin {\mathrm{\φ}}_z& 0\\ -\sin {\mathrm{\φ}}_z& \cos {\mathrm{\φ}}_z& 0\\ 0& 0& 1\end{array}\right].$

(3) after rocket sledge ignition trigger, at the t of rocket sledge motion _n+1moment, the acceleration recorded according to inertial measurement system and angular velocity, and t _nmoment, inertial measurement system was at OY _laxle and OZ _lthe speed of axle and positional information, calculate following parameter:

A () inertial measurement system is at OX _laxle, OY _laxle and OZ _lattitude error value on axle;

B () inertial measurement system is at OY _laxle and OZ _lspeed error value on axle;

C () inertial measurement system is at OY _laxle and OZ _lsite error value on axle;

D () inertial measurement system is at OX _lone dimension acceleration error value on direction of principal axis;

Wherein n=0,1,2 ... N, N are natural number;

At the t of rocket sledge motion _n+1in the moment, utilize following formulae discovery inertial measurement system at OX _laxle, OY _laxle and OZ _lattitude error value on axle, at OY _laxle and OZ _lspeed error value on axle, at OY _laxle and OZ _lsite error value on axle:

(1)X(t _n|t _n+1)＝Φ(t _n)X(t _n)

(2)P(t _n|t _n+1)＝Φ(t _n)P(t _n)Φ(t _n) ^T+Q·ΔT

(3)Κ(t _n)＝P(t _n|t _n+1)H ^T[HP(t _n|t _n+1)H ^T+R] ^-1

(4)X(t _n+1)＝X(t _n|t _n+1)+K(t _n)[Y(t _n)-HX(t _n)]

(5)P(t _n+1)＝[I ₇-K(t _n)H]P(t _n|t _n+1)[I ₇-K(t _n)H] ^T+K(t _n)RK(t _n) ^T

Wherein, $X\left(t_n\right)=\left[\begin{array}{c}\mathrm{\δ}{\mathrm{\φ}}_x\left(t_n\right)\\ \mathrm{\δ}{\mathrm{\φ}}_y\left(t_n\right)\\ \mathrm{\δ}{\mathrm{\φ}}_z\left(t_n\right)\\ \mathrm{\δ}{v}_y\left(t_n\right)\\ \mathrm{\δ}{v}_z\left(t_n\right)\\ \mathrm{\δ}{r}_y\left(t_n\right)\\ \mathrm{\δ}{r}_z\left(t_n\right)\end{array}\right]$ For t _nthe vector of moment each error coefficient composition, δ φ _x, δ φ _y, δ φ _zfor inertial measurement system is at OX _laxle, OY _laxle and OZ _lattitude error on axle, δ v _y, δ v _zfor inertial measurement system is at OY _laxle and OZ _lvelocity error on axle, δ r _y, δ r _zfor inertial measurement system is at OY _laxle and OZ _lsite error value on axle, at t ₀moment, X (t ₀)=[0 00000 0] ^t;

$X\left(t_n\right|t_{n+1})=\left[\begin{array}{c}\mathrm{\δ}{\mathrm{\φ}}_x\left(t_n\right|t_{n+1})\\ \mathrm{\δ}{\mathrm{\φ}}_y\left(t_n\right|t_{n+1})\\ \mathrm{\δ}{\mathrm{\φ}}_z\left(t_n\right|t_{n+1})\\ \mathrm{\δ}{v}_y\left(t_n\right|t_{n+1})\\ \mathrm{\δ}{v}_z\left(t_n\right|t_{n+1})\\ \mathrm{\δ}{r}_y\left(t_n\right|t_{n+1})\\ \mathrm{\δ}{r}_z\left(t_n\right|t_{n+1})\end{array}\right],$ For t _nmoment is to t _n+1the vector of moment each error coefficient one-step prediction value composition; $\mathrm{\Φ}\left(t_n\right)=I_7+\left[\begin{array}{ccccccc}0& A_{12}& A_{13}& 0& 0& 0& 0\\ A_{21}& A_{22}& A_{23}& 0& 0& 0& 0\\ A_{31}& A_{32}& A_{33}& 0& 0& 0& 0\\ A_{41}& A_{42}& A_{43}& 0& 2{\mathrm{\ω}}_{\mathrm{ie},x}^l& 0& 0\\ A_{51}& A_{52}& 0& -2{\mathrm{\ω}}_{\mathrm{ie},x}^l& 0& 0& 0\\ 0& 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 1& 0& 0\end{array}\right]\·\mathrm{\ΔT},$ For state transfer matrix, and

A ₁₂＝-ω _x(t _n)sinφ _y(t _n)+ω _z(t _n)cosφ _y(t _n)

$A_{13}={\mathrm{\ω}}_{\mathrm{ie},x}^l\sin {\mathrm{\φ}}_z\left(t_n\right)-{\mathrm{\ω}}_{\mathrm{ie},y}^l\cos {\mathrm{\φ}}_z\left(t_n\right)$

$\begin{array}{c}{A}_{21}=[{\mathrm{\ω}}_x\left(t_n\right)\sin {\mathrm{\φ}}_y\left(t_n\right)-{\mathrm{\ω}}_z\left(t_n\right)\cos {\mathrm{\φ}}_y{\left(t_n\right)]\sec }^2{\mathrm{\φ}}_x\left(t_n\right)\\ +[{\mathrm{\ω}}_{\mathrm{ie},x}^l\sin {\mathrm{\φ}}_z\left(t_n\right)-{\mathrm{\ω}}_{\mathrm{ie},y}^l\cos {\mathrm{\φ}}_z\left(t_n\right)]\tan {\mathrm{\φ}}_x\left(t_n\right)\sec {\mathrm{\φ}}_x\left(t_n\right)\end{array}$

A ₂₂＝[ω _x(t _n)cosφ _y(t _n)+ω _z(t _n)sinφ _y(t _n)]tanφ _x(t _n)

$A_{23}=[{\mathrm{\ω}}_{\mathrm{ie},x}^l\cos {\mathrm{\φ}}_z\left(t_n\right)+{\mathrm{\ω}}_{\mathrm{ie},y}^l\sin {\mathrm{\φ}}_z\left(t_n\right)]\sec {\mathrm{\φ}}_x\left(t_n\right)$

$\begin{array}{c}{A}_{31}=-[{\mathrm{\ω}}_x\left(t_n\right)\sin {\mathrm{\φ}}_y\left(t_n\right)-{\mathrm{\ω}}_z\left(t_n\right)\cos {\mathrm{\φ}}_y\left(t_n\right)]\tan {\mathrm{\φ}}_x\left(t_n\right)\sec {\mathrm{\φ}}_x\left(t_n\right)\\ +[{\mathrm{\ω}}_{\mathrm{ie},x}^l\sin {\mathrm{\φ}}_z\left(t_n\right)-{\mathrm{\ω}}_{\mathrm{ie},y}^l\cos {\mathrm{\φ}}_z\left(t_n\right)]{\sec }^2{\mathrm{\φ}}_x\left(t_n\right)\end{array}$

A ₃₂＝-[ω _x(t _n)cosφ _y(t _n)+ω _z(t _n)sinφ _y(t _n)]secφ _x(t _n)

$A_{33}=-[{\mathrm{\ω}}_{\mathrm{ie},x}^l\cos {\mathrm{\φ}}_z\left(t_n\right)+{\mathrm{\ω}}_{\mathrm{ie},y}^l\sin {\mathrm{\φ}}_z\left(t_n\right)]\tan {\mathrm{\φ}}_x\left(t_n\right)$

A ₄₁＝a _x(t _n)sinφ _y(t _n)cosφ _x(t _n)cosφ _z(t _n)-a _y(t _n)sinφ _x(t _n)cosφ _z(t _n)

-a _z(t _n)cosφ _y(t _n)cosφ _x(t _n)cosφ _z(t _n)

A ₄₂＝a _x(t _n)[-sinφ _y(t _n)sinφ _z(t _n)+cosφ _y(t _n)sinφ _x(t _n)cosφ _z(t _n)]

+a _z(t _n)[cosφ _y(t _n)sinφ _z(t _n)+sinφ _y(t _n)sinφ _x(t _n)cosφ _z(t _n)]

A ₄₃＝a _x(t _n)[cosφ _y(t _n)cosφ _z(t _n)-sinφ _y(t _n)sinφ _x(t _n)sinφ _z(t _n)]-a _y(t _n)cosφ _x(t _n)sinφ _z(t _n)

+a _z(t _n)[sinφ _y(t _n)cosφ _z(t _n)+cosφ _y(t _n)sinφ _x(t _n)sinφ _z(t _n)]

A ₅₁＝a _x(t _n)sinφ _y(t _n)sinφ _x(t _n)+a _y(t _n)cosφ _x(t _n)-a _z(t _n)cosφ _y(t _n)sinφ _x(t _n)

A ₅₂＝-a _x(t _n)cosφ _y(t _n)cosφ _x(t _n)-a _z(t _n)sinφ _y(t _n)cosφ _x(t _n)

Wherein, Δ T is the update cycle, Δ T=t _n+1-t _n; for at rocket sledge orbital coordinate system OX _laxle, OY _laxle and OZ _lcomponent on axle; φ _x(t _n), φ _y(t _n), φ _z(t _n) be respectively t _nmoment, inertial measurement system was at OX _laxle, OY _laxle and OZ _lattitude angle on axle; a _x(t _n), a _y(t _n), a _z(t _n) be respectively t _nthe accekeration that moment inertial measurement system obtains in three the axle measurements of strapdown body coordinate system; ω _x(t _n), ω _y(t _n), ω _z(t _n) be that rocket sledge skid body is through the angular velocity of over-compensation on strapdown body coordinate system three axles, computing formula is:

$\left[\begin{array}{c}{\mathrm{\ω}}_x\left(t_n\right)\\ {\mathrm{\ω}}_y\left(t_n\right)\\ {\mathrm{\ω}}_z\left(t_n\right)\end{array}\right]={\stackrel{\→}{\mathrm{\ω}}}_{\mathrm{ib}}^b\left(t_n\right)-R_l^b\left(t_{n-1}\right){\stackrel{\→}{\mathrm{\ω}}}_{\mathrm{ie}}^l$

For t ₀moment, $\left[\begin{array}{c}{\mathrm{\ω}}_x\left(t_0\right)\\ {\mathrm{\ω}}_y\left(t_0\right)\\ {\mathrm{\ω}}_z\left(t_0\right)\end{array}\right]={\stackrel{\→}{\mathrm{\ω}}}_{\mathrm{ib}}^b\left(t_0\right);$ for t _nthe magnitude of angular velocity that moment inertial measurement system gyroscope measures at strapdown body coordinate system three axles, form is the column vector that X, Y, Z axis forms to angular velocity; for the projection components of earth rate in orbital coordinate system, be fixed value in navigation calculates; for t _n-1moment rocket sledge orbit coordinate is tied to the posture changing matrix of strapdown body coordinate system; P (t _n| t _n+1) be one-step prediction square error; P (t _n) for estimating square error; Q is noise sequence variance matrix, is fixed value in navigation calculation process; Κ (t _n) be filter gain; $H=\left[\begin{array}{ccccccc}0& 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 0& 1\end{array}\right],$ For measuring battle array; R is the variance matrix of measurement noise sequence, is fixed value in navigation calculation; $Y\left(t_n\right)=\left[\begin{array}{c}{v}_y\left(t_n\right)\\ v_z\left(t_n\right)\\ r_y\left(t_n\right)\\ r_z\left(t_n\right)\end{array}\right],$ Wherein, v _y(t _n), v _z(t _n) be respectively t _nmoment, inertial navigation system was at OY _l, OZ _lthe velocity information of axle, r _y(t _n), r _z(t _n) be respectively t _nmoment, inertial navigation system was at OY _l, OZ _lthe positional information of axle; I ₇be 7 rank unit matrix.

At the t of rocket sledge motion _n+1in the moment, inertial measurement system is at OX _lone dimension acceleration error value computing formula on direction of principal axis is as follows:

Δa _x(t _n+1)

＝[-a _x(t _n+1)sinφ _y(t _n+1)cosφ _x(t _n+1)sinφ _z(t _n+1)+a _y(t _n+1)sinφ _x(t _n+1)sinφ _z(t _n+1)

+a _z(t _n+1)cosφ _y(t _n+1)cosφ _x(t _n+1)sinφ _z(t _n+1)]δφ _x(t _n+1)

+[-a _x(t _n+1)(sinφ _y(t _n+1)cosφ _z(t _n+1)+cosφ _y(t _n+1)sinφ _x(t _n+1)sinφ _z(t _n+1))

+a _z(t _n+1)(cosφ _y(t _n+1)cosφ _z(t _n+1)-sinφ _y(t _n+1)sinφ _x(t _n+1)sinφ _z(t _n+1))]δφ _y(t _n+1)

+[-a _x(t _n+1)(cosφ _y(t _n+1)sinφ _z(t _n+1)+sinφ _y(t _n+1)sinφ _x(t _n+1)cosφ _z(t _n+1))

-a _y(t _n+1)cosφ _x(t _n+1)cosφ _z(t _n+1)

+a _z(t _n+1)(-sinφ _y(t _n+1)sinφ _z(t _n+1)+cosφ _y(t _n+1)sinφ _x(t _n+1)cosφ _z(t _n+1))]δφ _z(t _n+1)

(4) according to the t that step (3) obtains _n+1moment, inertial measurement system was at OX _laxle, OY _laxle and OZ _lattitude error value on axle, obtains t _n+1moment, inertial measurement system was at OX _laxle, OY _laxle and OZ _lattitude angle on direction of principal axis;

T _n+1moment, inertial measurement system was at OX _laxle, OY _laxle and OZ _lattitude angle φ on axle _x(t _n+1), φ _y(t _n+1) and φ _z(t _n+1) utilize following formulae discovery to obtain:

$\begin{array}{c}\left[\begin{array}{c}{\mathrm{\φ}}_x\left(t_{n+1}\right)\\ {\mathrm{\φ}}_y\left(t_{n+1}\right)\\ {\mathrm{\φ}}_z\left(t_{n+!}\right)\end{array}\right]=\left[\begin{array}{c}{\mathrm{\φ}}_x\left(t_n\right)\\ {\mathrm{\φ}}_y\left(t_n\right)\\ {\mathrm{\φ}}_z\left(t_n\right)\end{array}\right]+\left[\begin{array}{ccc}\cos {\mathrm{\φ}}_y\left(t_n\right)& 0& \sin {\mathrm{\φ}}_y\left(t_n\right)\\ \sin {\mathrm{\φ}}_y\left(t_n\right)\tan {\mathrm{\φ}}_x\left(t_n\right)& 1& -\cos {\mathrm{\φ}}_y\left(t_n\right)\tan {\mathrm{\φ}}_x\left(t_n\right)\\ -\sin {\mathrm{\φ}}_y\left(t_n\right)\sec {\mathrm{\φ}}_x\left(t_n\right)& 0& \cos {\mathrm{\φ}}_y\left(t_n\right)\sec {\mathrm{\φ}}_x\left(t_n\right)\end{array}\right]{\stackrel{\→}{\mathrm{\ω}}}_{\mathrm{ib}}^b\left(t_n\right)\·\mathrm{\ΔT}\\ -\left[\begin{array}{ccc}\cos {\mathrm{\φ}}_z\left(t_n\right)& \sin {\mathrm{\φ}}_z\left(t_n\right)& 0\\ -\sin {\mathrm{\φ}}_z\left(t_n\right)\sec {\mathrm{\φ}}_x\left(t_n\right)& \cos {\mathrm{\φ}}_z\left(t_n\right)\sec {\mathrm{\φ}}_x\left(t_n\right)& 0\\ \sin {\mathrm{\φ}}_z\left(t_n\right)\tan {\mathrm{\φ}}_x\left(t_n\right)& -\cos {\mathrm{\φ}}_z\left(t_n\right)\tan {\mathrm{\φ}}_x\left(t_n\right)& 1\end{array}\right]{\stackrel{\→}{\mathrm{\ω}}}_{\mathrm{ie}}^l\·\mathrm{\ΔT}-\left[\begin{array}{c}\mathrm{\δ}{\mathrm{\φ}}_x\left(t_{n+1}\right)\\ \mathrm{\δ}{\mathrm{\φ}}_y\left(t_{n+1}\right)\\ \mathrm{\δ}{\mathrm{\φ}}_z\left(t_{n+1}\right)\end{array}\right]\end{array}$

Wherein, φ _x(t _n), φ _y(t _n), φ _z(t _n) be respectively t _nmoment, inertial measurement system was at OX _laxle, OY _laxle and OZ _lattitude angle on axle, for t _nthe magnitude of angular velocity that moment inertial measurement system gyroscope measures on strapdown body coordinate system three axles, form is the column vector that X, Y, Z axis forms to angular velocity; for the projection components of earth rate in orbital coordinate system, be fixed value in navigation calculates; Δ T is the update cycle, Δ T=t _n+1-t _n; δ φ _x(t _n+1), δ φ _y(t _n+1), δ φ _z(t _n+1) be t _n+1moment, inertial measurement system was at OX _laxle, OY _laxle and OZ _lattitude error value on axle, is obtained by step (3);

(5) t is utilized _n+1moment, inertial measurement system was at OX _laxle, OY _laxle and OZ _lattitude angle on direction of principal axis calculates t _n+1moment rocket sledge orbit coordinate is tied to the posture changing matrix of strapdown body coordinate system;

$R_l^b\left(t_{n+1}\right)=\left[\begin{array}{ccc}\cos {\mathrm{\φ}}_y\left(t_{n+1}\right)& 0& -\sin {\mathrm{\φ}}_y\left(t_{n+1}\right)\\ 0& 1& 0\\ \sin {\mathrm{\φ}}_y\left(t_{n+1}\right)& 0& \cos {\mathrm{\φ}}_y\left(t_{n+1}\right)\end{array}\right]\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos {\mathrm{\φ}}_x\left(t_{n+1}\right)& \sin {\mathrm{\φ}}_x\left(t_{n+1}\right)\\ 0& -\sin {\mathrm{\φ}}_x\left(t_{n+1}\right)& \cos {\mathrm{\φ}}_x\left(t_{n+1}\right)\end{array}\right]\left[\begin{array}{ccc}\cos {\mathrm{\φ}}_z\left(t_{n+1}\right)& \sin {\mathrm{\φ}}_z\left(t_{n+1}\right)& 0\\ -\sin {\mathrm{\φ}}_z\left(t_{n+1}\right)& \cos {\mathrm{\φ}}_z\left(t_{n+1}\right)& 0\\ 0& 0& 1\end{array}\right]$

(6) component of acceleration of gravity under rocket sledge orbital coordinate system is utilized, and t _n+1moment rocket sledge orbit coordinate is tied to the posture changing matrix of strapdown body coordinate system, the acceleration of inertial measurement system, inertial measurement system at OX _lone dimension acceleration error value on direction of principal axis, inertial measurement system are at OY _laxle and OZ _lspeed error value on axle and site error value, carry out navigation calculation and obtain t _n+1moment, inertial measurement system was at OX _laxle, OY _laxle and OZ _lspeed on axle and positional information, thus the real-time one dimension location realizing inertial measurement system.

The component of acceleration of gravity under rocket sledge orbital coordinate system is as follows:

$\left[\begin{array}{c}{g}_x^l\\ g_y^l\\ g_z^l\end{array}\right]=\left[\begin{array}{c}-(g_0+b_1{r}_x+b_2{r}_x^2)\sin \frac{\left|P_{0}P\right|-r_x}{N+h_p}\\ 0\\ (g_0+b_1{r}_x+b_2{r}_x^2)\cos \frac{\left|P_{0}P\right|-r_x}{N+h_p}\end{array}\right]$

Wherein, a is semimajor axis of ellipsoid, e ²for eccentricity of the earth, for the latitude value of rocket sledge skid body point; h _pfor the height of the relative level surface of skid body; | P ₀p|=(N+h _p) β ', β ' be vector O ₀p ₀and O ₀the angle of P, wherein vector O ₀p ₀for earth center O ₀to track initial point P ₀vector, O ₀p is O ₀to the vector of P point, P is track and earth surface point of contact, for rocket sledge track acceleration of gravity model, wherein r _xfor the Orbiting distance of skid body; g ₀for the acceleration of gravity of launching site position, b ₁and b ₂for constant value.

Utilize following formula to carry out navigation calculation (deducting error), obtain t _n+1moment, inertial measurement system was at OX _laxle, OY _laxle and OZ _lvelocity information v on axle _x(t _n+1), v _y(t _n+1) and v _z(t _n+1):

$\left[\begin{array}{c}{v}_x\left(t_{n+1}\right)\\ v_y\left(t_{n+1}\right)\\ v_z\left(t_{n+1}\right)\end{array}\right]=\left[\begin{array}{c}{v}_x\left(t_n\right)\\ v_y\left(t_n\right)\\ v_z\left(t_n\right)\end{array}\right]+(R_b^l\left(t_{n+1}\right)f^b\left(t_{n+1}\right)-2{\mathrm{\Ω}}_{\mathrm{ie}}^l\·\left[\begin{array}{c}{v}_x\left(t_n\right)\\ v_y\left(t_n\right)\\ v_z\left(t_n\right)\end{array}\right]+g^l-\left[\begin{array}{c}\mathrm{\Δ}{a}_x\left(t_{n+1}\right)\\ 0\\ 0\end{array}\right])\·\mathrm{\ΔT}-\left[\begin{array}{c}0\\ \mathrm{\δ}{v}_y\left(t_{n+1}\right)\\ \mathrm{\δ}{v}_z\left(t_{n+1}\right)\end{array}\right]$

Wherein, v _x(t _n), v _y(t _n), v _z(t _n) be t _nmoment, inertial measurement system was at OX _laxle, OY _laxle and OZ _lvelocity information on axle; for t _n+1moment rocket sledge orbit coordinate is tied to the posture changing matrix of strapdown body coordinate system, calculates in step (5); for earth rate is in orbital coordinate system projection components antisymmetric matrix; f ^b(t _n) be the measured value of inertial measurement system accelerometer, form is the column vector that X, Y, Z axis forms to acceleration; g ^lfor the component of acceleration of gravity under rocket sledge orbital coordinate system; Δ a _x(t _n+1) be t _n+1moment OX _lone dimension acceleration error value on direction of principal axis, calculates in step (3); Δ T is the update cycle, Δ T=t _n+1-t _n; δ v _y(t _n+1), δ v _z(t _n+1) be t _n+1moment, inertial measurement system was at OY _laxle and OZ _lvelocity error on axle, calculates in step (3);

Utilize following formula to carry out navigation calculation (deducting error), obtain t _n+1moment, inertial measurement system was at OX _laxle, OY _laxle and OZ _lpositional information r on axle _x(t _n+1), r _y(t _n+1) and r _z(t _n+1):

$\left[\begin{array}{c}{r}_x\left(t_{n+1}\right)\\ r_y\left(t_{n+1}\right)\\ r_z\left(t_{n+1}\right)\end{array}\right]=\left[\begin{array}{c}{r}_x\left(t_n\right)\\ r_y\left(t_n\right)\\ r_z\left(t_n\right)\end{array}\right]+\left[\begin{array}{c}{v}_x\left(t_{n+1}\right)\\ v_y\left(t_{n+1}\right)\\ v_z\left(t_{n+1}\right)\end{array}\right]\·\mathrm{\ΔT}-\left[\begin{array}{c}0\\ \mathrm{\δ}{r}_y\left(t_{n+1}\right)\\ \mathrm{\δ}{r}_z\left(t_{n+1}\right)\end{array}\right]$

Wherein, r _x(t _n), r _y(t _n), r _z(t _n) be t _nmoment position navigation value; δ r _y(t _n+1), δ r _z(t _n+1) be t _n+1moment, inertial measurement system was at OY _laxle and OZ _lsite error on axle, calculates in step (3).

The inventive method is the process of a loop iteration, namely according to t ₀the speed of moment inertial measurement system and positional information, navigational solution can calculate t ₁the speed of moment inertial measurement system and positional information; According to t ₁the speed of moment inertial measurement system and positional information, navigational solution can calculate t ₂the speed of moment inertial measurement system and positional information; The like, according to t _nthe speed of moment inertial measurement system and positional information, can draw t _n+1the speed of moment inertial measurement system and positional information.Fig. 1 lists according to t _nthe speed of moment inertial measurement system and positional information, navigational solution calculates t _n+1the speed of moment inertial measurement system and the flow process of positional information.

Embodiment

Rocket sled test track used is a straight straight line, as P in Fig. 2 ₀p ₁represent rocket sledge track, wherein P point is the points of tangency of track and earth surface.Describe the relation of orbital coordinate system and geographic coordinate system in Fig. 3, thus can determine that orbit coordinate is tied to the transition matrix of geographic coordinate system respectively describe matching acceleration of gravity model and matching acceleration of gravity residual error in Fig. 4, be less than 1 μ Gal by the difference can found out in Fig. 4 between matched curve and measured value.Adopt the navigation calculation result after above-mentioned orbit parameter and acceleration of gravity model do not carry out error deduction time as shown in Figure 5, three-dimensional position, speed and attitude angle information can be obtained.Apply method of the present invention and carry out the navigation results after error deduction as shown in Figure 6, contrast can obtain with Fig. 5, after carrying out error deduction, Y, Z axis speed and positional value are approximately zero, conform to actual result.

The non-detailed description of the present invention is known to the skilled person technology.

Claims (6)

1., based on the real-time one-dimensional positioning method of inertial measurement system of rocket sledge orbital coordinate system, it is characterized in that step is as follows:

(1) inertial measurement system is mounted on rocket sledge, with rocket sledge track starting point for initial point sets up rocket sledge orbital coordinate system OX _ly _lz _l, wherein OX _laxle points to rocket sledge skid body direction of motion, OZ _laxle upward perpendicular to track, OY _laxle in surface level perpendicular to track, and OX _laxle, OY _laxle and OZ _laxle meets right-handed coordinate system;

(2) inertial measurement system carries out autoregistration or Transfer Alignment, obtains t ₀moment, inertial measurement system was at OX _laxle, OY _laxle and OZ _lattitude angle on axle, and calculate t according to the attitude angle obtained ₀moment rocket sledge orbit coordinate is tied to the posture changing matrix of strapdown body coordinate system; Wherein strapdown body coordinate system initial point is the center of inertial measurement system, and x, y, z axle defines according to inertial measurement system prescribed direction;

(3) after rocket sledge ignition trigger, at the t of rocket sledge motion _n+1moment, the acceleration recorded according to inertial measurement system and angular velocity, and t _nmoment, inertial measurement system was at OY _laxle and OZ _lthe speed of axle and positional information, calculate following parameter:

A () inertial measurement system is at OX _laxle, OY _laxle and OZ _lattitude error value on axle;

B () inertial measurement system is at OY _laxle and OZ _lspeed error value on axle;

C () inertial measurement system is at OY _laxle and OZ _lsite error value on axle;

D () inertial measurement system is at OX _lone dimension acceleration error value on direction of principal axis;

(4) according to the t that step (3) obtains _n+1moment, inertial measurement system was at OX _laxle, OY _laxle and OZ _lattitude error value on axle, obtains t _n+1moment, inertial measurement system was at OX _laxle, OY _laxle and OZ _lattitude angle on direction of principal axis;

(5) t is utilized _n+1moment, inertial measurement system was at OX _laxle, OY _laxle and OZ _lattitude angle on direction of principal axis calculates t _n+1moment rocket sledge orbit coordinate is tied to the posture changing matrix of strapdown body coordinate system;

(6) component of acceleration of gravity under rocket sledge orbital coordinate system is utilized, and t _n+1moment rocket sledge orbit coordinate is tied to the posture changing matrix of strapdown body coordinate system, the acceleration of inertial measurement system, inertial measurement system at OX _lone dimension acceleration error value on direction of principal axis, inertial measurement system are at OY _laxle and OZ _lspeed error value on axle and site error value, carry out navigation calculation and obtain t _n+1moment, inertial measurement system was at OX _laxle, OY _laxle and OZ _lspeed on axle and positional information, thus the real-time one dimension location realizing inertial measurement system;

Wherein n=0,1,2 ... N, N are natural number.

2. the real-time one-dimensional positioning method of inertial measurement system based on rocket sledge orbital coordinate system according to claim 1, is characterized in that: the implementation of described step (2) is:

(2.1) when inertial measurement system carries out autoregistration, following formula is utilized to obtain t ₀moment, inertial measurement system was at OX _laxle, OY _laxle and OZ _lattitude angle φ on axle _x, φ _y, φ _z:

Wherein, a _x, a _y, a _zbe respectively t ₀time be engraved in the accekeration that on strapdown body coordinate system three axles, inertial measurement system measurement obtains, ω _x, ω _y, ω _zfor t ₀time be engraved in the magnitude of angular velocity that on strapdown body coordinate system three axles, inertial measurement system measurement obtains, ω _iefor earth rate, for test site latitude;

When carrying out Transfer Alignment, t ₀moment, inertial measurement system was at OX _laxle, OY _laxle and OZ _lattitude angle φ on axle _x, φ _yand φ _zprovided by external system;

(2.2) following formulae discovery t is utilized according to the attitude angle obtained ₀moment rocket sledge orbit coordinate is tied to the posture changing matrix of strapdown body coordinate system

$R_l^b=\left[\begin{array}{ccc}\cos {\mathrm{\φ}}_y& 0& -\sin {\mathrm{\φ}}_y\\ 0& 1& 0\\ \sin {\mathrm{\φ}}_y& 0& \cos {\mathrm{\φ}}_y\end{array}\right]\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos {\mathrm{\φ}}_x& \sin {\mathrm{\φ}}_x\\ 0& -\sin {\mathrm{\φ}}_x& \cos {\mathrm{\φ}}_x\end{array}\right]\left[\begin{array}{ccc}\cos {\mathrm{\φ}}_z& \sin {\mathrm{\φ}}_z& 0\\ -\sin {\mathrm{\φ}}_z& \cos {\mathrm{\φ}}_z& 0\\ 0& 0& 1\end{array}\right].$

3. the real-time one-dimensional positioning method of inertial measurement system based on rocket sledge orbital coordinate system according to claim 1, is characterized in that: the implementation of described step (3) is:

(3.1) at the t of rocket sledge motion _n+1in the moment, utilize following formulae discovery inertial measurement system at OX _laxle, OY _laxle and OZ _lattitude error value on axle, at OY _laxle and OZ _lspeed error value on axle, at OY _laxle and OZ _lsite error value on axle:

(1)X(t _n|t _n+1)＝Φ(t _n)X(t _n)

(2)P(t _n|t _n+1)＝Φ(t _n)P(t _n)Φ(t _n) ^T+Q·ΔT

(3)Κ(t _n)＝P(t _n|t _n+1)H ^T[HP(t _n|t _n+1)H ^T+R] ^-1

(4)X(t _n+1)＝X(t _n|t _n+1)+K(t _n)[Y(t _n)-HX(t _n)]

(5)P(t _n+1)＝[I ₇-K(t _n)H]P(t _n|t _n+1)[I ₇-K(t _n)H] ^T+K(t _n)RK(t _n) ^T

Wherein, $X\left(t_n\right)\left[\begin{array}{c}{\mathrm{\δ\φ}}_x\left(t_n\right)\\ {\mathrm{\δ\φ}}_y\left(t_n\right)\\ {\mathrm{\δ\φ}}_z\left(t_n\right)\\ {\mathrm{\δv}}_y\left(t_n\right)\\ {\mathrm{\δv}}_z\left(t_n\right)\\ {\mathrm{\δr}}_y\left(t_n\right)\\ {\mathrm{\δr}}_z\left(t_n\right)\end{array}\right]$ For t _nthe vector of moment each error coefficient composition, δ φ _x, δ φ _y, δ φ _zfor inertial measurement system is at OX _laxle, OY _laxle and OZ _lattitude error on axle, δ v _y, δ v _zfor inertial measurement system is at OY _laxle and OZ _lvelocity error on axle, δ r _y, δ r _zfor inertial measurement system is at OY _laxle and OZ _lsite error value on axle, at t ₀moment, X (t ₀)=[0 00000 0] ^t;

$X\left(t_n\right|t_{n+1})=\left[\begin{array}{c}{\mathrm{\δ\φ}}_x\left(t_n\right|t_{n+1})\\ {\mathrm{\δ\φ}}_y\left(t_n\right|t_{n+1})\\ {\mathrm{\δ\φ}}_z\left(t_n\right|t_{n+1})\\ {\mathrm{\δv}}_y\left(t_n\right|t_{n+1})\\ {\mathrm{\δv}}_z\left(t_n\right|t_{n+1})\\ {\mathrm{\δr}}_y\left(t_n\right|t_{n+1})\\ {\mathrm{\δr}}_z\left(t_n\right|t_{n+1})\end{array}\right],$ For t _nmoment is to t _n+1the vector of moment each error coefficient one-step prediction value composition; $\mathrm{\Φ}\left(t_n\right)=I_7+\left[\begin{array}{ccccccc}0& A_{12}& A_{13}& 0& 0& 0& 0\\ A_{21}& A_{22}& A_{23}& 0& 0& 0& 0\\ A_{31}& A_{32}& A_{33}& 0& 0& 0& 0\\ A_{41}& A_{42}& A_{43}& 0& {2\mathrm{\ω}}_{\mathrm{ie},x}^l& 0& 0\\ A_{51}& A_{52}& 0& -{2\mathrm{\ω}}_{\mathrm{ie},x}^l& 0& 0& 0\\ 0& 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 1& 0& 0\end{array}\right]\·\mathrm{\ΔT},$ For state transfer matrix, and

A ₁₂＝-ω _x(t _n)sinφ _y(t _n)+ω _z(t _n)cosφ _y(t _n)

$A_{13}={\mathrm{\ω}}_{\mathrm{ie},x}^l\sin {\mathrm{\φ}}_z\left(t_n\right)-{\mathrm{\ω}}_{\mathrm{ie},y}^l\cos {\mathrm{\φ}}_z\left(t_n\right)$

$\begin{array}{c}{A}_{21}=[{\mathrm{\ω}}_x\left(t_n\right)\sin {\mathrm{\φ}}_y\left(t_n\right)-{\mathrm{\ω}}_z\left(t_n\right)\cos {\mathrm{\φ}}_y\left(t_n\right)]{\sec }^2{\mathrm{\φ}}_x\left(t_n\right)\\ +[{\mathrm{\ω}}_{\mathrm{ie},x}^l\sin {\mathrm{\φ}}_z\left(t_n\right)-{\mathrm{\ω}}_{\mathrm{ie},y}^l\cos {\mathrm{\φ}}_z\left(t_n\right)]\tan {\mathrm{\φ}}_x\left(t_n\right)\sec {\mathrm{\φ}}_x\left(t_n\right)\end{array}$

A ₂₂＝[ω _x(t _n)cosφ _y(t _n)+ω _z(t _n)sinφ _y(t _n)]tanφ _x(t _n)

$A_{23}=[{\mathrm{\ω}}_{\mathrm{ie},x}^l\cos {\mathrm{\φ}}_z\left(t_n\right)+{\mathrm{\ω}}_{\mathrm{ie},y}^l\sin {\mathrm{\φ}}_z\left(t_n\right)]\sec {\mathrm{\φ}}_x\left(t_n\right)$

$\begin{array}{c}{A}_{31}=-[{\mathrm{\ω}}_x\left(t_n\right)\sin {\mathrm{\φ}}_y\left(t_n\right)-{\mathrm{\ω}}_z\left(t_n\right)\cos {\mathrm{\φ}}_y\left(t_n\right)]\tan {\mathrm{\φ}}_x\left(t_n\right)\sec {\mathrm{\φ}}_x\left(t_n\right)\\ -[{\mathrm{\ω}}_{\mathrm{ie},x}^l\sin {\mathrm{\φ}}_z\left(t_n\right)-{\mathrm{\ω}}_{\mathrm{ie},y}^l\cos {\mathrm{\φ}}_z\left(t_n\right)]{\sec }^2{\mathrm{\φ}}_x\left(t_n\right)\end{array}$

A ₃₂＝-[ω _x(t _n)cosφ _y(t _n)+ω _z(t _n)sinφ _y(t _n)]secφ _x(t _n)

$A_{33}=-[{\mathrm{\ω}}_{\mathrm{ie},x}^l\cos {\mathrm{\φ}}_z\left(t_n\right)+{\mathrm{\ω}}_{\mathrm{ie},y}^l\sin {\mathrm{\φ}}_z\left(t_n\right)]\tan {\mathrm{\φ}}_x\left(t_n\right)$

A ₄₁＝a _x(t _n)sinφ _y(t _n)cosφ _x(t _n)cosφ _z(t _n)-a _y(t _n)sinφ _x(t _n)cosφ _z(t _n)

-a _z(t _n)cosφ _y(t _n)cosφ _x(t _n)cosφ _z(t _n)

A ₄₂＝a _x(t _n)[-sinφ _y(t _n)sinφ _z(t _n)+cosφ _y(t _n)sinφ _x(t _n)cosφ _z(t _n)]

+a _z(t _n)[cosφ _y(t _n)sinφ _z(t _n)+sinφ _y(t _n)sinφ _x(t _n)cosφ _z(t _n)]

A ₄₃＝a _x(t _n)[cosφ _y(t _n)cosφ _z(t _n)-sinφ _y(t _n)sinφ _x(t _n)sinφ _z(t _n)]-a _y(t _n)cosφ _x(t _n)sinφ _z(t _n)

+a _z(t _n)[sinφ _y(t _n)cosφ _z(t _n)+cosφ _y(t _n)sinφ _x(t _n)sinφ _z(t _n)]

A ₅₁＝a _x(t _n)sinφ _y(t _n)sinφ _x(t _n)+a _y(t _n)cosφ _x(t _n)-a _z(t _n)cosφ _y(t _n)sinφ _x(t _n)

A ₅₂＝-a _x(t _n)cosφ _y(t _n)cosφ _x(t _n)-a _z(t _n)sinφ _y(t _n)cosφ _x(t _n)

Wherein, Δ T is the update cycle, Δ T=t _n+1-t _n; for at rocket sledge orbital coordinate system OX _laxle, OY _laxle and OZ _lcomponent on axle; φ _x(t _n), φ _y(t _n), φ _z(t _n) be respectively t _nmoment, inertial measurement system was at OX _laxle, OY _laxle and OZ _lattitude angle on axle; a _x(t _n), a _y(t _n), a _z(t _n) be respectively t _nmoment inertial measurement system measures the accekeration obtained on strapdown body coordinate system three axles; ω _x(t _n), ω _y(t _n), ω _z(t _n) be that rocket sledge skid body is through the angular velocity of over-compensation on strapdown body coordinate system three axles, computing formula is:

For t ₀moment, for t _nthe magnitude of angular velocity that moment inertial measurement system gyroscope measures on strapdown body coordinate system three axles, form is the column vector that X, Y, Z axis forms to angular velocity; for the projection components of earth rate in orbital coordinate system, be fixed value in navigation calculates; for t _n-1moment rocket sledge orbit coordinate is tied to the posture changing matrix of strapdown body coordinate system; P (t _n| t _n+1) be one-step prediction square error; P (t _n) for estimating square error; Q is noise sequence variance matrix, is fixed value in navigation calculation process; Κ (t _n) be filter gain; $H=\left[\begin{array}{ccccccc}0& 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 0& 1\end{array}\right],$ For measuring battle array; R is the variance matrix of measurement noise sequence, is fixed value in navigation calculation; $Y\left(t_n\right)=\left[\begin{array}{c}{v}_y\left(t_n\right)\\ v_z\left(t_n\right)\\ r_y\left(t_n\right)\\ r_z\left(t_n\right)\end{array}\right],$ Wherein, v _y(t _n), v _z(t _n) be respectively t _nmoment, inertial navigation system was at OY _l, OZ _lthe velocity information of axle, r _y(t _n), r _z(t _n) be respectively t _nmoment, inertial navigation system was at OY _l, OZ _lthe positional information of axle; I ₇be 7 rank unit matrix.

(3.2) at the t of rocket sledge motion _n+1in the moment, utilize following formulae discovery inertial measurement system at OX _lone dimension acceleration error value Δ a on direction of principal axis _x(t _n+1):

Δa _x(t _n+1)

＝[-a _x(t _n+1)sinφ _y(t _n+1)cosφ _x(t _n+1)sinφ _z(t _n+1)+a _y(t _n+1)sinφ _x(t _n+1)sinφ _z(t _n+1)

+a _z(t _n+1)cosφ _y(t _n+1)cosφ _x(t _n+1)sinφ _z(t _n+1)]δφ _x(t _n+1)

+[-a _x(t _n+1)(sinφ _y(t _n+1)cosφ _z(t _n+1)+cosφ _y(t _n+1)sinφ _x(t _n+1)sinφ _z(t _n+1))

+a _z(t _n+1)(cosφ _y(t _n+1)cosφ _z(t _n+1)-sinφ _y(t _n+1)sinφ _x(t _n+1)sinφ _z(t _n+1))]δφ _y(t _n+1)

+[-a _x(t _n+1)(cosφ _y(t _n+1)sinφ _z(t _n+1)+sinφ _y(t _n+1)sinφ _x(t _n+1)cosφ _z(t _n+1))

-a _y(t _n+1)cosφ _x(t _n+1)cosφ _z(t _n+1)

+a _z(t _n+1)(-sinφ _y(t _n+1)sinφ _z(t _n+1)+cosφ _y(t _n+1)sinφ _x(t _n+1)cosφ _z(t _n+1))]δφ _z(t _n+1)

Wherein, be respectively t _n+1moment, inertial measurement system was at OX _laxle, OY _laxle and OZ _lattitude angle on axle; a _x(t _n+1), a _y(t _n+1), a _z(t _n+1) be respectively t _n+1moment inertial measurement system measures the accekeration obtained on strapdown body coordinate system three axles.

4. the real-time one-dimensional positioning method of inertial measurement system based on rocket sledge orbital coordinate system according to claim 1, is characterized in that: t in described step (4) _n+1moment, inertial measurement system was at OX _laxle, OY _laxle and OZ _lattitude angle φ on axle _x(t _n+1), φ _y(t _n+1) and φ _z(t _n+1) utilize following formulae discovery to obtain:

Wherein, φ _x(t _n), φ _y(t _n), φ _z(t _n) be respectively t _nmoment, inertial measurement system was at OX _laxle, OY _laxle and OZ _lattitude angle on axle, for t _nthe magnitude of angular velocity that moment inertial measurement system gyroscope measures on strapdown body coordinate system three axles, form is the column vector that X, Y, Z axis forms to angular velocity; for the projection components of earth rate in orbital coordinate system, be fixed value in navigation calculates; Δ T is the update cycle, Δ T=t _n+1-t _n; δ φ _x(t _n+1), δ φ _y(t _n+1), δ φ _z(t _n+1) be t _n+1moment, inertial measurement system was at OX _laxle, OY _laxle and OZ _lattitude error value on axle.

5. the real-time one-dimensional positioning method of inertial measurement system based on rocket sledge orbital coordinate system according to claim 1, is characterized in that: in described step (6), the component of acceleration of gravity under rocket sledge orbital coordinate system is as follows:

$\left[\begin{array}{c}{g}_x^l\\ g_y^l\\ g_z^l\end{array}\right]=\left[\begin{array}{c}-(g_0+b_1{r}_x+b_2{r}_x^2)\sin \frac{\left|P_{0}P\right|-r_x}{N+h_p}\\ 0\\ (g_0+b_1{r}_x+b_2{r}_x^2)\cos \frac{\left|P_{0}P\right|-r_x}{N+h_p}\end{array}\right]$

Wherein, a is semimajor axis of ellipsoid, e ²for eccentricity of the earth, for the latitude value of rocket sledge skid body point; h _pfor the height of the relative level surface of skid body; | P ₀p|=(N+h _p) β ', β ' be vector O ₀p ₀and O ₀the angle of P, wherein vector O ₀p ₀for earth center O ₀to track initial point P ₀vector, O ₀p is O ₀to the vector of P point, P is track and earth surface point of contact, for rocket sledge track acceleration of gravity model, wherein r _xfor the Orbiting distance of skid body; g ₀for the acceleration of gravity of launching site position, b ₁and b ₂for constant value.

6. the real-time one-dimensional positioning method of inertial measurement system based on rocket sledge orbital coordinate system according to claim 1, is characterized in that: the implementation of described step (6) is:

(6.1) utilize following formula to carry out navigation calculation, obtain t _n+1moment, inertial measurement system was at OX _laxle, OY _laxle and OZ _lvelocity information v on axle _x(t _n+1), v _y(t _n+1) and v _z(t _n+1):

$\left[\begin{array}{c}{v}_x\left(t_{n+1}\right)\\ v_y\left(t_{n+1}\right)\\ v_z\left(t_{n+1}\right)\end{array}\right]=\left[\begin{array}{c}{v}_x\left(t_n\right)\\ v_y\left(t_n\right)\\ v_z\left(t_n\right)\end{array}\right]+(R_b^l\left(t_{n+1}\right)f^b\left(t_{n+1}\right)-{2\mathrm{\Ω}}_{\mathrm{ie}}^l\·\left[\begin{array}{c}{v}_x\left(t_n\right)\\ v_y\left(t_n\right)\\ v_z\left(t_n\right)\end{array}\right]+g^l-\left[\begin{array}{c}{\mathrm{\Δa}}_x\left(t_{n+1}\right)\\ 0\\ 0\end{array}\right])\·\mathrm{\ΔT}-\left[\begin{array}{c}0\\ {\mathrm{\δv}}_y\left(t_{n+1}\right)\\ {\mathrm{\δv}}_z\left(t_{n+1}\right)\end{array}\right]$

Wherein, v _x(t _n), v _y(t _n), v _z(t _n) be t _nmoment, inertial measurement system was at OX _laxle, OY _laxle and OZ _lvelocity information on axle; for t _n+1moment rocket sledge orbit coordinate is tied to the posture changing matrix of strapdown body coordinate system; for earth rate is in orbital coordinate system projection components antisymmetric matrix; f ^b(t _n) be the measured value of inertial measurement system accelerometer, form is the column vector that X, Y, Z axis forms to acceleration; g ^lfor the component of acceleration of gravity under rocket sledge orbital coordinate system; Δ a _x(t _n+1) be t _n+1moment, inertial measurement system was at OX _lone dimension acceleration error value on direction of principal axis; Δ T is the update cycle, Δ T=t _n+1-t _n; δ v _y(t _n+1), δ v _z(t _n+1) be t _n+1moment, inertial measurement system was at OY _laxle and OZ _lspeed error value on axle;

(6.2) utilize following formula to carry out navigation calculation, obtain t _n+1moment, inertial measurement system was at OX _laxle, OY _laxle and OZ _lpositional information r on axle _x(t _n+1), r _y(t _n+1) and r _z(t _n+1):

$\left[\begin{array}{c}{r}_x\left(t_{n+1}\right)\\ r_y\left(t_{n+1}\right)\\ r_z\left(t_{n+1}\right)\end{array}\right]=\left[\begin{array}{c}{r}_x\left(t_n\right)\\ r_y\left(t_n\right)\\ r_z\left(t_n\right)\end{array}\right]+\left[\begin{array}{c}{v}_x\left(t_{n+1}\right)\\ v_y\left(t_{n+1}\right)\\ v_z\left(t_{n+1}\right)\end{array}\right]\·\mathrm{\ΔT}-\left[\begin{array}{c}0\\ {\mathrm{\δr}}_y\left(t_{n+1}\right)\\ {\mathrm{\δr}}_z\left(t_{n+1}\right)\end{array}\right]$

Wherein, r _x(t _n), r _y(t _n), r _z(t _n) be t _nmoment, inertial measurement system was at OX _laxle, OY _laxle and OZ _lpositional information on axle; δ r _y(t _n+1), δ r _z(t _n+1) be t _n+1moment, inertial measurement system was at OY _laxle and OZ _lsite error value on axle.